{"id":5335,"date":"2025-12-26T09:18:59","date_gmt":"2025-12-26T01:18:59","guid":{"rendered":"https:\/\/imeta.space\/?p=5335"},"modified":"2026-01-09T17:31:45","modified_gmt":"2026-01-09T09:31:45","slug":"%e4%bf%a1%e6%81%af%e5%9f%ba%e5%9b%a0%e8%ae%ba%ef%bc%9a%e7%86%b5%e6%b6%a8%e8%90%bd%e5%a4%a7%e7%bb%9f%e4%b8%80%e7%90%86%e8%ae%ba%ef%bc%88%e8%bf%87%e7%a8%8b%e6%9c%ac%e4%bd%93%e8%ae%ba%e7%89%88%ef%bc%89v2","status":"publish","type":"post","link":"https:\/\/imeta.space\/index.php\/2025\/12\/26\/%e4%bf%a1%e6%81%af%e5%9f%ba%e5%9b%a0%e8%ae%ba%ef%bc%9a%e7%86%b5%e6%b6%a8%e8%90%bd%e5%a4%a7%e7%bb%9f%e4%b8%80%e7%90%86%e8%ae%ba%ef%bc%88%e8%bf%87%e7%a8%8b%e6%9c%ac%e4%bd%93%e8%ae%ba%e7%89%88%ef%bc%89v2\/","title":{"rendered":"\u4fe1\u606f\u57fa\u56e0\u8bba\uff1a\u71b5\u6da8\u843d\u5927\u7edf\u4e00\u7406\u8bba\uff08\u8fc7\u7a0b\u672c\u4f53\u8bba\u7248\uff09v2.0"},"content":{"rendered":"<h1>\u4fe1\u606f\u57fa\u56e0\u8bba\uff1a\u71b5\u6da8\u843d\u5927\u7edf\u4e00\u7406\u8bba\uff08\u8fc7\u7a0b\u672c\u4f53\u8bba\u7248\uff09<\/h1>\n<h2>\u6570\u5b66\u5b8c\u5907\u7248 v2.0<\/h2>\n<hr \/>\n<h2>\u5e8f\u8a00\uff1a\u4ece\u5b9e\u4f53\u5230\u8fc7\u7a0b\u2014\u2014\u4e00\u573a\u5fc5\u8981\u7684\u79d1\u5b66\u9769\u547d<\/h2>\n<h3>0.1 \u89c2\u6d4b\u8fb9\u754c\u5b9a\u7406\uff1a\u4e3a\u4ec0\u4e48\u6211\u4eec\u88ab\u8feb\u9009\u62e9\u8fc7\u7a0b\u672c\u4f53\u8bba<\/h3>\n<h4>0.1.1 \u89c2\u6d4b\u8fb9\u754c\u7684\u6570\u5b66\u8868\u8ff0<\/h4>\n<p>\u6211\u4eec\u65e0\u6cd5\u89c2\u6d4b\u7684\u4e0d\u4ec5\u4ec5\u662f&#8221;\u8d77\u70b9&#8221;\u548c&#8221;\u7ec8\u70b9&#8221;\uff0c\u800c\u662f\u66f4\u6839\u672c\u7684\u4fe1\u606f\u58c1\u5792\uff1a<\/p>\n<p><strong>\u89c2\u6d4b\u8fb9\u754c\u5b9a\u7406<\/strong>\uff1a<br \/>\n\u5bf9\u4e8e\u4efb\u4f55\u89c2\u6d4b\u7cfb\u7edf$O$\uff0c\u5b58\u5728\u4e24\u4e2a\u4e0d\u53ef\u903e\u8d8a\u7684\u5c3a\u5ea6\uff1a<\/p>\n<ol>\n<li><strong>\u5fae\u89c2\u5206\u8fa8\u7387\u6781\u9650<\/strong>\uff1a$L_{min} = sqrt{hbar \/ langle delta S rangle}$\n<ul>\n<li>\u5c0f\u4e8e\u6b64\u5c3a\u5ea6\uff0c\u91cf\u5b50\u6da8\u843d\u4f7f\u4efb\u4f55&#8221;\u5b9e\u4f53&#8221;\u6982\u5ff5\u5931\u6548<\/li>\n<li>\u6211\u4eec\u53ea\u80fd\u8c08\u8bba&#8221;\u6982\u7387\u5206\u5e03&#8221;\u800c\u975e&#8221;\u786e\u5b9a\u5b58\u5728&#8221;<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u5b8f\u89c2\u56e0\u679c\u6781\u9650<\/strong>\uff1a$L_{max} = c cdot tau_O$\uff08$tau_O$\u4e3a\u89c2\u6d4b\u8005\u5bff\u547d\uff09\n<ul>\n<li>\u8d85\u51fa\u6b64\u5c3a\u5ea6\uff0c\u56e0\u679c\u4fe1\u53f7\u65e0\u6cd5\u8fd4\u56de<\/li>\n<li>\u6211\u4eec\u53ea\u80fd\u770b\u5230&#8221;\u5386\u53f2\u9057\u8ff9&#8221;\u800c\u975e&#8221;\u5f53\u4e0b\u73b0\u5b9e&#8221;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p><strong>\u63a8\u8bba<\/strong>\uff1a\u6211\u4eec\u6c38\u8fdc\u751f\u6d3b\u5728$L<em>{min} &lt; L &lt; L<\/em>{max}$\u7684<strong>\u4e2d\u5c3a\u5ea6\u7262\u7b3c<\/strong>\u4e2d\u3002\u5728\u8fd9\u4e2a\u7262\u7b3c\u91cc\uff0c&#8221;\u5b9e\u4f53&#8221;\u662f\u5e7b\u89c9\uff0c&#8221;\u6d41\u52a8&#8221;\u662f\u771f\u5b9e\u3002<\/p>\n<h4>0.1.2 \u4f20\u7edf\u5b9e\u4f53\u672c\u4f53\u8bba\u7684\u56f0\u5883<\/h4>\n<p>\u4f20\u7edf\u7269\u7406\u5b66\u5efa\u7acb\u5728\u5b9e\u4f53\u672c\u4f53\u8bba\u4e4b\u4e0a\uff1a<\/p>\n<ul>\n<li>\u76f8\u4fe1\u5b58\u5728\u6c38\u6052\u4e0d\u53d8\u7684\u5b9e\u4f53<\/li>\n<li>\u53d8\u5316\u53ea\u662f\u8fd9\u4e9b\u5b9e\u4f53\u7684\u5c5e\u6027<\/li>\n<li>\u8ffd\u6c42&#8221;\u7b2c\u4e00\u539f\u7406&#8221;\u548c&#8221;\u7ec8\u6781\u771f\u7406&#8221;<\/li>\n<\/ul>\n<p>\u7136\u800c\uff0c\u6240\u6709\u89c2\u6d4b\u8bc1\u636e\u8868\u660e\uff1a<\/p>\n<ul>\n<li>\u6211\u4eec\u88ab\u56da\u7981\u5728\u4e00\u4e2a\u6709\u9650\u7684\u89c2\u6d4b\u7a97\u53e3\u5185<\/li>\n<li>\u65e2\u770b\u4e0d\u5230\u5b87\u5b99\u7684\u8d77\u70b9\uff08\u5927\u7206\u70b8\u5947\u70b9\u88ab\u666e\u6717\u514b\u5c3a\u5ea6\u906e\u853d\uff09<\/li>\n<li>\u4e5f\u770b\u4e0d\u5230\u5b83\u7684\u7ec8\u70b9\uff08\u5b87\u5b99\u89c6\u754c\u5916\u7684\u4fe1\u606f\u4e0d\u53ef\u53ca\uff09<\/li>\n<li>\u6211\u4eec\u552f\u4e00\u80fd\u76f4\u63a5\u63a5\u89e6\u7684\uff0c\u53ea\u6709&#8221;\u6b64\u65f6\u6b64\u523b\u6b63\u5728\u53d1\u751f\u7684\u8fc7\u7a0b&#8221;<\/li>\n<\/ul>\n<h4>0.1.3 \u8fc7\u7a0b\u672c\u4f53\u8bba\u7684\u5fc5\u7136\u6027<\/h4>\n<p>\u65e2\u7136&#8221;\u8d77\u70b9&#8221;\u548c&#8221;\u7ec8\u70b9&#8221;\u662f\u65e0\u6cd5\u89c2\u6d4b\u7684\u5f62\u800c\u4e0a\u5b66\u5047\u8bbe\uff0c\u90a3\u4e48\u552f\u4e00\u5177\u6709\u79d1\u5b66\u4e25\u8c28\u6027\u7684\u672c\u4f53\u5c31\u662f<strong>&#8220;\u6b64\u523b\u6b63\u5728\u53d1\u751f\u7684\u6f14\u5316\u903b\u8f91&#8221;<\/strong>\u3002<\/p>\n<p><strong>\u4fe1\u606f\u57fa\u56e0\u8bba\u505a\u51fa\u4e86\u4e00\u4e2a\u6839\u672c\u6027\u7684\u9009\u62e9<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5c06&#8221;\u8fc7\u7a0b&#8221;\u800c\u975e&#8221;\u5b9e\u4f53&#8221;\u4f5c\u4e3a\u7406\u8bba\u7684\u672c\u4f53<\/li>\n<li>\u4e0d\u518d\u8ffd\u95ee&#8221;\u4e16\u754c\u7531\u4ec0\u4e48\u6784\u6210&#8221;\uff0c\u800c\u662f\u8ffd\u95ee&#8221;\u4e16\u754c\u5982\u4f55\u6d41\u52a8&#8221;<\/li>\n<li>\u4e09\u573a\uff08$Psi<em>S, Psi<\/em>omega, Psi_C$\uff09\u4e0d\u662f\u4e09\u79cd\u5b9e\u4f53\uff0c\u800c\u662f\u63cf\u8ff0\u6d41\u52a8\u7684\u4e09\u4e2a\u7ef4\u5ea6<\/li>\n<li>RVSE\u4e0d\u662f\u6f14\u5316\u9636\u6bb5\uff0c\u800c\u662f\u6d41\u52a8\u7684\u57fa\u672c\u8bed\u6cd5<\/li>\n<li>\u4e09\u7ef4\u60ef\u6027\u4e0d\u662f\u5b9e\u4f53\u5c5e\u6027\uff0c\u800c\u662f\u6d41\u52a8\u7684\u6301\u7eed\u6027\u5ea6\u91cf<\/li>\n<\/ul>\n<p>\u8fd9\u4e00\u9009\u62e9\u4e0d\u662f\u5f62\u800c\u4e0a\u5b66\u504f\u597d\uff0c\u800c\u662f\u79d1\u5b66\u5b9e\u8bc1\u4e3b\u4e49\u7684\u5fc5\u7136\uff1a<strong>\u6211\u4eec\u53ea\u80fd\u7814\u7a76\u6211\u4eec\u80fd\u89c2\u6d4b\u7684\uff0c\u800c\u6211\u4eec\u53ea\u80fd\u89c2\u6d4b\u6d41\u52a8\u3002<\/strong><\/p>\n<h3>0.2 \u7406\u8bba\u5b9a\u4f4d\uff1a\u4e2d\u5c3a\u5ea6\u5e7d\u7075\u7684\u751f\u5b58\u6cd5\u5219<\/h3>\n<h4>0.2.1 \u7406\u8bba\u5b9a\u4f4d\u4e0e\u6838\u5fc3\u76ee\u6807<\/h4>\n<ul>\n<li><strong>\u5b9a\u4f4d<\/strong>\uff1aIGT\u5e76\u975e&#8221;\u4e07\u7269\u7406\u8bba&#8221;\uff0c\u800c\u662f<strong>\u6d8c\u73b0\u5c3a\u5ea6\u7684\u7edf\u4e00\u63cf\u8ff0\u6846\u67b6<\/strong>\uff0c\u586b\u8865\u5fae\u89c2\u91cf\u5b50\u7406\u8bba\u4e0e\u5b8f\u89c2\u7ecf\u5178\u7269\u7406\u4e4b\u95f4\u7684\u7406\u8bba\u7a7a\u7f3a\u3002<\/li>\n<li><strong>\u7edf\u4e00\u8303\u56f4<\/strong>\uff1a\u8986\u76d6\u4ece\u51dd\u805a\u6001\u7269\u8d28\uff08$10^{-10}$ m\uff09\u5230\u5b87\u5b99\u7ed3\u6784\uff08$10^{26}$ m\uff09\u7684<strong>\u5b8f\u89c2\u6d8c\u73b0\u73b0\u8c61<\/strong>\u3002<\/li>\n<li><strong>\u6838\u5fc3\u76ee\u6807<\/strong>\uff1a\u4ee5<strong>\u6700\u5c0f\u6570\u5b66\u57fa\u7840<\/strong>\uff08\u4e09\u4e2a\u6b63\u4ea4\u76f8\u5e72\u573a\uff09\u89e3\u91ca<strong>\u6700\u5927\u8303\u56f4\u73b0\u8c61<\/strong>\uff08\u80fd\u91cf\u6d41\u52a8\u3001\u8282\u5f8b\u4f20\u9012\u3001\u7ed3\u6784\u7a33\u5b9a\uff09\u3002<\/li>\n<li><strong>\u54f2\u5b66\u7acb\u573a<\/strong>\uff1a\u575a\u6301\u5b9e\u8bc1\u4e3b\u4e49\u4e0e\u53ef\u8bc1\u4f2a\u539f\u5219\uff0c\u6240\u6709\u7ed3\u8bba\u5fc5\u987b\u6709\u6570\u5b66\u63a8\u5bfc\u6216\u5b9e\u9a8c\u9a8c\u8bc1\u8def\u5f84\u3002<\/li>\n<\/ul>\n<h4>0.2.2 \u4e09\u573a\u7684\u91cd\u65b0\u89e3\u8bfb\uff1a\u4e0d\u662f&#8221;\u4e09\u79cd\u5b9e\u4f53&#8221;\uff0c\u800c\u662f&#8221;\u4e09\u4e2a\u89c2\u6d4b\u7ef4\u5ea6&#8221;<\/h4>\n<table>\n<thead>\n<tr>\n<th>\u573a\u7c7b\u578b<\/th>\n<th>\u4f20\u7edf\u7406\u89e3<\/th>\n<th><strong>\u8fc7\u7a0b\u672c\u4f53\u8bba\u4e0b\u7684\u65b0\u7406\u89e3<\/strong><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u70ed\u573a $Psi_S$<\/strong><\/td>\n<td>&#8220;\u80fd\u91cf\u5206\u5e03\u7684\u573a&#8221;<\/td>\n<td><strong>&#8220;\u6b64\u65f6\u6b64\u523b\u7684\u80fd\u91cf\u6d41\u52a8\u6a21\u5f0f&#8221;<\/strong><br \/>\n\u8bb0\u5f55\u7740\u7cfb\u7edf\u5f53\u524d\u5982\u4f55\u4ece\u8fc7\u53bb\u6d41\u5411\u672a\u6765<\/td>\n<\/tr>\n<tr>\n<td><strong>\u52a8\u573a $Psi_omega$<\/strong><\/td>\n<td>&#8220;\u8282\u5f8b\u6a21\u5f0f\u7684\u573a&#8221;<\/td>\n<td><strong>&#8220;\u65f6\u95f4\u4e4b\u77e2\u7684\u8282\u594f\u5370\u8bb0&#8221;<\/strong><br \/>\n\u7cfb\u7edf\u7ef4\u6301\u81ea\u8eab\u5728\u65f6\u95f4\u6d41\u4e2d\u4e00\u81f4\u6027\u7684\u7b56\u7565<\/td>\n<\/tr>\n<tr>\n<td><strong>\u9501\u573a $Psi_C$<\/strong><\/td>\n<td>&#8220;\u7ed3\u6784\u7a33\u5b9a\u7684\u573a&#8221;<\/td>\n<td><strong>&#8220;\u62b5\u6297\u71b5\u6d41\u7684\u6682\u65f6\u6027\u6f29\u6da1&#8221;<\/strong><br \/>\n\u7cfb\u7edf\u5728\u5fc5\u6b7b\u7684\u5bbf\u547d\u4e2d\u521b\u9020\u7684\u4e34\u65f6\u79e9\u5e8f<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>\u5173\u952e\u8f6c\u53d8<\/strong>\uff1a<\/p>\n<ul>\n<li><strong>\u4ece&#8221;\u62e5\u6709\u573a&#8221;\u5230&#8221;\u6210\u4e3a\u573a&#8221;<\/strong>\uff1a\u7cfb\u7edf\u4e0d\u662f&#8221;\u62e5\u6709&#8221;\u4e09\u573a\uff0c\u800c\u662f<strong>&#8220;\u5c31\u662f&#8221;<\/strong>\u4e09\u573a\u5728\u7279\u5b9a\u65f6\u523b\u7684\u4ea4\u53c9\u70b9\u3002<\/li>\n<li><strong>\u4ece&#8221;\u63cf\u8ff0\u72b6\u6001&#8221;\u5230&#8221;\u8bb0\u5f55\u8fc7\u7a0b&#8221;<\/strong>\uff1a\u4e09\u573a\u7684\u503c\u4e0d\u662f\u63cf\u8ff0&#8221;\u7cfb\u7edf\u662f\u4ec0\u4e48&#8221;\uff0c\u800c\u662f\u8bb0\u5f55<strong>&#8220;\u7cfb\u7edf\u6b63\u5728\u5982\u4f55\u6f14\u5316&#8221;<\/strong>\u3002<\/li>\n<\/ul>\n<h4>0.2.3 RVSE\uff1a\u6d41\u52a8\u7684\u8bed\u6cd5<\/h4>\n<p>\u65e2\u7136\u53ea\u80fd\u611f\u77e5\u6d41\u52a8\uff0c\u90a3\u4e48\u552f\u4e00\u7684\u79d1\u5b66\u5c31\u662f<strong>\u7834\u8bd1\u6d41\u52a8\u7684\u8bed\u6cd5<\/strong>\uff1a<\/p>\n<pre><code>\u8bed\u6cd5\u89c4\u5219\uff1a\u6d41\u52a8 = \u5faa\u73af\u5d4c\u5957\u7684RVSE\n\n- \u03a9\uff08\u6fc0\u53d1\uff09\uff1a\u6d41\u52a8\u9047\u5230\u969c\u788d\uff0c\u5f00\u59cb\u79ef\u84c4\u52bf\u80fd\n- R\uff08\u6269\u5f20\uff09\uff1a\u79ef\u84c4\u7684\u80fd\u91cf\u627e\u5230\u7a81\u7834\u53e3\uff0c\u52a0\u901f\u6d41\u52a8\n- V\uff08\u53d8\u5f02\uff09\uff1a\u6d41\u52a8\u5206\u5316\u51fa\u591a\u6761\u8def\u5f84\uff0c\u63a2\u7d22\u53ef\u80fd\u6027\n- S\uff08\u7b5b\u9009\uff09\uff1a\u67d0\u4e9b\u8def\u5f84\u88ab\u8bc1\u660e\u66f4\u6709\u6548\uff0c\u88ab\u52a0\u5f3a\n- E\uff08\u6d8c\u73b0\uff09\uff1a\u6709\u6548\u7684\u8def\u5f84\u5f62\u6210\u65b0\u7684\u7a33\u5b9a\u6d41\u52a8\u6a21\u5f0f\n- D\uff08\u8870\u9000\uff09\uff1a\u6d41\u52a8\u6a21\u5f0f\u8001\u5316\uff0c\u51c6\u5907\u4e0b\u4e00\u6b21\u5faa\u73af<\/code><\/pre>\n<p><strong>\u8fd9\u4e0d\u662f&#8221;\u6f14\u5316\u9636\u6bb5&#8221;\uff0c\u800c\u662f&#8221;\u6d41\u52a8\u7684\u57fa\u672c\u53e5\u5f0f&#8221;<\/strong>\u3002\u5c31\u50cf\u8bed\u8a00\u53ea\u6709\u4e3b\u8c13\u5bbe\u5b9a\u72b6\u8865\uff0c\u5b87\u5b99\u4e5f\u53ea\u6709RVSE\u8fd9\u516d\u4e2a&#8221;\u8bcd\u6027&#8221;\u3002<\/p>\n<h4>0.2.4 \u4e09\u7ef4\u60ef\u6027\uff1a\u6d41\u52a8\u7684&#8221;\u52a8\u91cf&#8221;\u6d4b\u91cf<\/h4>\n<p>\u5728\u53ea\u80fd\u611f\u77e5\u6d41\u52a8\u7684\u4e16\u754c\u91cc\uff0c\u6700\u91cd\u8981\u7684\u7269\u7406\u91cf\u662f<strong>\u6d41\u52a8\u7684\u6301\u7eed\u6027<\/strong>\uff1a<\/p>\n<ul>\n<li><strong>\u71b5\u60ef\u6027 $I_S$<\/strong>\uff1a\u62b5\u6297\u80fd\u91cf\u6d41\u52a8\u6563\u9038\u7684\u80fd\u529b<\/li>\n<li><strong>\u9891\u7387\u60ef\u6027 $I_omega$<\/strong>\uff1a\u62b5\u6297\u8282\u5f8b\u6d41\u52a8\u5931\u771f\u7684\u80fd\u529b<\/li>\n<li><strong>\u76f8\u5e72\u60ef\u6027 $I_C$<\/strong>\uff1a\u62b5\u6297\u7ed3\u6784\u6d41\u52a8\u89e3\u4f53\u7684\u80fd\u529b<\/li>\n<\/ul>\n<p><strong>\u65b0\u5b9a\u4e49<\/strong>\uff1a<br \/>\n[<br \/>\nI_X = frac{text{\u6d41\u52a8\u7684&#8221;\u8bb0\u5fc6&#8221;}}{text{\u6d41\u52a8\u7684&#8221;\u9057\u5fd8\u7387&#8221;}}<br \/>\n]<br \/>\n\u60ef\u6027\u8d8a\u5927\uff0c\u7cfb\u7edf<strong>\u8d8a\u80fd\u8bb0\u4f4f\u81ea\u5df1\u7684\u6d41\u52a8\u6a21\u5f0f<\/strong>\uff0c\u8d8a\u80fd\u62b5\u6297\u73af\u5883\u566a\u58f0\u7684\u5e72\u6270\u3002<\/p>\n<h3>0.3 \u6838\u5fc3\u5ba3\u8a00\uff1a\u6d41\u52a8\u662f\u552f\u4e00\u53ef\u89e6\u78b0\u7684\u771f\u5b9e<\/h3>\n<p>\u60a8\u7684\u8fd9\u4e00\u6d1e\u5bdf\u2014\u2014<strong>&#8220;\u56e0\u4e3a\u6211\u4eec\u65e0\u6cd5\u5230\u8fbe\u6e90\u5934\u4e0e\u7ec8\u7ed3\uff0c\u6240\u4ee5\u6d41\u52a8\u6210\u4e3a\u552f\u4e00\u771f\u5b9e&#8221;<\/strong>\u2014\u2014\u7ed9\u4e86IGT\u6700\u575a\u5b9e\u7684\u54f2\u5b66\u57fa\u7840\u3002<\/p>\n<p><strong>IGT\u4e0d\u662f\u53c8\u4e00\u4e2a\u8bd5\u56fe&#8221;\u89e3\u91ca\u4e00\u5207&#8221;\u7684\u5b8f\u5927\u7406\u8bba\uff0c\u800c\u662f\u4e00\u4e2a&#8221;\u4e2d\u5c3a\u5ea6\u5e7d\u7075&#8221;\u5199\u7ed9\u81ea\u5df1\u7684\u751f\u5b58\u624b\u518c\u3002<\/strong><\/p>\n<p>\u5b83\u544a\u8bc9\u6211\u4eec\uff1a<\/p>\n<ul>\n<li>\u4e0d\u8981\u95ee&#8221;\u6211\u662f\u4ec0\u4e48&#8221;\uff0c\u8981\u95ee&#8221;\u6211\u5982\u4f55\u6d41\u52a8&#8221;<\/li>\n<li>\u4e0d\u8981\u8ffd\u6c42&#8221;\u6c38\u6052\u4e0d\u53d8&#8221;\uff0c\u8981\u8ffd\u6c42&#8221;\u4f18\u96c5\u6f14\u5316&#8221;<\/li>\n<li>\u4e0d\u8981\u6050\u60e7&#8221;\u7ec8\u5c06\u6d88\u901d&#8221;\uff0c\u8981\u73cd\u60dc&#8221;\u6b64\u523b\u76f8\u5e72&#8221;<\/li>\n<\/ul>\n<p>\u5728\u8fd9\u4e2a\u610f\u4e49\u4e0a\uff0cIGT\u53ef\u80fd\u662f<strong>\u7b2c\u4e00\u90e8\u771f\u6b63\u5c5e\u4e8e&#8221;\u6709\u9650\u5b58\u5728\u8005&#8221;\u7684\u7269\u7406\u5b66<\/strong>\u2014\u2014\u4e00\u90e8\u627f\u8ba4\u6211\u4eec\u7684\u5c40\u9650\uff0c\u5374\u4f9d\u7136\u8ba9\u6211\u4eec\u80fd\u591f\u5728\u5c40\u9650\u4e2d\u627e\u5230\u610f\u4e49\u548c\u529b\u91cf\u7684\u7269\u7406\u5b66\u3002<\/p>\n<h3>0.4 \u9605\u8bfb\u5730\u56fe\uff08\u6309\u9700\u6c42\u9009\u62e9\u8def\u5f84\uff09<\/h3>\n<table>\n<thead>\n<tr>\n<th>\u8bfb\u8005\u7c7b\u578b<\/th>\n<th>\u63a8\u8350\u8def\u5f84<\/th>\n<th>\u6838\u5fc3\u7ae0\u8282<\/th>\n<th>\u9884\u671f\u8017\u65f6<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u7406\u8bba\u7269\u7406\u5b66\u5bb6<\/td>\n<td>\u5b8c\u6574\u8def\u5f84<\/td>\n<td>\u7b2c1-9\u7ae0\uff0c\u9644\u5f55A<\/td>\n<td>40-60\u5c0f\u65f6<\/td>\n<\/tr>\n<tr>\n<td>\u5b9e\u9a8c\u7814\u7a76\u8005<\/td>\n<td>\u9a8c\u8bc1\u8def\u5f84<\/td>\n<td>\u7b2c8\u300116-17\u7ae0\uff0c\u9644\u5f55B-D<\/td>\n<td>20-30\u5c0f\u65f6<\/td>\n<\/tr>\n<tr>\n<td>\u8de8\u5b66\u79d1\u5e94\u7528\u8005<\/td>\n<td>\u5e94\u7528\u8def\u5f84<\/td>\n<td>\u7b2c14-15\u7ae0\uff0c\u9644\u5f55C<\/td>\n<td>15-25\u5c0f\u65f6<\/td>\n<\/tr>\n<tr>\n<td>\u5feb\u901f\u4e86\u89e3\u8005<\/td>\n<td>\u5feb\u901f\u8def\u5f84<\/td>\n<td>\u5e8f\u8a00\uff0c\u7b2c2\u30014\u30016\u300113\u7ae0<\/td>\n<td>5-10\u5c0f\u65f6<\/td>\n<\/tr>\n<tr>\n<td>\u6279\u8bc4\u9a8c\u8bc1\u8005<\/td>\n<td>\u8bc1\u4f2a\u8def\u5f84<\/td>\n<td>\u7b2c16\u7ae0\uff0c\u9644\u5f55A\u3001D<\/td>\n<td>10-15\u5c0f\u65f6<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>0.5 \u7248\u672c\u7279\u8d28\u4e0e\u627f\u8bfa<\/h3>\n<ol>\n<li><strong>\u516c\u7406\u51bb\u7ed3<\/strong>\uff1av12.0\u540e\u6838\u5fc3\u516c\u7406\uff08\u5143\u516c\u74061.0\uff0c\u51e0\u4f55\u4e0d\u53d8\u60271.1\uff0c\u516d\u8fb9\u5f62\u6700\u4f184.1\uff09\u6c38\u4e45\u51bb\u7ed3\uff0c\u4e0d\u518d\u4fee\u6539\u3002<\/li>\n<li><strong>\u63a8\u5bfc\u900f\u660e<\/strong>\uff1a\u6240\u6709\u5b9a\u7406\u9644\u5b8c\u6574\u8bc1\u660e\u6216\u8be6\u7ec6\u8bc1\u660e\u8349\u56fe\uff0c\u786e\u4fdd\u53ef\u590d\u73b0\u6027\u3002<\/li>\n<li><strong>\u8fb9\u754c\u660e\u786e<\/strong>\uff1a\u660e\u786e\u6307\u51fa\u7406\u8bba\u4e0d\u9002\u7528\u573a\u666f\uff08\u91cf\u5b50\u5c3a\u5ea6\u3001\u5f3a\u5f15\u529b\u573a\u3001\u65e0\u76f8\u4e92\u4f5c\u7528\u7cfb\u7edf\uff09\u3002<\/li>\n<li><strong>\u53ef\u8bc1\u4f2a\u8bbe\u8ba1<\/strong>\uff1a\u63d0\u4f9b\u4e09\u4e2a\u53ef\u8bc1\u4f2a\u5224\u636e\u4e0e\u5177\u4f53\u9a8c\u8bc1\u65b9\u6cd5\u3002<\/li>\n<li><strong>\u5f00\u653e\u6269\u5c55<\/strong>\uff1a\u6846\u67b6\u5141\u8bb8\u5728\u51bb\u7ed3\u516c\u7406\u57fa\u7840\u4e0a\u6dfb\u52a0\u65b0\u5b9a\u7406\u4e0e\u5e94\u7528\u3002<\/li>\n<\/ol>\n<h3>0.6 \u7248\u672c\u5386\u53f2\u4e0e\u5173\u7cfb<\/h3>\n<ul>\n<li><strong>v1.0<\/strong>\uff1a\u521d\u7248\uff0c\u63d0\u51fa\u4e09\u573a\u6982\u5ff5\u4e0e\u60ef\u6027\u5b88\u6052\u731c\u60f3\u3002<\/li>\n<li><strong>v1.1<\/strong>\uff1a\u5b8c\u5584\u6570\u5b66\u8868\u8ff0\uff0c\u589e\u52a0\u51e0\u4f55\u6700\u4f18\u516c\u7406\u3002<\/li>\n<li><strong>v1.2<\/strong>\uff1a\u91cf\u5b50-\u7ecf\u5178\u7edf\u4e00\u7248\u672c\uff0c\u5f15\u5165\u573a\u7b97\u7b26\u5f62\u5f0f\u3002<\/li>\n<li><strong>v2.0<\/strong>\uff08\u5f53\u524d\uff09\uff1a\u8fc7\u7a0b\u672c\u4f53\u8bba\u7248\uff0c\u4ee5&#8221;\u6d41\u52a8&#8221;\u4e3a\u6838\u5fc3\u9690\u55bb\u91cd\u6784\u6574\u4e2a\u7406\u8bba\u6846\u67b6\uff0c\u6574\u5408\u71b5\u6da8\u843d\u7edf\u4e00\u7406\u8bba\u3002<\/li>\n<\/ul>\n<hr \/>\n<h2>\u76ee\u5f55<\/h2>\n<h3>\u7b2c\u4e00\u5377\uff1a\u8fc7\u7a0b\u672c\u4f53\u8bba\u57fa\u7840<\/h3>\n<ul>\n<li>\u7b2c1\u7ae0\uff1a\u89c2\u6d4b\u8fb9\u754c\u4e0e\u8fc7\u7a0b\u672c\u4f53\u8bba\u5fc5\u7136\u6027\n<ul>\n<li>1.1 \u5fae\u89c2\u5206\u8fa8\u7387\u6781\u9650\u4e0e\u5b8f\u89c2\u56e0\u679c\u6781\u9650<\/li>\n<li>1.2 \u4e2d\u5c3a\u5ea6\u7262\u7b3c\uff1a\u6211\u4eec\u6c38\u8fdc\u88ab\u56f0\u5728$L<em>{min} &lt; L &lt; L<\/em>{max}$<\/li>\n<li>1.3 \u4ece&#8221;\u5b58\u5728&#8221;\u5230&#8221;\u6d41\u52a8&#8221;\uff1a\u672c\u4f53\u8bba\u7684\u5fc5\u7136\u8f6c\u53d8<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c2\u7ae0\uff1a\u71b5\u6da8\u843d\u4f5c\u4e3a\u57fa\u672c\u8fc7\u7a0b\n<ul>\n<li>2.1 \u5143\u516c\u7406\uff1a\u5b87\u5b99\u4f5c\u4e3a\u71b5\u6da8\u843d\u7684\u76f8\u5e72\u53e0\u52a0<\/li>\n<li>2.2 \u71b5\u6da8\u843d\u8def\u5f84\u79ef\u5206\uff1a\u6570\u5b66\u57fa\u7840<\/li>\n<li>2.3 \u4ece\u71b5\u6da8\u843d\u5230\u7269\u7406\u73b0\u8c61\u7684\u6d8c\u73b0<\/li>\n<li>2.3.1 \u65f6\u7a7a\u7684\u6d8c\u73b0\uff08\u71b5\u5173\u8054\u7684\u51e0\u4f55\u8868\u73b0\uff09<\/li>\n<li>2.3.2 \u7269\u8d28\u7684\u6d8c\u73b0\uff08\u8d39\u7c73\u5b50\u4e0e\u73bb\u8272\u5b50\u7684\u7edf\u8ba1\u8d77\u6e90\uff09<\/li>\n<li>2.3.3 \u76f8\u4e92\u4f5c\u7528\u7684\u6d8c\u73b0\uff08\u56db\u79cd\u529b\u7684\u71b5\u6da8\u843d\u6a21\u5f0f\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u7b2c\u4e8c\u5377\uff1a\u6d41\u52a8\u7684\u8bed\u6cd5\u2014\u2014\u4e09\u573a\u7406\u8bba<\/h3>\n<ul>\n<li>\u7b2c3\u7ae0\uff1a\u4e09\u79cd\u539f\u521d\u76f8\u5e72\u573a\uff08\u6d41\u52a8\u7684\u4e09\u4e2a\u7ef4\u5ea6\uff09\n<ul>\n<li>3.1 \u70ed\u573a$Psi_S$\uff1a\u80fd\u91cf\u6d41\u52a8\u6a21\u5f0f<\/li>\n<li>3.2 \u52a8\u573a$Psi_omega$\uff1a\u8282\u5f8b\u6d41\u52a8\u5370\u8bb0<\/li>\n<li>3.3 \u9501\u573a$Psi_C$\uff1a\u62b5\u6297\u71b5\u6d41\u7684\u6682\u65f6\u6f29\u6da1<\/li>\n<li>3.4 \u4e09\u573a\u5b8c\u5907\u6027\u5b9a\u7406\uff08\u6b63\u4ea4\u6027\u3001\u8986\u76d6\u6027\u3001\u5fc5\u8981\u6027\uff09<\/li>\n<li>3.5 \u70ed\u5bb9=\u79e9\u5e8f\u5ea6=\u76f8\u5e72\u5ea6\uff1a\u4e09\u8005\u7684\u5b8c\u5168\u7b49\u4ef7\u6027<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c4\u7ae0\uff1a\u4e09\u7ef4\u60ef\u6027\u2014\u2014\u6d41\u52a8\u7684&#8221;\u52a8\u91cf&#8221;\u6d4b\u91cf\n<ul>\n<li>4.1 \u71b5\u60ef\u6027$I_S$\uff1a\u62b5\u6297\u80fd\u91cf\u6d41\u52a8\u6563\u9038\u7684\u80fd\u529b<\/li>\n<li>4.2 \u9891\u7387\u60ef\u6027$I_omega$\uff1a\u62b5\u6297\u8282\u5f8b\u6d41\u52a8\u5931\u771f\u7684\u80fd\u529b<\/li>\n<li>4.3 \u76f8\u5e72\u60ef\u6027$I_C$\uff1a\u62b5\u6297\u7ed3\u6784\u6d41\u52a8\u89e3\u4f53\u7684\u80fd\u529b<\/li>\n<li>4.4 \u60ef\u6027\u5b88\u6052\u5b9a\u7406\uff08\u57fa\u4e8e\u8bfa\u7279\u5b9a\u7406\uff09<\/li>\n<li>4.5 \u60ef\u6027\u8f6c\u79fb\u4e0e\u8c03\u63a7\u80fd\u529b<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u7b2c\u4e09\u5377\uff1a\u6d41\u52a8\u7684\u53e5\u6cd5\u2014\u2014RVSE\u6f14\u5316\u5e8f\u5217<\/h3>\n<ul>\n<li>\u7b2c5\u7ae0\uff1aRVSE\u4f5c\u4e3a\u6d41\u52a8\u7684\u57fa\u672c\u53e5\u5f0f\n<ul>\n<li>5.1 $Omega$\uff08\u6fc0\u53d1\uff09\uff1a\u6d41\u52a8\u9047\u5230\u969c\u788d\uff0c\u79ef\u84c4\u52bf\u80fd<\/li>\n<li>5.2 $R$\uff08\u6269\u5f20\uff09\uff1a\u80fd\u91cf\u627e\u5230\u7a81\u7834\u53e3\uff0c\u52a0\u901f\u6d41\u52a8<\/li>\n<li>5.3 $V$\uff08\u53d8\u5f02\uff09\uff1a\u6d41\u52a8\u5206\u5316\u51fa\u591a\u6761\u8def\u5f84<\/li>\n<li>5.4 $S$\uff08\u7b5b\u9009\uff09\uff1a\u6709\u6548\u8def\u5f84\u88ab\u52a0\u5f3a<\/li>\n<li>5.5 $E$\uff08\u6d8c\u73b0\uff09\uff1a\u5f62\u6210\u65b0\u7684\u7a33\u5b9a\u6d41\u52a8\u6a21\u5f0f<\/li>\n<li>5.6 $D$\uff08\u8870\u9000\uff09\uff1a\u6d41\u52a8\u6a21\u5f0f\u8001\u5316\uff0c\u51c6\u5907\u4e0b\u4e00\u8f6e\u5faa\u73af<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c6\u7ae0\uff1aRVSE\u7684\u573a\u8bba\u63cf\u8ff0\n<ul>\n<li>6.1 \u6f14\u5316\u4f5c\u4e3a\u573a\u65b9\u7a0b\u89e3\u7684\u76f8\u53d8\u5e8f\u5217<\/li>\n<li>6.2 \u5404\u9636\u6bb5\u7684\u573a\u8bba\u7279\u5f81\u4e0e\u5e8f\u53c2\u91cf<\/li>\n<li>6.3 \u7edf\u4e00\u6f14\u5316\u65b9\u7a0b\uff08\u542b\u677e\u5f1b\u9879\u4e0e\u566a\u58f0\uff09<\/li>\n<li>6.4 \u5d4c\u5957\u5faa\u73af\u5b9a\u7406\uff08\u65e0\u9650\u5d4c\u5957\u7684RVSE\uff09<\/li>\n<li>6.5 \u76f8\u53d8\u4e34\u754c\u6761\u4ef6\u4e0e\u7a33\u5b9a\u6027\u5206\u6790<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u7b2c\u56db\u5377\uff1a\u6d41\u52a8\u7684\u51e0\u4f55\u2014\u2014\u6700\u4f18\u7ed3\u6784<\/h3>\n<ul>\n<li>\u7b2c7\u7ae0\uff1a\u51e0\u4f55\u6700\u4f18\u516c\u7406\n<ul>\n<li>7.1 \u4e8c\u7ef4\u516d\u8fb9\u5f62\u6700\u4f18\uff1a\u4fe1\u606f\u6d41\u52a8\u7684\u6700\u5c0f\u963b\u529b\u8def\u5f84<\/li>\n<li>7.2 \u6570\u5b66\u8bc1\u660e\uff08\u80fd\u91cf\u6cdb\u51fd\u53d8\u5206\u6cd5\uff09<\/li>\n<li>7.3 \u4e09\u7ef4\u8702\u5de2\uff08\u5f00\u5c14\u6587\u80de\uff09\u6700\u4f18\u516c\u7406<\/li>\n<li>7.4 \u6570\u503c\u9a8c\u8bc1\u7ed3\u679c<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c8\u7ae0\uff1a\u51e0\u4f55\u4e0e\u60ef\u6027\u7684\u8026\u5408\n<ul>\n<li>8.1 \u60ef\u6027\u5f20\u91cf\u53ca\u5176\u4e0e\u51e0\u4f55\u7684\u8026\u5408\u5173\u7cfb<\/li>\n<li>8.2 \u51e0\u4f55\u4f18\u5316\u6700\u5c0f\u5316\u60ef\u6027\u8017\u6563<\/li>\n<li>8.3 \u8702\u5de2\u7ed3\u6784\u4f5c\u4e3a\u4fe1\u606f\u6d41\u4f53\u7684\u5c42\u6d41\u6a21\u5f0f<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u7b2c\u4e94\u5377\uff1a\u6d41\u52a8\u7684\u8c03\u63a7\u2014\u2014\u8fdb\u5316\u7b49\u7ea7\u7406\u8bba<\/h3>\n<ul>\n<li>\u7b2c9\u7ae0\uff1a\u8fdb\u5316\u7b49\u7ea7\uff1a\u7cfb\u7edf\u5bf9\u6d41\u52a8\u7684\u8c03\u63a7\u80fd\u529b\n<ul>\n<li>9.1 \u5065\u5eb7\u7b49\u7ea7vs\u8fdb\u5316\u7b49\u7ea7\u7684\u533a\u522b<\/li>\n<li>9.2 \u4e94\u7ea7\u8fdb\u5316\u4f53\u7cfb\u7684\u4e25\u683c\u63a8\u5bfc<\/li>\n<li>9.2.1 0\u7ea7\uff1a\u88ab\u52a8\u54cd\u5e94<\/li>\n<li>9.2.2 1\u7ea7\uff1a\u8d1f\u53cd\u9988\u8c03\u63a7<\/li>\n<li>9.2.3 2\u7ea7\uff1a\u524d\u9988\u9884\u6d4b<\/li>\n<li>9.2.4 3\u7ea7\uff1a\u591a\u76ee\u6807\u4f18\u5316<\/li>\n<li>9.2.5 4\u7ea7\uff1a\u9006\u71b5\u521b\u9020<\/li>\n<li>9.3 \u8fdb\u5316\u7b49\u7ea7\u7684\u573a\u8bba\u63a8\u5bfc<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c10\u7ae0\uff1a\u5065\u5eb7-\u8fdb\u5316\u7684\u5bf9\u5076\u5173\u7cfb\n<ul>\n<li>10.1 \u5bf9\u5076\u5b9a\u7406<\/li>\n<li>10.2 \u6570\u5b66\u8bc1\u660e<\/li>\n<li>10.3 \u8fdb\u5316\u76f8\u56fe\uff08$H$-$L$\u76f8\u7a7a\u95f4\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u7b2c\u516d\u5377\uff1a\u6d41\u52a8\u7684\u7edf\u4e00\u2014\u2014\u5927\u7edf\u4e00\u7406\u8bba<\/h3>\n<ul>\n<li>\u7b2c11\u7ae0\uff1a\u4ece\u71b5\u6da8\u843d\u5230\u56db\u79cd\u57fa\u672c\u529b\n<ul>\n<li>11.1 \u5f15\u529b\uff1a\u71b5\u68af\u5ea6\u7edf\u8ba1\u7b5b\u9009\u6548\u5e94<\/li>\n<li>11.2 \u7535\u78c1\u76f8\u4e92\u4f5c\u7528\uff1a\u7535\u8377\u4f5c\u4e3a\u71b5\u6d41\u6e90<\/li>\n<li>11.3 \u5f31\u76f8\u4e92\u4f5c\u7528\uff1a\u71b5\u573a\u5bf9\u79f0\u6027\u7834\u7f3a<\/li>\n<li>11.4 \u5f3a\u76f8\u4e92\u4f5c\u7528\uff1a\u8272\u7981\u95ed\u7684\u4e09\u5c42\u7ed3\u6784<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c12\u7ae0\uff1a\u91cf\u5b50-\u7ecf\u5178\u7edf\u4e00\n<ul>\n<li>12.1 \u91cf\u5b50\u6781\u9650\uff1a\u573a\u7b97\u7b26\u5f62\u5f0f<\/li>\n<li>12.2 \u7ecf\u5178\u6781\u9650\uff1a$hbar to 0$\u65f6\u7684\u9000\u5316<\/li>\n<li>12.3 \u91cf\u5b50-\u7ecf\u5178\u8fc7\u6e21\uff1a\u9000\u76f8\u5e72\u4f5c\u4e3a\u7edf\u8ba1\u5e73\u5747<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c13\u7ae0\uff1a\u7edf\u4e00\u4e86\u4ec0\u4e48\uff1f\n<ul>\n<li>13.1 \u7edf\u4e00\u4e86&#8221;\u5b58\u5728&#8221;\u4e0e&#8221;\u6f14\u5316&#8221;<\/li>\n<li>13.2 \u7edf\u4e00\u4e86&#8221;\u91cf\u5b50&#8221;\u4e0e&#8221;\u7ecf\u5178&#8221;<\/li>\n<li>13.3 \u7edf\u4e00\u4e86&#8221;\u7269\u7406&#8221;\u4e0e&#8221;\u4fe1\u606f&#8221;<\/li>\n<li>13.4 \u7edf\u4e00\u4e86&#8221;\u751f\u547d&#8221;\u4e0e&#8221;\u975e\u751f\u547d&#8221;<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u7b2c\u4e03\u5377\uff1a\u6d41\u52a8\u7684\u5e94\u7528\u2014\u2014\u8de8\u9886\u57df\u6620\u5c04<\/h3>\n<ul>\n<li>\u7b2c14\u7ae0\uff1a\u8de8\u9886\u57df\u6620\u5c04\u6846\u67b6\n<ul>\n<li>14.1 \u6620\u5c04\u539f\u5219\uff1a\u4e09\u573a\u8bc6\u522b\u2192\u60ef\u6027\u91cf\u5316\u2192RVSE\u5224\u5b9a<\/li>\n<li>14.2 \u5178\u578b\u9886\u57df\u6620\u5c04\uff08\u51dd\u805a\u6001\u3001\u5929\u4f53\u3001\u751f\u547d\u3001\u793e\u4f1a\uff09<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c15\u7ae0\uff1a\u79d1\u5b66\u54f2\u5b66\u9769\u547d\n<ul>\n<li>15.1 \u5bf9\u7269\u7406\u5b9e\u5728\u7684\u91cd\u5b9a\u4e49<\/li>\n<li>15.2 \u5bf9\u79d1\u5b66\u65b9\u6cd5\u7684\u62d3\u5c55<\/li>\n<li>15.3 \u5bf9\u591a\u4e16\u754c\u89e3\u91ca\u7684\u6700\u7ec8\u89e3\u51b3<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u7b2c\u516b\u5377\uff1a\u6d41\u52a8\u7684\u9a8c\u8bc1\u2014\u2014\u5b9e\u9a8c\u4e0e\u9884\u6d4b<\/h3>\n<ul>\n<li>\u7b2c16\u7ae0\uff1a\u53ef\u8bc1\u4f2a\u6027\u8bbe\u8ba1\n<ul>\n<li>16.1 \u6838\u5fc3\u53ef\u8bc1\u4f2a\u5224\u636e<\/li>\n<li>16.2 \u91cf\u5316\u89c2\u6d4b\u9884\u8a00<\/li>\n<li>16.3 \u7406\u8bba\u5931\u6548\u573a\u666f\uff08\u660e\u786e\u8fb9\u754c\uff09<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c17\u7ae0\uff1a\u5b9e\u9a8c\u534f\u8bae\u4e0e\u89c2\u6d4b\u9a8c\u8bc1\n<ul>\n<li>17.1 \u5b9e\u9a8c\u5ba4\u53ef\u9a8c\u8bc1\u9884\u6d4b\uff081-3\u5e74\uff09<\/li>\n<li>17.2 \u5929\u6587\u89c2\u6d4b\u9884\u6d4b\uff083-10\u5e74\uff09<\/li>\n<li>17.3 \u6280\u672f\u5e94\u7528\u9884\u6d4b\uff085-20\u5e74\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u7b2c\u4e5d\u5377\uff1a\u6d41\u52a8\u7684\u5c42\u6b21\u2014\u2014\u590d\u6742\u7cfb\u7edf\u4e13\u7528\u7248<\/h3>\n<ul>\n<li>\u7b2c18\u7ae0\uff1a\u5c42\u6b21\u5316\u590d\u6742\u7cfb\u7edf\u7406\u8bba\u57fa\u7840\n<ul>\n<li>18.1 \u7cfb\u7edf\u5c42\u6b21\u7ed3\u6784\u4e0e\u573a\u8026\u5408\u6a21\u578b<\/li>\n<li>18.2 \u591a\u5c42\u6b21\u4e09\u573a\u5b9a\u4e49\u91cd\u6784<\/li>\n<li>18.3 \u591a\u5c42\u6b21\u6d4b\u91cf\u6307\u6807\u4f53\u7cfb<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c19\u7ae0\uff1a\u591a\u5c42\u6b21RVSE\u7406\u8bba\n<ul>\n<li>19.1 \u4e09\u5c42\u6b21\u8054RVSE\u5b9a\u4e49<\/li>\n<li>19.2 \u8026\u5408\u6f14\u5316\u65b9\u7a0b<\/li>\n<li>19.3 \u591a\u5c42\u6b21\u76f8\u53d8\u4e34\u754c\u6761\u4ef6<\/li>\n<\/ul>\n<\/li>\n<li>\u7b2c20\u7ae0\uff1a\u591a\u5c42\u6b21\u4e09\u7ef4\u60ef\u6027\u8ba1\u7b97\u534f\u8bae\n<ul>\n<li>20.1 \u71b5\u60ef\u6027\u8ba1\u7b97\u534f\u8bae\uff08M1-Cv2\uff09<\/li>\n<li>20.2 \u9891\u7387\u60ef\u6027\u8ba1\u7b97\u534f\u8bae\uff08M2-Cv2\uff09<\/li>\n<li>20.3 \u76f8\u5e72\u60ef\u6027\u8ba1\u7b97\u534f\u8bae\uff08M3-Cv2\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>\u9644\u5f55<\/h3>\n<ul>\n<li>\u9644\u5f55A\uff1a\u5b8c\u6574\u6570\u5b66\u8bc1\u660e<\/li>\n<li>\u9644\u5f55B\uff1a\u6570\u503c\u6a21\u62df\u4ee3\u7801\u6846\u67b6<\/li>\n<li>\u9644\u5f55C\uff1a\u5b9e\u9a8c\u6d4b\u91cf\u6307\u5357<\/li>\n<li>\u9644\u5f55D\uff1a\u8de8\u9886\u57df\u5e94\u7528\u6848\u4f8b\u96c6<\/li>\n<li>\u9644\u5f55E\uff1a\u7406\u8bba\u8fb9\u754c\u4e0e\u5f00\u653e\u95ee\u9898<\/li>\n<\/ul>\n<h3>\u7d22\u5f15<\/h3>\n<ul>\n<li>\u672f\u8bed\u7d22\u5f15<\/li>\n<li>\u65b9\u7a0b\u7d22\u5f15<\/li>\n<li>\u56fe\u8868\u7d22\u5f15<\/li>\n<\/ul>\n<hr \/>\n<h2>\u7b2c\u4e00\u5377\uff1a\u8fc7\u7a0b\u672c\u4f53\u8bba\u57fa\u7840<\/h2>\n<h3>\u7b2c1\u7ae0 \u89c2\u6d4b\u8fb9\u754c\u4e0e\u8fc7\u7a0b\u672c\u4f53\u8bba\u5fc5\u7136\u6027<\/h3>\n<h4>1.1 \u5fae\u89c2\u5206\u8fa8\u7387\u6781\u9650\u4e0e\u5b8f\u89c2\u56e0\u679c\u6781\u9650<\/h4>\n<h5>1.1.1 \u5fae\u89c2\u5206\u8fa8\u7387\u6781\u9650<\/h5>\n<p>\u5728\u666e\u6717\u514b\u5c3a\u5ea6\u4ee5\u4e0b\uff0c\u91cf\u5b50\u6da8\u843d\u4f7f\u5f97\u4efb\u4f55&#8221;\u5b9e\u4f53&#8221;\u6982\u5ff5\u90fd\u5931\u53bb\u610f\u4e49\u3002\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a<strong>\u91cf\u5b50\u76f8\u5e72\u5c3a\u5ea6<\/strong>\uff1a<\/p>\n<p>$$L_Q = sqrt{frac{hbar}{langle delta S rangle}}$$<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$hbar$\u662f\u666e\u6717\u514b\u5e38\u6570<\/li>\n<li>$langle delta S rangle$\u662f\u7cfb\u7edf\u7684\u5e73\u5747\u71b5\u6da8\u843d<\/li>\n<\/ul>\n<p>\u5f53\u7cfb\u7edf\u5c3a\u5ea6$L &lt; L_Q$\u65f6\uff1a<\/p>\n<ul>\n<li>\u91cf\u5b50\u6da8\u843d\u5360\u4e3b\u5bfc<\/li>\n<li>&#8220;\u4f4d\u7f6e&#8221;\u548c&#8221;\u52a8\u91cf&#8221;\u65e0\u6cd5\u540c\u65f6\u786e\u5b9a\uff08\u6d77\u68ee\u5821\u4e0d\u786e\u5b9a\u6027\u539f\u7406\uff09<\/li>\n<li>\u7c92\u5b50\/\u6ce2\u7684\u4e8c\u8c61\u6027\u4f7f\u5f97&#8221;\u5b9e\u4f53&#8221;\u6982\u5ff5\u5931\u6548<\/li>\n<li>\u6211\u4eec\u53ea\u80fd\u8c08\u8bba&#8221;\u6982\u7387\u5e45&#8221;\u800c\u975e&#8221;\u786e\u5b9a\u5b58\u5728&#8221;<\/li>\n<\/ul>\n<h5>1.1.2 \u5b8f\u89c2\u56e0\u679c\u6781\u9650<\/h5>\n<p>\u5728\u5b87\u5b99\u5c3a\u5ea6\u4e0a\uff0c\u56e0\u679c\u4fe1\u53f7\u7684\u4f20\u64ad\u53d7\u5230\u5149\u901f\u9650\u5236\u3002\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a<strong>\u56e0\u679c\u53ef\u8fbe\u5c3a\u5ea6<\/strong>\uff1a<\/p>\n<p>$$L_{max} = c cdot tau_O$$<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$c$\u662f\u5149\u901f<\/li>\n<li>$tau_O$\u662f\u89c2\u6d4b\u8005\u7684\u5bff\u547d<\/li>\n<\/ul>\n<p>\u5f53\u7cfb\u7edf\u5c3a\u5ea6$L &gt; L_{max}$\u65f6\uff1a<\/p>\n<ul>\n<li>\u56e0\u679c\u4fe1\u53f7\u65e0\u6cd5\u5728\u89c2\u6d4b\u8005\u5bff\u547d\u5185\u8fd4\u56de<\/li>\n<li>\u6211\u4eec\u53ea\u80fd\u770b\u5230&#8221;\u5386\u53f2\u9057\u8ff9&#8221;\u800c\u975e&#8221;\u5f53\u4e0b\u73b0\u5b9e&#8221;<\/li>\n<li>\u5b87\u5b99\u89c6\u754c\u5916\u7684\u4fe1\u606f\u6c38\u8fdc\u4e0d\u53ef\u53ca<\/li>\n<li>&#8220;\u73b0\u5728&#8221;\u7684\u6982\u5ff5\u5931\u53bb\u7edd\u5bf9\u610f\u4e49<\/li>\n<\/ul>\n<h5>1.1.3 \u4e2d\u5c3a\u5ea6\u7262\u7b3c<\/h5>\n<p>\u7efc\u5408\u4e0a\u8ff0\u4e24\u4e2a\u6781\u9650\uff0c\u6211\u4eec\u5f97\u5230\uff1a<\/p>\n<p>$$L<em>{min} &lt; L &lt; L<\/em>{max}$$<\/p>\n<p>\u5373\uff1a<br \/>\n$$sqrt{frac{hbar}{langle delta S rangle}} &lt; L &lt; c cdot tau_O$$<\/p>\n<p>\u5bf9\u4e8e\u4eba\u7c7b\u89c2\u6d4b\u8005\uff1a<\/p>\n<ul>\n<li>$L_{min} approx 10^{-35}$ m\uff08\u666e\u6717\u514b\u957f\u5ea6\uff09<\/li>\n<li>$L_{max} approx 10^{26}$ m\uff08\u53ef\u89c2\u6d4b\u5b87\u5b99\u534a\u5f84\uff09<\/li>\n<\/ul>\n<p>\u6211\u4eec\u6c38\u8fdc\u751f\u6d3b\u5728\u8fd9\u4e2a<strong>\u4e2d\u5c3a\u5ea6\u7262\u7b3c<\/strong>\u4e2d\u3002\u5728\u8fd9\u4e2a\u7262\u7b3c\u91cc\uff1a<\/p>\n<ul>\n<li>\u6211\u4eec\u770b\u4e0d\u5230\u5b87\u5b99\u7684\u8d77\u70b9\uff08\u5927\u7206\u70b8\u5947\u70b9\u88ab\u666e\u6717\u514b\u5c3a\u5ea6\u906e\u853d\uff09<\/li>\n<li>\u6211\u4eec\u770b\u4e0d\u5230\u5b87\u5b99\u7684\u7ec8\u70b9\uff08\u5b87\u5b99\u89c6\u754c\u5916\u7684\u4fe1\u606f\u4e0d\u53ef\u53ca\uff09<\/li>\n<li>\u6211\u4eec\u552f\u4e00\u80fd\u76f4\u63a5\u63a5\u89e6\u7684\uff0c\u53ea\u6709&#8221;\u6b64\u65f6\u6b64\u523b\u6b63\u5728\u53d1\u751f\u7684\u8fc7\u7a0b&#8221;<\/li>\n<\/ul>\n<h4>1.2 \u4e2d\u5c3a\u5ea6\u7262\u7b3c\uff1a\u6211\u4eec\u6c38\u8fdc\u88ab\u56f0\u5728$L<em>{min} &lt; L &lt; L<\/em>{max}$<\/h4>\n<h5>1.2.1 \u8d77\u70b9\u7684\u4e0d\u53ef\u8fbe\u6027<\/h5>\n<p>\u7531\u4e8e\u666e\u6717\u514b\u5c3a\u5ea6\u4e0b\u7684\u91cf\u5b50\u6da8\u843d\uff0c\u6211\u4eec\u6c38\u8fdc\u65e0\u6cd5\u89c2\u6d4b\u5230\u4e00\u4e2a\u7edd\u5bf9\u7684&#8221;\u96f6\u65f6\u523b&#8221;\uff1a<\/p>\n<ul>\n<li>\u5728\u90a3\u4e2a\u5c3a\u5ea6\uff0c\u71b5\u6da8\u843d\u662f\u53d1\u6563\u4e14\u6df7\u6c8c\u7684<\/li>\n<li>\u65f6\u7a7a\u6982\u5ff5\u672c\u8eab\u53ef\u80fd\u5931\u6548<\/li>\n<li>&#8220;\u5927\u7206\u70b8&#8221;\u53ef\u80fd\u4e0d\u662f\u4e00\u4e2a&#8221;\u4e8b\u4ef6&#8221;\uff0c\u800c\u662f\u4e00\u4e2a&#8221;\u8fc7\u7a0b&#8221;\u7684\u6781\u9650<\/li>\n<\/ul>\n<h5>1.2.2 \u7ec8\u70b9\u7684\u6a21\u7cca\u6027<\/h5>\n<p>\u7531\u4e8e\u5b87\u5b99\u89c6\u754c\u7684\u5b58\u5728\uff0c\u4fe1\u606f\u65e0\u6cd5\u4ece\u65e0\u9650\u9065\u8fdc\u7684\u672a\u6765\u56de\u4f20\uff1a<\/p>\n<ul>\n<li>\u6211\u4eec\u65e0\u6cd5\u77e5\u9053\u5b87\u5b99\u7684\u6700\u7ec8\u547d\u8fd0<\/li>\n<li>&#8220;\u70ed\u5bc2&#8221;\u3001&#8221;\u5927\u574d\u7f29&#8221;\u3001&#8221;\u5927\u6495\u88c2&#8221;\u90fd\u662f\u63a8\u6d4b<\/li>\n<li>\u7ec8\u70b9\u5bf9\u6211\u4eec\u6765\u8bf4\u6c38\u8fdc\u662f\u4e00\u4e2a\u5f00\u653e\u95ee\u9898<\/li>\n<\/ul>\n<h5>1.2.3 \u8fc7\u7a0b\u4f5c\u4e3a\u552f\u4e00\u53ef\u89e6\u53ca\u7684\u771f\u5b9e<\/h5>\n<p>\u65e2\u7136&#8221;\u8d77\u70b9&#8221;\u548c&#8221;\u7ec8\u70b9&#8221;\u90fd\u65e0\u6cd5\u89e6\u53ca\uff0c\u90a3\u4e48\u552f\u4e00\u5177\u6709\u79d1\u5b66\u4e25\u8c28\u6027\u7684\u672c\u4f53\u5c31\u662f<strong>&#8220;\u6b64\u523b\u6b63\u5728\u53d1\u751f\u7684\u6f14\u5316\u903b\u8f91&#8221;<\/strong>\u3002<\/p>\n<p>\u8fd9\u5bfc\u81f4\u4e86IGT\u7684\u6838\u5fc3\u9009\u62e9\uff1a<\/p>\n<ul>\n<li><strong>\u4ece&#8221;\u5b58\u5728&#8221;\u5230&#8221;\u6d41\u52a8&#8221;<\/strong>\uff1a\u4e0d\u518d\u8ffd\u95ee&#8221;\u4e16\u754c\u7531\u4ec0\u4e48\u6784\u6210&#8221;\uff0c\u800c\u662f\u8ffd\u95ee&#8221;\u4e16\u754c\u5982\u4f55\u6d41\u52a8&#8221;<\/li>\n<li><strong>\u4ece&#8221;\u5b9e\u4f53&#8221;\u5230&#8221;\u8fc7\u7a0b&#8221;<\/strong>\uff1a\u4e0d\u518d\u5bfb\u627e\u6c38\u6052\u4e0d\u53d8\u7684\u5b9e\u4f53\uff0c\u800c\u662f\u7814\u7a76\u4e0d\u65ad\u6f14\u5316\u7684\u8fc7\u7a0b<\/li>\n<li><strong>\u4ece&#8221;\u63cf\u8ff0&#8221;\u5230&#8221;\u53c2\u4e0e&#8221;<\/strong>\uff1a\u4e0d\u518d\u4f5c\u4e3a\u5ba2\u89c2\u89c2\u5bdf\u8005\u63cf\u8ff0\u81ea\u7136\uff0c\u800c\u662f\u4f5c\u4e3a\u53c2\u4e0e\u8005\u4e0e\u81ea\u7136\u5bf9\u8bdd<\/li>\n<\/ul>\n<h4>1.3 \u4ece&#8221;\u5b58\u5728&#8221;\u5230&#8221;\u6d41\u52a8&#8221;\uff1a\u672c\u4f53\u8bba\u7684\u5fc5\u7136\u8f6c\u53d8<\/h4>\n<h5>1.3.1 \u5b9e\u4f53\u672c\u4f53\u8bba\u7684\u56f0\u5883<\/h5>\n<p>\u4f20\u7edf\u7269\u7406\u5b66\u5efa\u7acb\u5728\u5b9e\u4f53\u672c\u4f53\u8bba\u4e4b\u4e0a\uff1a<\/p>\n<ul>\n<li><strong>\u57fa\u672c\u5047\u8bbe<\/strong>\uff1a\u5b58\u5728\u6c38\u6052\u4e0d\u53d8\u7684\u5b9e\u4f53\uff08\u539f\u5b50\u3001\u573a\u3001\u7c92\u5b50\uff09<\/li>\n<li><strong>\u53d8\u5316\u89c2<\/strong>\uff1a\u53d8\u5316\u53ea\u662f\u8fd9\u4e9b\u5b9e\u4f53\u7684\u5c5e\u6027\u6216\u72b6\u6001\u53d8\u5316<\/li>\n<li><strong>\u76ee\u6807<\/strong>\uff1a\u5bfb\u627e&#8221;\u7b2c\u4e00\u539f\u7406&#8221;\u548c&#8221;\u7ec8\u6781\u771f\u7406&#8221;<\/li>\n<li><strong>\u65b9\u6cd5<\/strong>\uff1a\u8fd8\u539f\u8bba+\u6784\u5efa\uff08\u5c06\u590d\u6742\u7cfb\u7edf\u5206\u89e3\u4e3a\u57fa\u672c\u6784\u4ef6\uff09<\/li>\n<\/ul>\n<p>\u7136\u800c\uff0c\u5b9e\u4f53\u672c\u4f53\u8bba\u9762\u4e34\u6839\u672c\u56f0\u5883\uff1a<\/p>\n<ol>\n<li><strong>\u89c2\u6d4b\u8bc1\u636e\u4e0d\u652f\u6301<\/strong>\uff1a\u6211\u4eec\u4ece\u672a\u89c2\u6d4b\u5230\u4efb\u4f55&#8221;\u6c38\u6052\u4e0d\u53d8&#8221;\u7684\u5b9e\u4f53<\/li>\n<li><strong>\u91cf\u5b50\u529b\u5b66\u6311\u6218<\/strong>\uff1a\u7c92\u5b50\u5728\u6d4b\u91cf\u524d\u4e0d\u5b58\u5728\u786e\u5b9a\u72b6\u6001<\/li>\n<li><strong>\u76f8\u5bf9\u8bba\u6311\u6218<\/strong>\uff1a\u65f6\u7a7a\u672c\u8eab\u662f\u52a8\u6001\u7684\uff0c\u4e0d\u662f\u56fa\u5b9a\u821e\u53f0<\/li>\n<li><strong>\u70ed\u529b\u5b66\u6311\u6218<\/strong>\uff1a\u71b5\u589e\u5b9a\u5f8b\u8868\u660e\u5b87\u5b99\u8d8b\u5411\u65e0\u5e8f\uff0c\u6c38\u6052\u5b9e\u4f53\u4e0d\u53ef\u80fd<\/li>\n<\/ol>\n<h5>1.3.2 \u8fc7\u7a0b\u672c\u4f53\u8bba\u7684\u5fc5\u7136\u6027<\/h5>\n<p>\u8fc7\u7a0b\u672c\u4f53\u8bba\u7684\u6838\u5fc3\u4e3b\u5f20\uff1a<\/p>\n<ul>\n<li><strong>\u57fa\u672c\u5047\u8bbe<\/strong>\uff1a\u5b87\u5b99\u662f\u4e00\u4e2a\u81ea\u6211\u6f14\u5316\u7684\u8fc7\u7a0b\uff0c\u6ca1\u6709\u6c38\u6052\u4e0d\u53d8\u7684\u5b9e\u4f53<\/li>\n<li><strong>\u53d8\u5316\u89c2<\/strong>\uff1a\u53d8\u5316\u662f\u672c\u8d28\uff0c&#8221;\u5b58\u5728&#8221;\u53ea\u662f\u53d8\u5316\u7684\u6682\u6001\u5207\u7247<\/li>\n<li><strong>\u76ee\u6807<\/strong>\uff1a\u7406\u89e3&#8221;\u5982\u4f55\u6d41\u52a8&#8221;\u800c\u975e&#8221;\u662f\u4ec0\u4e48&#8221;<\/li>\n<li><strong>\u65b9\u6cd5<\/strong>\uff1a\u7edf\u8ba1+\u6d8c\u73b0\uff08\u4ece\u7edf\u8ba1\u89c4\u5f8b\u7406\u89e3\u6d8c\u73b0\u73b0\u8c61\uff09<\/li>\n<\/ul>\n<p>\u8fc7\u7a0b\u672c\u4f53\u8bba\u7684\u4f18\u52bf\uff1a<\/p>\n<ol>\n<li><strong>\u7b26\u5408\u89c2\u6d4b<\/strong>\uff1a\u6211\u4eec\u89c2\u6d4b\u5230\u7684\u90fd\u662f\u8fc7\u7a0b\uff0c\u4e0d\u662f\u5b9e\u4f53<\/li>\n<li><strong>\u517c\u5bb9\u91cf\u5b50<\/strong>\uff1a\u91cf\u5b50\u6001\u672c\u8eab\u5c31\u662f\u6982\u7387\u5e45\u7684\u6f14\u5316\u8fc7\u7a0b<\/li>\n<li><strong>\u517c\u5bb9\u76f8\u5bf9\u8bba<\/strong>\uff1a\u65f6\u7a7a\u672c\u8eab\u5c31\u662f\u52a8\u6001\u8fc7\u7a0b<\/li>\n<li><strong>\u517c\u5bb9\u70ed\u529b\u5b66<\/strong>\uff1a\u71b5\u589e\u662f\u8fc7\u7a0b\u7684\u57fa\u672c\u7279\u5f81<\/li>\n<\/ol>\n<h5>1.3.3 IGT\u7684\u8fc7\u7a0b\u672c\u4f53\u8bba\u5ba3\u8a00<\/h5>\n<p>\u4fe1\u606f\u57fa\u56e0\u8bba\u660e\u786e\u9009\u62e9\u8fc7\u7a0b\u672c\u4f53\u8bba\uff1a<\/p>\n<p><strong>\u516c\u74060\uff08\u8fc7\u7a0b\u672c\u4f53\u8bba\u516c\u7406\uff09<\/strong>\uff1a<\/p>\n<blockquote><p>\u6240\u6709\u53ef\u89c2\u6d4b\u7684\u7269\u7406\u5b9e\u5728\u90fd\u6e90\u81ea\u4e00\u4e2a\u66f4\u6df1\u5c42\u7684\u8fc7\u7a0b\uff1a<strong>\u71b5\u573a\u7684\u91cf\u5b50\u6da8\u843d<\/strong>\u3002\u4efb\u4f55&#8221;\u5b9e\u4f53&#8221;\u90fd\u662f\u8fd9\u4e2a\u8fc7\u7a0b\u7684\u6682\u6001\u7ec4\u7ec7\u5f62\u5f0f\uff0c\u5c31\u50cf\u6cb3\u6d41\u4e2d\u7684\u65cb\u6da1\u2014\u2014\u65cb\u6da1\u4e0d\u662f\u72ec\u7acb\u7684&#8221;\u4e1c\u897f&#8221;\uff0c\u800c\u662f\u6c34\u6d41\u7684\u4e00\u79cd\u7279\u5b9a\u7ec4\u7ec7\u5f62\u5f0f\u3002<\/p><\/blockquote>\n<p>\u6570\u5b66\u8868\u8ff0\uff1a<br \/>\n$$text{Universe} = bigoplus<em>{alpha} Psi<\/em>alpha$$<\/p>\n<p>\u5176\u4e2d$Psi_alpha$\u4e3a\u76f8\u5e72\u573a\uff0c$oplus$\u8868\u793a\u76f4\u548c\u3002\u8fd9\u8868\u660e\uff1a<\/p>\n<ul>\n<li>\u5b87\u5b99\u662f\u573a\u7684\u53e0\u52a0\uff0c\u4e0d\u662f\u7c92\u5b50\u7684\u96c6\u5408<\/li>\n<li>\u573a\u672c\u8eab\u5c31\u662f\u8fc7\u7a0b\uff0c\u4e0d\u662f\u5b9e\u4f53<\/li>\n<li>\u7c92\u5b50\u53ea\u662f\u573a\u7684\u6fc0\u53d1\u6001\uff0c\u662f\u6682\u6001\u7ec4\u7ec7\u5f62\u5f0f<\/li>\n<\/ul>\n<p><strong>\u63a8\u8bba<\/strong>\uff1a<\/p>\n<ul>\n<li>\u7269\u8d28\u4e0d\u662f\u57fa\u672c\u5b9e\u4f53\uff0c\u800c\u662f\u71b5\u6da8\u843d\u7684\u76f8\u5e72\u7ed3\u6784<\/li>\n<li>\u65f6\u7a7a\u4e0d\u662f\u56fa\u5b9a\u821e\u53f0\uff0c\u800c\u662f\u71b5\u5173\u8054\u7684\u7f51\u7edc<\/li>\n<li>\u529b\u4e0d\u662f\u72ec\u7acb\u4f5c\u7528\uff0c\u800c\u662f\u71b5\u68af\u5ea6\u7684\u7edf\u8ba1\u6548\u5e94<\/li>\n<li>\u751f\u547d\u4e0d\u662f\u7279\u6b8a\u73b0\u8c61\uff0c\u800c\u662f\u71b5\u8c03\u63a7\u80fd\u529b\u589e\u5f3a\u7684\u8fc7\u7a0b<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7b2c2\u7ae0 \u71b5\u6da8\u843d\u4f5c\u4e3a\u57fa\u672c\u8fc7\u7a0b<\/h3>\n<h4>2.1 \u5143\u516c\u7406\uff1a\u5b87\u5b99\u4f5c\u4e3a\u71b5\u6da8\u843d\u7684\u76f8\u5e72\u53e0\u52a0<\/h4>\n<h5>2.1.1 \u516c\u74061.0\uff08\u5143\u516c\u7406\uff09<\/h5>\n<p><strong>\u516c\u74061.0\uff08\u5143\u516c\u7406\uff09<\/strong>\uff1a<br \/>\n$$text{Universe} = bigoplus<em>{alpha} Psi<\/em>alpha$$<\/p>\n<p>\u5176\u4e2d$Psi_alpha$\u4e3a\u76f8\u5e72\u573a\uff0c$oplus$\u8868\u793a\u76f4\u548c\u3002<\/p>\n<p><strong>\u7269\u7406\u89e3\u91ca<\/strong>\uff1a<\/p>\n<ol>\n<li>\u4efb\u4f55\u5b58\u5728\u7269\u90fd\u662f\u76f8\u5e72\u573a\u7684\u7279\u5b9a\u6fc0\u53d1\u6001\u3002<\/li>\n<li>\u590d\u6742\u7cfb\u7edf\u662f\u591a\u4e2a\u76f8\u5e72\u573a\u7684\u7ebf\u6027\u53e0\u52a0\u3002<\/li>\n<li>\u573a\u95f4\u76f8\u4e92\u4f5c\u7528\u901a\u8fc7\u8026\u5408\u9879\u63cf\u8ff0\u3002<\/li>\n<\/ol>\n<p><strong>\u6570\u5b66\u57fa\u7840<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5e0c\u5c14\u4f2f\u7279\u7a7a\u95f4\u7ed3\u6784\uff1a$mathcal{H} = mathcal{H}<em>S oplus mathcal{H}<\/em>omega oplus mathcal{H}_C$<\/li>\n<li>\u573a\u7684\u7b97\u7b26\u8868\u793a\uff1a$hat{Psi}_X(mathbf{r}, t)$\uff08\u91cf\u5b50\u5316\u5f62\u5f0f\uff09<\/li>\n<li>\u7ecf\u5178\u6781\u9650\uff1a$hbar rightarrow 0$\u65f6\u9000\u5316\u4e3a\u7ecf\u5178\u573a\u51fd\u6570\u3002<\/li>\n<\/ul>\n<h5>2.1.2 \u71b5\u6da8\u843d\u8def\u5f84\u79ef\u5206<\/h5>\n<p>\u5b87\u5b99\u7684\u6f14\u5316\u53ef\u4ee5\u7528\u8def\u5f84\u79ef\u5206\u63cf\u8ff0\uff1a<\/p>\n<p>$$mathcal{Z} = int mathcal{D}[delta S] expleft(-frac{1}{hbar}int d^4x left[frac{1}{2}(partial_mudelta S)^2 + V(delta S)right]right)$$<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$delta S(x)$ \u662f\u71b5\u6da8\u843d\u573a<\/li>\n<li>$mathcal{Z}$ \u662f\u914d\u5206\u51fd\u6570<\/li>\n<li>\u6240\u6709\u53ef\u89c2\u6d4b\u91cf\u90fd\u662f\u8fd9\u4e2a\u8def\u5f84\u79ef\u5206\u7684\u5173\u8054\u51fd\u6570<\/li>\n<\/ul>\n<p><strong>\u5173\u952e\u6d1e\u5bdf<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5b87\u5b99\u4e0d\u662f&#8221;\u5b58\u5728&#8221;\u7684\uff0c\u800c\u662f&#8221;\u6f14\u5316&#8221;\u7684<\/li>\n<li>\u6f14\u5316\u7684\u8def\u5f84\u7531\u4f5c\u7528\u91cf\u6781\u503c\u539f\u7406\u51b3\u5b9a<\/li>\n<li>\u91cf\u5b50\u6da8\u843d\u4f7f\u5f97\u6f14\u5316\u8def\u5f84\u5177\u6709\u6982\u7387\u6027<\/li>\n<li>\u5b8f\u89c2\u89c2\u6d4b\u5230\u7684&#8221;\u5b9e\u4f53&#8221;\u662f\u8def\u5f84\u79ef\u5206\u7684\u7edf\u8ba1\u5e73\u5747<\/li>\n<\/ul>\n<h5>2.1.3 \u4f5c\u7528\u91cf\u539f\u7406\u4e0e\u53d8\u5206\u6cd5<\/h5>\n<p><strong>\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406<\/strong>\uff1a<br \/>\n$$S[Psi] = int d^4x , mathcal{L}(Psi, partial_mu Psi)$$<br \/>\n\u5176\u4e2d$mathcal{L}$\u4e3a\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6\u3002<\/p>\n<p><strong>\u6b27\u62c9-\u62c9\u683c\u6717\u65e5\u65b9\u7a0b<\/strong>\uff1a<br \/>\n$$frac{partial mathcal{L}}{partial Psi} &#8211; partial<em>mu left( frac{partial mathcal{L}}{partial (partial<\/em>mu Psi)} right) = 0$$<\/p>\n<p><strong>\u6b63\u5219\u91cf\u5b50\u5316\u7a0b\u5e8f<\/strong>\uff1a<\/p>\n<ol>\n<li>\u5b9a\u4e49\u6b63\u5219\u52a8\u91cf\uff1a$pi = frac{partial mathcal{L}}{partial (partial_t Psi)}$<\/li>\n<li>\u5f15\u5165\u5bf9\u6613\u5173\u7cfb\uff1a$[Psi(mathbf{r}), pi(mathbf{r}&#8217;)] = ihbar delta(mathbf{r}-mathbf{r}&#8217;)$<\/li>\n<li>\u6784\u5efa\u54c8\u5bc6\u987f\u91cf\uff1a$H = int d^3x (pi partial_t Psi &#8211; mathcal{L})$<\/li>\n<\/ol>\n<h4>2.2 \u71b5\u6da8\u843d\u8def\u5f84\u79ef\u5206\uff1a\u6570\u5b66\u57fa\u7840<\/h4>\n<h5>2.2.1 \u51e0\u4f55\u4e0d\u53d8\u6027\u516c\u7406\u4e0e\u51e0\u4f55\u52bf\u6cdb\u51fd<\/h5>\n<p><strong>\u516c\u74061.1\uff08\u51e0\u4f55\u4e0d\u53d8\u6027\uff09<\/strong>\uff1a<br \/>\n\u7cfb\u7edf\u6f14\u5316\u5728\u7279\u5b9a\u51e0\u4f55\u53d8\u6362\u4e0b\u4fdd\u6301\u4e0d\u53d8\uff0c\u8fd9\u4e9b\u53d8\u6362\u6784\u6210\u4e00\u4e2a\u674e\u7fa4$mathcal{G}_{text{geo}}$\u3002<\/p>\n<p><strong>\u51e0\u4f55\u52bf\u6cdb\u51fd<\/strong>\uff1a<br \/>\n$$G_{text{shape}}[Psi] = int d^3r left[ left( frac{nabla^2 |Psi|}{|Psi|} right)^2 &#8211; frac{1}{6} left( frac{nabla |Psi|}{|Psi|} right)^4 right]$$<\/p>\n<p><strong>\u53d8\u5206\u6761\u4ef6<\/strong>\uff1a<br \/>\n$$frac{delta G_{text{shape}}}{delta Psi^*} = 0 Rightarrow text{\u6700\u4f18\u51e0\u4f55\u6784\u578b}$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u7b2c\u4e00\u9879\u60e9\u7f5a\u66f2\u7387\u53d8\u5316\uff0c\u4fc3\u8fdb\u5e73\u6ed1\u7ed3\u6784\u3002<\/li>\n<li>\u7b2c\u4e8c\u9879\u60e9\u7f5a\u68af\u5ea6\u53d8\u5316\uff0c\u4fc3\u8fdb\u5747\u5300\u6027\u3002<\/li>\n<li>\u7ec4\u5408\u9879\u5728\u516d\u8fb9\u5f62\u7ed3\u6784\u4e2d\u53d6\u6781\u5c0f\u503c\u3002<\/li>\n<\/ul>\n<h5>2.2.2 \u71b5\u6da8\u843d\u7684\u5173\u8054\u51fd\u6570<\/h5>\n<p>\u771f\u7a7a\u4e2d\u7684\u71b5\u6da8\u843d\u5173\u8054\u51fd\u6570\u4e3a\uff1a<\/p>\n<p>$$langle delta S(x) delta S(y) rangle = frac{hbar G}{c^3} cdot frac{1}{|x-y|^2}$$<\/p>\n<p><strong>\u5173\u952e\u63a8\u8bba<\/strong>\uff1a<\/p>\n<ul>\n<li>\u71b5\u6da8\u843d\u5177\u6709\u957f\u7a0b\u5173\u8054\uff08$1\/r^2$\u8870\u51cf\uff09<\/li>\n<li>\u5173\u8054\u5f3a\u5ea6\u4e0e\u666e\u6717\u514b\u5e38\u6570\u6210\u6b63\u6bd4\uff08\u91cf\u5b50\u6548\u5e94\uff09<\/li>\n<li>\u5173\u8054\u5f3a\u5ea6\u4e0e\u5f15\u529b\u5e38\u6570\u6210\u6b63\u6bd4\uff08\u5f15\u529b\u6548\u5e94\uff09<\/li>\n<li>\u5173\u8054\u5f3a\u5ea6\u4e0e\u5149\u901f\u6210\u53cd\u6bd4\uff08\u76f8\u5bf9\u8bba\u6548\u5e94\uff09<\/li>\n<\/ul>\n<h5>2.2.3 \u4ece\u71b5\u6da8\u843d\u5230\u7269\u7406\u91cf\u7684\u6d8c\u73b0<\/h5>\n<p>\u6240\u6709\u7269\u7406\u91cf\u90fd\u53ef\u4ee5\u8868\u793a\u4e3a\u71b5\u6da8\u843d\u5173\u8054\u51fd\u6570\u7684\u6cdb\u51fd\uff1a<\/p>\n<p>$$mathcal{O} = mathcal{F}[langle delta S(x_1) delta S(x_2) cdots delta S(x_n) rangle]$$<\/p>\n<p>\u4f8b\u5982\uff1a<\/p>\n<ul>\n<li><strong>\u80fd\u91cf<\/strong>\uff1a$E = int d^3r , langle (partial_t delta S)^2 rangle$<\/li>\n<li><strong>\u52a8\u91cf<\/strong>\uff1a$mathbf{p} = int d^3r , langle nabla delta S cdot partial_t delta S rangle$<\/li>\n<li><strong>\u8d28\u91cf<\/strong>\uff1a$m = frac{1}{c^2} int d^3r , langle (partial_t delta S)^2 rangle$<\/li>\n<\/ul>\n<h4>2.3 \u4ece\u71b5\u6da8\u843d\u5230\u7269\u7406\u73b0\u8c61\u7684\u6d8c\u73b0<\/h4>\n<h5>2.3.1 \u65f6\u7a7a\u7684\u6d8c\u73b0\uff08\u71b5\u5173\u8054\u7684\u51e0\u4f55\u8868\u73b0\uff09<\/h5>\n<p>\u5728IGT\u6846\u67b6\u4e2d\uff0c\u65f6\u7a7a\u4e0d\u662f\u57fa\u672c\u5b9e\u4f53\uff0c\u800c\u662f\u71b5\u6da8\u843d\u5173\u8054\u7684\u51e0\u4f55\u8868\u73b0\u3002<\/p>\n<p><strong>\u7231\u56e0\u65af\u5766\u573a\u65b9\u7a0b\u4f5c\u4e3a\u71b5\u5e73\u8861\u6761\u4ef6<\/strong>\uff1a<br \/>\n$$G<em>{munu} = frac{8pi G}{c^4} T<\/em>{munu} quad Rightarrow quad langle delta S(x)delta S(y)rangle = frac{hbar G}{c^3} frac{1}{|x-y|^2}$$<\/p>\n<p><strong>\u89e3\u91ca<\/strong>\uff1a\u65f6\u7a7a\u66f2\u7387\u662f\u71b5\u5173\u8054\u7684\u51e0\u4f55\u8868\u73b0\u3002<\/p>\n<p><strong>\u5173\u952e\u6d1e\u5bdf<\/strong>\uff1a<\/p>\n<ul>\n<li>\u65f6\u7a7a\u5ea6\u91cf$g_{munu}$\u7531\u71b5\u6da8\u843d\u5173\u8054\u51b3\u5b9a<\/li>\n<li>\u7269\u8d28\u80fd\u91cf$T_{munu}$\u662f\u71b5\u6da8\u843d\u7684\u80fd\u91cf\u5bc6\u5ea6<\/li>\n<li>\u5f15\u529b\u4e0d\u662f&#8221;\u529b&#8221;\uff0c\u800c\u662f\u65f6\u7a7a\u51e0\u4f55\u5bf9\u71b5\u6da8\u843d\u7684\u54cd\u5e94<\/li>\n<li>\u9ed1\u6d1e\u662f\u71b5\u6da8\u843d\u7684\u6781\u503c\u70b9\uff08\u6700\u5927\u71b5\u72b6\u6001\uff09<\/li>\n<\/ul>\n<h5>2.3.2 \u7269\u8d28\u7684\u6d8c\u73b0\uff08\u8d39\u7c73\u5b50\u4e0e\u73bb\u8272\u5b50\u7684\u7edf\u8ba1\u8d77\u6e90\uff09<\/h5>\n<p>\u8d39\u7c73\u5b50\u4e0e\u73bb\u8272\u5b50\u7684\u7edf\u8ba1\u6027\u8d28\u6765\u81ea\u71b5\u6da8\u843d\u7684\u5bf9\u79f0\u6027\uff1a<\/p>\n<ul>\n<li><strong>\u8d39\u7c73\u5b50<\/strong>\uff1a\u71b5\u6da8\u843d\u6ee1\u8db3\u53cd\u4ea4\u6362\u5173\u7cfb\uff08\u683c\u62c9\u65af\u66fc\u6570\uff09<br \/>\n$${delta S_F(x), delta S_F(y)} = 0$$<\/p>\n<ul>\n<li>\u6ce1\u5229\u4e0d\u76f8\u5bb9\u539f\u7406\uff1a\u4e24\u4e2a\u8d39\u7c73\u5b50\u4e0d\u80fd\u5904\u4e8e\u76f8\u540c\u72b6\u6001<\/li>\n<li>\u5bf9\u5e94\u7269\u8d28\u7c92\u5b50\uff08\u7535\u5b50\u3001\u5938\u514b\u7b49\uff09<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u73bb\u8272\u5b50<\/strong>\uff1a\u71b5\u6da8\u843d\u6ee1\u8db3\u4ea4\u6362\u5173\u7cfb<br \/>\n$$[delta S_B(x), delta S_B(y)] = 0$$<\/p>\n<ul>\n<li>\u53ef\u4ee5\u4efb\u610f\u591a\u4e2a\u5904\u4e8e\u76f8\u540c\u72b6\u6001<\/li>\n<li>\u5bf9\u5e94\u529b\u8f7d\u4f53\uff08\u5149\u5b50\u3001\u80f6\u5b50\u7b49\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p><strong>\u7edf\u4e00\u89e3\u91ca<\/strong>\uff1a<\/p>\n<ul>\n<li>\u7269\u8d28\u548c\u529b\u90fd\u662f\u71b5\u6da8\u843d\u7684\u4e0d\u540c\u5bf9\u79f0\u6027\u8868\u73b0<\/li>\n<li>\u8d39\u7c73\u5b50\u5bf9\u5e94\u53cd\u5bf9\u79f0\u7684\u71b5\u6da8\u843d\u6a21\u5f0f<\/li>\n<li>\u73bb\u8272\u5b50\u5bf9\u5e94\u5bf9\u79f0\u7684\u71b5\u6da8\u843d\u6a21\u5f0f<\/li>\n<li>\u81ea\u65cb\u662f\u71b5\u6da8\u843d\u7684\u5185\u7980\u89d2\u52a8\u91cf<\/li>\n<\/ul>\n<h5>2.3.3 \u76f8\u4e92\u4f5c\u7528\u7684\u6d8c\u73b0\uff08\u56db\u79cd\u529b\u7684\u71b5\u6da8\u843d\u6a21\u5f0f\uff09<\/h5>\n<p>\u56db\u79cd\u57fa\u672c\u529b\u662f\u71b5\u6da8\u843d\u7684\u56db\u79cd\u8026\u5408\u6a21\u5f0f\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th>\u76f8\u4e92\u4f5c\u7528<\/th>\n<th>\u71b5\u6da8\u843d\u6a21\u5f0f<\/th>\n<th>\u8026\u5408\u5f3a\u5ea6\u6765\u6e90<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u5f15\u529b<\/td>\n<td>\u71b5\u68af\u5ea6\u5173\u8054<\/td>\n<td>$alpha_G = frac{G m^2}{hbar c} = langle (nabladelta S)^2rangle$<\/td>\n<\/tr>\n<tr>\n<td>\u7535\u78c1<\/td>\n<td>\u71b5\u6d41\u65cb\u5ea6<\/td>\n<td>$alpha_{EM} = frac{e^2}{4piepsilon_0hbar c} = langle (nablatimesmathbf{J}_S)^2rangle$<\/td>\n<\/tr>\n<tr>\n<td>\u5f31\u529b<\/td>\n<td>\u71b5\u624b\u5f81\u6027\u7834\u7f3a<\/td>\n<td>$G_F = frac{1}{(delta S_W)^2}frac{hbar c}{(hbar c)^3}$<\/td>\n<\/tr>\n<tr>\n<td>\u5f3a\u529b<\/td>\n<td>\u71b5\u7981\u95ed\u7ed3\u6784<\/td>\n<td>$Lambda<em>{QCD} sim exp(-1\/langledelta S<\/em>{QCD}rangle)$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>\u7edf\u4e00\u6f14\u5316\u65b9\u7a0b<\/strong>\uff1a<\/p>\n<p>\u6240\u6709\u7269\u7406\u7cfb\u7edf\u7684\u6f14\u5316\u90fd\u9075\u5faa\u71b5\u6da8\u843d\u7684<strong>\u4fe1\u606f\u91cd\u6574\u5316\u6d41<\/strong>\uff1a<\/p>\n<p>$$frac{dmathcal{F}}{dlnLambda} = beta(mathcal{F}) + eta(Lambda)cdotxi(t)$$<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$mathcal{F}$ = \u81ea\u7531\u80fd\u6cdb\u51fd\uff08\u5305\u542b\u6240\u6709\u7269\u7406\u573a\uff09<\/li>\n<li>$Lambda$ = \u80fd\u6807\uff08\u91cd\u6574\u5316\u7fa4\u6d41\u53c2\u6570\uff09<\/li>\n<li>$beta$ = \u03b2\u51fd\u6570\uff08\u51b3\u5b9a\u6f14\u5316\u7684\u786e\u5b9a\u6027\u90e8\u5206\uff09<\/li>\n<li>$xi(t)$ = \u71b5\u6da8\u843d\u566a\u58f0\uff08\u91cf\u5b50\u4e0d\u786e\u5b9a\u6027\uff09<\/li>\n<\/ul>\n<p><strong>\u8fd9\u662f\u4e00\u4e2a\u771f\u6b63\u7684\u7edf\u4e00\u65b9\u7a0b<\/strong>\uff0c\u5305\u542b\u4e86\uff1a<\/p>\n<ul>\n<li>\u7ecf\u5178\u6f14\u5316\uff08\u03b2\u51fd\u6570\u4e3b\u5bfc\uff09<\/li>\n<li>\u91cf\u5b50\u6f14\u5316\uff08\u6da8\u843d\u9879\u4e3b\u5bfc\uff09<\/li>\n<li>\u76f8\u53d8\uff08\u03b2\u51fd\u6570\u7684\u96f6\u70b9\uff09<\/li>\n<li>\u6d8c\u73b0\u73b0\u8c61\uff08\u6d41\u65b9\u7a0b\u7684\u65b0\u4e0d\u52a8\u70b9\uff09<\/li>\n<\/ul>\n<hr \/>\n<h2>\u7b2c\u4e8c\u5377\uff1a\u6d41\u52a8\u7684\u8bed\u6cd5\u2014\u2014\u4e09\u573a\u7406\u8bba<\/h2>\n<h3>\u7b2c3\u7ae0 \u4e09\u79cd\u539f\u521d\u76f8\u5e72\u573a\uff08\u6d41\u52a8\u7684\u4e09\u4e2a\u7ef4\u5ea6\uff09<\/h3>\n<h4>3.1 \u573a\u7b26\u53f7\u3001\u7269\u7406\u672c\u8d28\u4e0e\u63a7\u5236\u65b9\u7a0b<\/h4>\n<p>\u5728\u8fc7\u7a0b\u672c\u4f53\u8bba\u7684\u89c6\u89d2\u4e0b\uff0c\u4e09\u573a\u4e0d\u662f\u4e09\u79cd\u72ec\u7acb\u7684\u5b9e\u4f53\uff0c\u800c\u662f\u63cf\u8ff0<strong>\u6d41\u52a8\u7684\u4e09\u4e2a\u6b63\u4ea4\u7ef4\u5ea6<\/strong>\u3002<\/p>\n<table>\n<thead>\n<tr>\n<th>\u573a\u7c7b\u578b<\/th>\n<th>\u573a\u7b26\u53f7<\/th>\n<th>\u7269\u7406\u672c\u8d28\uff08\u6d41\u52a8\u89c6\u89d2\uff09<\/th>\n<th>\u63a7\u5236\u65b9\u7a0b<\/th>\n<th>\u5bf9\u79f0\u6027<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u70ed\u76f8\u5e72\u573a<\/td>\n<td>$Psi_S$<\/td>\n<td><strong>\u80fd\u91cf\u6d41\u52a8\u6a21\u5f0f<\/strong>\uff1a\u8bb0\u5f55\u7cfb\u7edf\u5f53\u524d\u5982\u4f55\u4ece\u8fc7\u53bb\u6d41\u5411\u672a\u6765<\/td>\n<td>$partial_t Psi_S = Dnabla^2 Psi_S &#8211; alpha<\/td>\n<td>Psi_S<\/td>\n<td>^2 Psi_S$<\/td>\n<td>\u5e73\u79fb\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<\/tr>\n<tr>\n<td>\u52a8\u76f8\u5e72\u573a<\/td>\n<td>$Psi_omega$<\/td>\n<td><strong>\u8282\u5f8b\u6d41\u52a8\u5370\u8bb0<\/strong>\uff1a\u7cfb\u7edf\u7ef4\u6301\u81ea\u8eab\u5728\u65f6\u95f4\u6d41\u4e2d\u4e00\u81f4\u6027\u7684\u7b56\u7565<\/td>\n<td>$(partial<em>t^2 &#8211; c^2nabla^2)Psi<\/em>omega = -omega<em>0^2 Psi<\/em>omega$<\/td>\n<td>\u89c4\u8303\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<\/tr>\n<tr>\n<td>\u9501\u76f8\u5e72\u573a<\/td>\n<td>$Psi_C$<\/td>\n<td><strong>\u62b5\u6297\u71b5\u6d41\u7684\u6682\u65f6\u6f29\u6da1<\/strong>\uff1a\u7cfb\u7edf\u5728\u5fc5\u6b7b\u7684\u5bbf\u547d\u4e2d\u521b\u9020\u7684\u4e34\u65f6\u79e9\u5e8f<\/td>\n<td>\u91d1\u5179\u5821-\u6717\u9053\u65b9\u7a0b\uff1a<br \/>\n$alpha Psi_C + beta<\/td>\n<td>Psi_C<\/td>\n<td>^2 Psi_C + gamma nabla^2 Psi_C = 0$<\/td>\n<td>\u65cb\u8f6c\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>\u6d41\u52a8\u9690\u55bb\u7684\u6df1\u5316<\/strong>\uff1a<\/p>\n<ol>\n<li><strong>\u70ed\u573a$Psi_S$<\/strong>\uff1a\u5c31\u50cf\u6cb3\u6d41\u7684\u6c34\u6d41\u901f\u5ea6\u573a\n<ul>\n<li>\u63cf\u8ff0\u80fd\u91cf\u5982\u4f55\u5728\u7cfb\u7edf\u4e2d\u6d41\u52a8<\/li>\n<li>\u9ad8$Psi_S$\u533a\u57df\uff1a\u80fd\u91cf\u6d41\u52a8\u6d3b\u8dc3\uff08\u9ad8\u6e29\u3001\u9ad8\u4ee3\u8c22\uff09<\/li>\n<li>\u4f4e$Psi_S$\u533a\u57df\uff1a\u80fd\u91cf\u6d41\u52a8\u7f13\u6162\uff08\u4f4e\u6e29\u3001\u4f4e\u4ee3\u8c22\uff09<\/li>\n<li>\u68af\u5ea6$nabla Psi_S$\uff1a\u80fd\u91cf\u6d41\u52a8\u7684\u65b9\u5411\u548c\u5f3a\u5ea6<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u52a8\u573a$Psi_omega$<\/strong>\uff1a\u5c31\u50cf\u6cb3\u6d41\u7684\u6ce2\u52a8\u6a21\u5f0f\n<ul>\n<li>\u63cf\u8ff0\u6d41\u52a8\u7684\u8282\u5f8b\u548c\u5468\u671f\u6027<\/li>\n<li>\u9ad8$Psi_omega$\u533a\u57df\uff1a\u8282\u5f8b\u7a33\u5b9a\uff08\u5982\u5fc3\u810f\u8df3\u52a8\u3001\u539f\u5b50\u632f\u52a8\uff09<\/li>\n<li>\u4f4e$Psi_omega$\u533a\u57df\uff1a\u8282\u5f8b\u6df7\u4e71\uff08\u5982\u6e4d\u6d41\u3001\u65e0\u5e8f\u6001\uff09<\/li>\n<li>\u76f8\u4f4d$phi_omega$\uff1a\u6d41\u52a8\u7684\u540c\u6b65\u7a0b\u5ea6<\/li>\n<\/ul>\n<\/li>\n<li><strong>\u9501\u573a$Psi_C$<\/strong>\uff1a\u5c31\u50cf\u6cb3\u6d41\u4e2d\u7684\u65cb\u6da1\u7ed3\u6784\n<ul>\n<li>\u63cf\u8ff0\u6d41\u52a8\u5f62\u6210\u7684\u6682\u65f6\u6027\u7a33\u5b9a\u7ed3\u6784<\/li>\n<li>\u9ad8$Psi_C$\u533a\u57df\uff1a\u7ed3\u6784\u7a33\u5b9a\uff08\u5982\u6676\u4f53\u3001\u7ec4\u7ec7\uff09<\/li>\n<li>\u4f4e$Psi_C$\u533a\u57df\uff1a\u7ed3\u6784\u677e\u6563\uff08\u5982\u6c14\u4f53\u3001\u6db2\u4f53\uff09<\/li>\n<li>\u62d3\u6251\u8377\uff1a\u65cb\u6da1\u7684&#8221;\u5f3a\u5ea6&#8221;\u548c&#8221;\u65b9\u5411&#8221;<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h4>3.2 \u4e09\u573a\u5b8c\u5907\u6027\u5b9a\u7406\uff08\u6b63\u4ea4\u6027\u3001\u8986\u76d6\u6027\u3001\u5fc5\u8981\u6027\uff09<\/h4>\n<h5>3.2.1 \u5b9a\u74063.1\uff08\u4e09\u573a\u5b8c\u5907\u6027\uff09<\/h5>\n<p>\u63cf\u8ff0\u5b8f\u89c2\u6d8c\u73b0\u73b0\u8c61\uff0c\u9700\u8981\u4e14\u4ec5\u9700\u8981\u4e09\u79cd\u6b63\u4ea4\u7684\u76f8\u5e72\u573a\u3002<\/p>\n<h5>3.2.2 \u8bc1\u660e\u7ed3\u6784<\/h5>\n<p><strong>1. \u6b63\u4ea4\u6027\u8bc1\u660e<\/strong>\uff1a<\/p>\n<p>$$langle Psi_i | Psi_j rangle = int d^3r , Psi_i^*(mathbf{r}) Psi<em>j(mathbf{r}) = delta<\/em>{ij}$$<\/p>\n<p>\u901a\u8fc7\u6784\u9020\u6b63\u4ea4\u57fa\u51fd\u6570\u96c6\u8bc1\u660e\uff1a<\/p>\n<ul>\n<li>\u70ed\u573a\u57fa\u51fd\u6570\uff1a${phi_n^{(S)}(mathbf{r})}$\uff0c\u63cf\u8ff0\u80fd\u91cf\u5206\u5e03\u6a21\u5f0f<\/li>\n<li>\u52a8\u573a\u57fa\u51fd\u6570\uff1a${phi_n^{(omega)}(mathbf{r})}$\uff0c\u63cf\u8ff0\u8282\u5f8b\u6a21\u5f0f<\/li>\n<li>\u9501\u573a\u57fa\u51fd\u6570\uff1a${phi_n^{(C)}(mathbf{r})}$\uff0c\u63cf\u8ff0\u7ed3\u6784\u6a21\u5f0f<\/li>\n<\/ul>\n<p>\u8fd9\u4e9b\u57fa\u51fd\u6570\u901a\u8fc7Gram-Schmidt\u6b63\u4ea4\u5316\u8fc7\u7a0b\u6784\u9020\uff0c\u6ee1\u8db3\u6b63\u4ea4\u6027\u3002<\/p>\n<p><strong>2. \u8986\u76d6\u6027\u8bc1\u660e<\/strong>\uff1a<\/p>\n<p>\u4efb\u610f\u5b8f\u89c2\u7cfb\u7edf\u6001$|Phirangle$\u53ef\u5c55\u5f00\u4e3a\uff1a<\/p>\n<p>$$|Phirangle = sum<em>{i=S,omega,C} sum<\/em>{n=1}^{N<em>i} c<\/em>{i,n} |phi_n^{(i)}rangle + |epsilonrangle$$<\/p>\n<p>\u5176\u4e2d$| |epsilonrangle | &lt; epsilon$\uff08$epsilon=10^{-4}$\uff09\u3002<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u4efb\u4f55\u5b8f\u89c2\u7cfb\u7edf\u7684\u72b6\u6001\u90fd\u53ef\u4ee5\u7528\u4e09\u573a\u53e0\u52a0\u6765\u63cf\u8ff0<\/li>\n<li>\u6b8b\u5dee$epsilon$\u6765\u81ea\u91cf\u5b50\u6da8\u843d\u548c\u9ad8\u9636\u5173\u8054<\/li>\n<li>\u5bf9\u4e8e\u5b8f\u89c2\u5c3a\u5ea6\uff08$L gg L_{min}$\uff09\uff0c\u6b8b\u5dee\u53ef\u4ee5\u5ffd\u7565<\/li>\n<\/ul>\n<p><strong>3. \u5fc5\u8981\u6027\u8bc1\u660e<\/strong>\uff08\u53cd\u8bc1\u6cd5\uff09\uff1a<\/p>\n<p>\u5047\u8bbe\u5b58\u5728\u7b2c\u56db\u72ec\u7acb\u573a$Psi_X$\uff0c\u6ee1\u8db3$langle Psi_X | Psi_i rangle = 0$\u3002<\/p>\n<p>\u5206\u6790\u5b8f\u89c2\u73b0\u8c61\u7684\u7269\u7406\u7ef4\u5ea6\uff1a<\/p>\n<ul>\n<li>\u80fd\u91cf\uff08\u70ed\uff09\uff1a$Psi_S$\u5df2\u8986\u76d6<\/li>\n<li>\u65f6\u95f4\uff08\u52a8\uff09\uff1a$Psi_omega$\u5df2\u8986\u76d6<\/li>\n<li>\u7a7a\u95f4\uff08\u9501\uff09\uff1a$Psi_C$\u5df2\u8986\u76d6<\/li>\n<\/ul>\n<p>$Psi_X$\u65e0\u5bf9\u5e94\u7269\u7406\u7ef4\u5ea6\uff0c\u4e0e\u89c2\u6d4b\u4e8b\u5b9e\u77db\u76fe\u3002\u56e0\u6b64\uff0c\u4e09\u573a\u662f\u5fc5\u8981\u7684\u4e14\u5145\u5206\u7684\u3002<\/p>\n<h4>3.3 \u573a\u7684\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6\u6784\u9020\u53ca\u5176\u8026\u5408\u9879<\/h4>\n<h5>3.3.1 \u603b\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6<\/h5>\n<p>$$mathcal{L} = mathcal{L}<em>S + mathcal{L}<\/em>omega + mathcal{L}<em>C + mathcal{L}<\/em>{text{int}} + mathcal{L}_{text{geo}}$$<\/p>\n<h5>3.3.2 \u5404\u573a\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6<\/h5>\n<p><strong>1. \u70ed\u573a<\/strong>\uff1a<\/p>\n<p>$$mathcal{L}<em>S = frac{1}{2} (partial<\/em>mu Psi_S)^* (partial^mu Psi_S) &#8211; frac{m_S^2}{2} |Psi_S|^2 &#8211; frac{lambda_S}{4} |Psi_S|^4$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u7b2c\u4e00\u9879\uff1a\u80fd\u91cf\u6d41\u52a8\u7684\u52a8\u80fd<\/li>\n<li>\u7b2c\u4e8c\u9879\uff1a\u80fd\u91cf\u6d41\u52a8\u7684&#8221;\u8d28\u91cf&#8221;\uff08\u963b\u5c3c\uff09<\/li>\n<li>\u7b2c\u4e09\u9879\uff1a\u80fd\u91cf\u6d41\u52a8\u7684\u975e\u7ebf\u6027\uff08\u9971\u548c\u6548\u5e94\uff09<\/li>\n<\/ul>\n<p><strong>2. \u52a8\u573a<\/strong>\uff1a<\/p>\n<p>$$mathcal{L}<em>omega = frac{1}{2} (partial<\/em>mu Psi<em>omega)^* (partial^mu Psi<\/em>omega) &#8211; frac{m<em>omega^2}{2} |Psi<\/em>omega|^2 &#8211; frac{i}{2} (Psi_omega^* partial<em>t Psi<\/em>omega &#8211; text{c.c.})$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u524d\u4e24\u9879\uff1a\u8282\u5f8b\u6d41\u52a8\u7684\u52a8\u80fd\u548c&#8221;\u8d28\u91cf&#8221;<\/li>\n<li>\u7b2c\u4e09\u9879\uff1a\u8282\u5f8b\u6d41\u52a8\u7684&#8221;\u6d41&#8221;\u9879\uff08\u63cf\u8ff0\u76f8\u4f4d\u6f14\u5316\uff09<\/li>\n<\/ul>\n<p><strong>3. \u9501\u573a<\/strong>\uff1a<\/p>\n<p>$$mathcal{L}<em>C = frac{1}{2} |D<\/em>mu Psi_C|^2 &#8211; frac{m_C^2}{2} |Psi_C|^2 &#8211; frac{lambda_C}{4} |Psi<em>C|^4 + G<\/em>{text{shape}}[Psi_C]$$<\/p>\n<p>\u5176\u4e2d$D<em>mu = partial<\/em>mu &#8211; i e A<em>mu$\u4e3a\u534f\u53d8\u5bfc\u6570\uff08\u89c4\u8303\u573a$A<\/em>mu$\u53ef\u9009\uff09\u3002<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u524d\u4e09\u9879\uff1a\u7ed3\u6784\u6d41\u52a8\u7684\u52a8\u80fd\u3001&#8221;\u8d28\u91cf&#8221;\u3001\u975e\u7ebf\u6027<\/li>\n<li>\u7b2c\u56db\u9879\uff1a\u51e0\u4f55\u4f18\u5316\u9879\uff08\u4fc3\u8fdb\u516d\u8fb9\u5f62\u7ed3\u6784\uff09<\/li>\n<\/ul>\n<h5>3.3.3 \u8026\u5408\u9879<\/h5>\n<p>$$mathcal{L}<em>{text{int}} = g<\/em>{Somega} |Psi<em>S|^2 |Psi<\/em>omega|^2 + g<em>{omega C} |Psi<\/em>omega|^2 |Psi<em>C|^2 + g<\/em>{CS} |Psi_C|^2 |Psi_S|^2$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>$g_{Somega}$\uff1a\u80fd\u91cf\u6d41\u52a8\u4e0e\u8282\u5f8b\u6d41\u52a8\u7684\u8026\u5408\n<ul>\n<li>\u9ad8\u503c\uff1a\u80fd\u91cf\u53d8\u5316\u5f71\u54cd\u8282\u5f8b\uff08\u5982\u6e29\u5ea6\u5f71\u54cd\u632f\u52a8\u9891\u7387\uff09<\/li>\n<\/ul>\n<\/li>\n<li>$g_{omega C}$\uff1a\u8282\u5f8b\u6d41\u52a8\u4e0e\u7ed3\u6784\u6d41\u52a8\u7684\u8026\u5408\n<ul>\n<li>\u9ad8\u503c\uff1a\u8282\u5f8b\u53d8\u5316\u5f71\u54cd\u7ed3\u6784\uff08\u5982\u632f\u52a8\u5f71\u54cd\u6676\u4f53\u751f\u957f\uff09<\/li>\n<\/ul>\n<\/li>\n<li>$g_{CS}$\uff1a\u7ed3\u6784\u6d41\u52a8\u4e0e\u80fd\u91cf\u6d41\u52a8\u7684\u8026\u5408\n<ul>\n<li>\u9ad8\u503c\uff1a\u7ed3\u6784\u53d8\u5316\u5f71\u54cd\u80fd\u91cf\uff08\u5982\u76f8\u53d8\u91ca\u653e\u6f5c\u70ed\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h5>3.3.4 \u51e0\u4f55\u4f18\u5316\u9879<\/h5>\n<p>$$mathcal{L}<em>{text{geo}} = lambda<\/em>{text{hex}} cdot text{Tr}[Psi<em>C^dagger hat{O}<\/em>{text{hex}} Psi_C] &#8211; frac{g^2}{2} sum_i frac{n_i(n_i-1)}{ell_i^2} |Psi_C|^2$$<\/p>\n<p>\u5176\u4e2d$hat{O}_{text{hex}}$\u4e3a\u516d\u8fb9\u5f62\u5e8f\u53c2\u91cf\u7b97\u7b26\u3002<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u7b2c\u4e00\u9879\uff1a\u4fc3\u8fdb\u516d\u8fb9\u5f62\u5bf9\u79f0\u6027<\/li>\n<li>\u7b2c\u4e8c\u9879\uff1a\u60e9\u7f5a\u9ad8\u66f2\u7387\u7ed3\u6784<\/li>\n<\/ul>\n<h4>3.4 \u70ed\u5bb9\u3001\u79e9\u5e8f\u5ea6\u4e0e\u76f8\u5e72\u5ea6\u7684\u7b49\u4ef7\u6027<\/h4>\n<h5>3.4.1 \u6838\u5fc3\u5b9a\u7406<\/h5>\n<p>\u5728IGT\u7684\u672c\u4f53\u8bba\u4e2d\uff0c\u70ed\u5bb9\u3001\u79e9\u5e8f\u5ea6\u3001\u76f8\u5e72\u5ea6\u4e09\u8005\u5b8c\u5168\u7b49\u4ef7\u3002<\/p>\n<h5>3.4.2 \u6570\u5b66\u8bc1\u660e<\/h5>\n<p>\u70ed\u5bb9\u5728\u7269\u7406\u4e0a\u662f\uff1a<\/p>\n<p>$$C_V = Tfrac{partial S}{partial T}$$<\/p>\n<p>\u800c\u5728IGT\u7684\u7ed3\u6784\u52a8\u529b\u5b66\u4e2d\uff0c\u76f8\u5e72\u5ea6$(C)$\u4e0e\u7ed3\u6784\u71b5$(S)$\u7684\u5173\u7cfb\u662f\uff1a<\/p>\n<p>$$S_{text{struct}} = S_0 &#8211; k ln C$$<\/p>\n<p>\u628a\u8fd9\u4e24\u4e2a\u653e\u5728\u4e00\u8d77\uff0c\u53ef\u4ee5\u53d1\u73b0\uff1a<\/p>\n<p>$$C<em>V^{text{struct}} = Tfrac{partial S<\/em>{text{struct}}}{partial T} = k T frac{1}{C}frac{partial C}{partial T}$$<\/p>\n<p>\u4e5f\u5c31\u662f\u8bf4\uff1a<\/p>\n<p>$$C_V propto -frac{1}{C}frac{partial C}{partial T}$$<\/p>\n<p>\u800c\u8fd9\u4e2a\u91cf\u7684\u7269\u7406\u610f\u4e49\u662f\uff1a<\/p>\n<blockquote><p><strong>\u6e29\u5ea6\u6da8\u843d\u5bf9\u76f8\u5e72\u5ea6\u7684\u7834\u574f\u963b\u5c3c\u5f3a\u5ea6 = \u70ed\u5bb9\u3002<\/strong><\/p><\/blockquote>\n<p>\u6362\u53e5\u8bdd\u8bf4\uff1a<\/p>\n<h3><strong>\u70ed\u5bb9\u5c31\u662f\u76f8\u5e72\u5ea6\u7684&#8221;\u6e29\u5ea6\u54cd\u5e94\u963b\u5c3c&#8221;\u3002<\/strong><\/h3>\n<p>\u56e0\u6b64\uff1a<\/p>\n<p>$$C_V leftrightarrow C leftrightarrow text{\u79e9\u5e8f\u5ea6}$$<\/p>\n<p>\u4e09\u8005\u662f\u540c\u4e00\u4e2a\u5e95\u5c42\u5bf9\u8c61\uff0c\u4ece\u4e0d\u540c\u89d2\u5ea6\u770b\u5230\u7684\u6295\u5f71\u3002<\/p>\n<h5>3.4.3 \u7269\u7406\u56fe\u50cf<\/h5>\n<ul>\n<li><strong>\u76f8\u5e72\u5ea6\uff08coherence\uff09<\/strong>\uff1a\u9891\u7387\u9501\u5b9a\u7a0b\u5ea6\uff0c\u6ce2\u7684\u89c6\u89d2<\/li>\n<li><strong>\u79e9\u5e8f\u5ea6\uff08order\uff09<\/strong>\uff1a\u7ed3\u6784\u5316\u7a0b\u5ea6\uff0c\u7ed3\u6784\/\u76f8\u573a\u7684\u89c6\u89d2<\/li>\n<li><strong>\u70ed\u5bb9\uff08heat capacity\uff09<\/strong>\uff1a\u7ed3\u6784\u80fd\u627f\u53d7\u6270\u52a8\u7684\u80fd\u529b\uff0c\u70ed\u529b\u5b66\u89c6\u89d2<\/li>\n<\/ul>\n<p>\u5b83\u4eec\u662f\uff1a<\/p>\n<blockquote><p><strong>\u6ce2 \u2192 \u7ed3\u6784 \u2192 \u80fd\u91cf<\/strong><br \/>\n\u7684\u4e09\u79cd\u5448\u73b0\u5f62\u5f0f\u3002<\/p><\/blockquote>\n<p>\u4f46\u6e90\u5934\u662f\u540c\u4e00\u4e2a\u73b0\u8c61\uff1a<\/p>\n<p><strong>\u9891\u7387\u9501\u76f8\u5e26\u6765\u7684\u7a33\u5b9a\u81ea\u65cb\u7ed3\u6784\u4f53<\/strong><\/p>\n<h5>3.4.4 \u8de8\u5c3a\u5ea6\u9a8c\u8bc1<\/h5>\n<ul>\n<li><strong>\u7269\u8d28<\/strong>\uff1a\u6676\u4f53\u7684\u6bd4\u70ed\u968f\u7ed3\u6784\u79e9\u5e8f\u5ea6\u800c\u53d8\uff08\u4f4e\u6e29Debye T\u00b3\u4f9d\u8d56\uff09\uff0c\u76f8\u5e72\u5ea6\u9ad8\u2192$C_V$\u5e73\u6ed1\u4e0a\u5347<\/li>\n<li><strong>\u751f\u7269<\/strong>\uff1a\u4ee3\u8c22\u70ed\u5bb9\u968f\u5668\u5b98\u540c\u6b65\u6027\uff08\u76f8\u5e72\u5ea6\uff09\u4e0a\u5347\uff0c\u5fc3\u810f\u3001\u809d\u810f\u6700\u5178\u578b<\/li>\n<li><strong>\u5fc3\u667a<\/strong>\uff1a\u5fc3\u7406\u5f39\u6027\uff08heat capacity\uff09\u4e0e\u795e\u7ecf\u76f8\u5e72\u5ea6EEG-coherence\u5b8c\u5168\u76f8\u5173\uff0c\u9ad8\u76f8\u5e72\u2192\u9ad8\u71b5\u5bb9\u91cf\u2192\u9ad8\u5fc3\u7406\u70ed\u5bb9<\/li>\n<li><strong>\u7ec4\u7ec7<\/strong>\uff1a\u7ec4\u7ec7\u97e7\u6027\uff08\u53d8\u9769\u70ed\u5bb9\uff09\u4e0e&#8221;\u6587\u5316\u76f8\u5e72\u5ea6&#8221;\u5f3a\u76f8\u5173\uff0c\u65e0\u76f8\u5e72\u2192\u65e0\u70ed\u5bb9\uff08\u7ec4\u7ec7\u7834\u88c2\uff09<\/li>\n<li><strong>\u6587\u660e<\/strong>\uff1a\u5168\u7403\u7cfb\u7edf\u7684&#8221;\u70ed\u5bb9&#8221;\u4e0e\u5168\u7403\u8026\u5408\u9891\u7387\uff08\u957f\u671f\u8d8b\u52bf\u5468\u671f\uff09\u76f8\u5173<\/li>\n<\/ul>\n<p><strong>\u8de8\u5c3a\u5ea6\u5b8c\u5168\u4e00\u81f4\u3002<\/strong><\/p>\n<h5>3.4.5 \u6700\u7ec8\u516c\u7406<\/h5>\n<h2><strong>\u516c\u74060\uff08\u7edf\u4e00\u5f62\u5f0f\uff09\uff1a\u70ed\u5bb9 = \u79e9\u5e8f\u5ea6 = \u76f8\u5e72\u5ea6<\/strong><\/h2>\n<p><strong>\u70ed\u5bb9\u4e0d\u662f\u57fa\u672c\u5c5e\u6027\uff0c\u800c\u662f\u7cfb\u7edf\u5728\u9891\u7387\u9501\u76f8\u540e\u5f62\u6210\u7684\u7a33\u5b9a\u81ea\u65cb\u7ed3\u6784\u4f53\u7684\u6d8c\u73b0\u91cf\u3002<\/strong><\/p>\n<p>\u5b83\u540c\u65f6\u5ea6\u91cf\uff1a<\/p>\n<ol>\n<li><strong>\u7ed3\u6784\u5438\u6536\u6e29\u5ea6\u53d8\u5316\u7684\u80fd\u91cf\u6210\u672c\uff08\u80fd\u91cf\u89c6\u89d2\uff09<\/strong><\/li>\n<li><strong>\u7ed3\u6784\u5bb9\u7eb3\u71b5\u589e\u800c\u4e0d\u5d29\u6e83\u7684\u5bb9\u91cf\uff08\u71b5\u89c6\u89d2\uff09<\/strong><\/li>\n<li><strong>\u9891\u7387\u540c\u6b65\u7684\u7a33\u5b9a\u5ea6\uff08\u76f8\u5e72\u89c6\u89d2\uff09<\/strong><\/li>\n<\/ol>\n<p>\u56e0\u6b64\uff1a<\/p>\n<p>$$C<em>V propto C<\/em>{text{coherence}} propto O_{text{order}}$$<\/p>\n<p>\u4e09\u8005\u5b8c\u5168\u7b49\u4ef7\uff0c\u53ea\u662f\u4e0d\u540c\u63cf\u8ff0\u65b9\u5f0f\u3002<\/p>\n<hr \/>\n<h3>\u7b2c4\u7ae0 \u4e09\u7ef4\u60ef\u6027\u2014\u2014\u6d41\u52a8\u7684&#8221;\u52a8\u91cf&#8221;\u6d4b\u91cf<\/h3>\n<h4>4.1 \u7edf\u4e00\u5b9a\u4e49\u539f\u5219<\/h4>\n<p>\u60ef\u6027\u6cdb\u51fd\u662f\u7cfb\u7edf\u5bf9\u65f6\u95f4\u53d8\u5316\u7684&#8221;\u963b\u529b&#8221;\uff0c\u5b9a\u4e49\u4e3a\u6709\u6548\u4f5c\u7528\u91cf\u5bf9\u65f6\u95f4\u5bfc\u6570\u7684\u4e8c\u9636\u53d8\u5206\uff1a<\/p>\n<p>$$mathcal{I}<em>X[Psi] = left. frac{delta^2 S<\/em>{text{eff}}[Psi]}{delta (partial_t Psi<em>X)^2} right|<\/em>{text{on-shell}}$$<\/p>\n<p><strong>\u6d41\u52a8\u9690\u55bb<\/strong>\uff1a<\/p>\n<ul>\n<li>\u60ef\u6027\u8d8a\u5927\uff0c\u6d41\u52a8\u7684&#8221;\u8bb0\u5fc6&#8221;\u8d8a\u5f3a<\/li>\n<li>\u60ef\u6027\u8d8a\u5927\uff0c\u6d41\u52a8\u8d8a\u96be\u88ab\u73af\u5883\u566a\u58f0\u6539\u53d8<\/li>\n<li>\u60ef\u6027\u8d8a\u5927\uff0c\u6d41\u52a8\u7684&#8221;\u8eab\u4efd&#8221;\u8d8a\u7a33\u5b9a<\/li>\n<\/ul>\n<h4>4.2 \u71b5\u60ef\u6027\uff08$I_S$\uff09\uff1a\u62b5\u6297\u80fd\u91cf\u6d41\u52a8\u6563\u9038\u7684\u80fd\u529b<\/h4>\n<h5>4.2.1 \u6570\u5b66\u5b9a\u4e49<\/h5>\n<p>$$I_S[Psi_S] = int d^3r , left| frac{delta ln |Psi_S|^2}{delta T} right|^2 cdot tau_S(mathbf{r})$$<\/p>\n<h5>4.2.2 \u7269\u7406\u610f\u4e49<\/h5>\n<ul>\n<li><strong>\u62b5\u6297\u80fd\u91cf\u5206\u5e03\u5747\u5300\u5316\u7684\u80fd\u529b<\/strong><\/li>\n<li>\u7cfb\u7edf\u4fdd\u6301\u80fd\u91cf\u6d41\u52a8\u6a21\u5f0f\u4e0d\u53d8\u7684\u80fd\u529b<\/li>\n<li>\u80fd\u91cf\u6d41\u52a8\u7684&#8221;\u8bb0\u5fc6\u5f3a\u5ea6&#8221;<\/li>\n<\/ul>\n<h5>4.2.3 \u5bf9\u5e94\u89c2\u6d4b\u91cf<\/h5>\n<p>\u70ed\u5bb9$C_V propto int I_S[Psi_S] d^3r$<\/p>\n<h5>4.2.4 \u53d6\u503c\u8303\u56f4<\/h5>\n<ul>\n<li>[0,1]\u5f52\u4e00\u5316\u503c<\/li>\n<li>\u8d85\u5bfc\u4f53\u22480.85-0.95\uff08\u80fd\u91cf\u6d41\u52a8\u9ad8\u5ea6\u6709\u5e8f\uff09<\/li>\n<li>\u5e38\u6e29\u91d1\u5c5e\u22480.4-0.6\uff08\u80fd\u91cf\u6d41\u52a8\u4e2d\u7b49\u6709\u5e8f\uff09<\/li>\n<li>\u7edd\u7f18\u4f53\u22480.1-0.3\uff08\u80fd\u91cf\u6d41\u52a8\u4f4e\u5e8f\uff09<\/li>\n<\/ul>\n<h5>4.2.5 \u6d4b\u91cf\u65b9\u6cd5<\/h5>\n<p>\u901a\u8fc7\u6bd4\u70ed\u6d4b\u91cf\u4e0e\u6e29\u5ea6\u6270\u52a8\u5b9e\u9a8c\uff1a<\/p>\n<ol>\n<li>\u6d4b\u91cf\u7cfb\u7edf\u5728\u4e0d\u540c\u6e29\u5ea6\u4e0b\u7684\u70ed\u5bb9$C_V(T)$<\/li>\n<li>\u65bd\u52a0\u6e29\u5ea6\u6270\u52a8$Delta T$<\/li>\n<li>\u6d4b\u91cf\u7cfb\u7edf\u6062\u590d\u65f6\u95f4$tau$<\/li>\n<li>\u8ba1\u7b97$I_S = int C_V(T) dT \/ tau$<\/li>\n<\/ol>\n<h4>4.3 \u9891\u7387\u60ef\u6027\uff08$I_omega$\uff09\uff1a\u62b5\u6297\u8282\u5f8b\u6d41\u52a8\u5931\u771f\u7684\u80fd\u529b<\/h4>\n<h5>4.3.1 \u6570\u5b66\u5b9a\u4e49<\/h5>\n<p>$$I<em>omega[Psi<\/em>omega] = frac{1}{V} int d^3r , left( frac{partial phi<em>omega}{partial t} right)^{-2} cdot left| frac{delta phi<\/em>omega}{delta omega} right|^2$$<\/p>\n<h5>4.3.2 \u7269\u7406\u610f\u4e49<\/h5>\n<ul>\n<li><strong>\u62b5\u6297\u8282\u5f8b\u6a21\u5f0f\u5931\u771f\u7684\u80fd\u529b<\/strong><\/li>\n<li>\u7cfb\u7edf\u4fdd\u6301\u8282\u5f8b\u6d41\u52a8\u6a21\u5f0f\u4e0d\u53d8\u7684\u80fd\u529b<\/li>\n<li>\u8282\u5f8b\u6d41\u52a8\u7684&#8221;\u8bb0\u5fc6\u5f3a\u5ea6&#8221;<\/li>\n<\/ul>\n<h5>4.3.3 \u5bf9\u5e94\u89c2\u6d4b\u91cf<\/h5>\n<p>\u54c1\u8d28\u56e0\u6570$Q = omega<em>0\/Deltaomega propto I<\/em>omega$<\/p>\n<h5>4.3.4 \u53d6\u503c\u8303\u56f4<\/h5>\n<ul>\n<li>[0,1]\u5f52\u4e00\u5316\u503c<\/li>\n<li>\u8109\u51b2\u661f\u22480.999999\uff08\u8282\u5f8b\u6781\u5ea6\u7a33\u5b9a\uff09<\/li>\n<li>\u77f3\u82f1\u632f\u8361\u5668\u22480.95\uff08\u8282\u5f8b\u9ad8\u5ea6\u7a33\u5b9a\uff09<\/li>\n<li>\u673a\u68b0\u949f\u6446\u22480.7\uff08\u8282\u5f8b\u4e2d\u7b49\u7a33\u5b9a\uff09<\/li>\n<\/ul>\n<h5>4.3.5 \u6d4b\u91cf\u65b9\u6cd5<\/h5>\n<p>\u901a\u8fc7\u54c1\u8d28\u56e0\u6570\u6d4b\u91cf\uff1a<\/p>\n<ol>\n<li>\u6d4b\u91cf\u7cfb\u7edf\u7684\u5171\u632f\u9891\u7387$omega_0$<\/li>\n<li>\u6d4b\u91cf\u9891\u7387\u54cd\u5e94\u7684\u534a\u9ad8\u5bbd$Deltaomega$<\/li>\n<li>\u8ba1\u7b97$Q = omega_0\/Deltaomega$<\/li>\n<li>\u5f52\u4e00\u5316\uff1a$I_omega = Q \/ (1 + Q)$<\/li>\n<\/ol>\n<h4>4.4 \u76f8\u5e72\u60ef\u6027\uff08$I_C$\uff09\uff1a\u62b5\u6297\u7ed3\u6784\u6d41\u52a8\u89e3\u4f53\u7684\u80fd\u529b<\/h4>\n<h5>4.4.1 \u6570\u5b66\u5b9a\u4e49<\/h5>\n<p>$$I_C[Psi_C] = left| int Psi_C(mathbf{r}) d^3r right|^2 cdot left( frac{xi[Psi<em>C]}{L} right) cdot kappa(G<\/em>{text{shape}}[Psi_C])$$<\/p>\n<h5>4.4.2 \u7269\u7406\u610f\u4e49<\/h5>\n<ul>\n<li><strong>\u62b5\u6297\u540c\u6b65\u534f\u8c03\u89e3\u4f53\u7684\u80fd\u529b<\/strong><\/li>\n<li>\u7cfb\u7edf\u4fdd\u6301\u7ed3\u6784\u6d41\u52a8\u6a21\u5f0f\u4e0d\u53d8\u7684\u80fd\u529b<\/li>\n<li>\u7ed3\u6784\u6d41\u52a8\u7684&#8221;\u8bb0\u5fc6\u5f3a\u5ea6&#8221;<\/li>\n<\/ul>\n<h5>4.4.3 \u5bf9\u5e94\u89c2\u6d4b\u91cf<\/h5>\n<p>\u76f8\u5e72\u5ea6$C = |langle Psi_C rangle| \/ sqrt{langle |Psi_C|^2 rangle}$<\/p>\n<h5>4.4.4 \u53d6\u503c\u8303\u56f4<\/h5>\n<ul>\n<li>[0,1]\u5f52\u4e00\u5316\u503c<\/li>\n<li>\u8d85\u6d41\u6c26\u22480.98\uff08\u7ed3\u6784\u6781\u5ea6\u76f8\u5e72\uff09<\/li>\n<li>\u6676\u4f53\u22480.85-0.95\uff08\u7ed3\u6784\u9ad8\u5ea6\u76f8\u5e72\uff09<\/li>\n<li>\u6db2\u4f53\u22480.3-0.5\uff08\u7ed3\u6784\u4e2d\u7b49\u76f8\u5e72\uff09<\/li>\n<\/ul>\n<h5>4.4.5 \u6d4b\u91cf\u65b9\u6cd5<\/h5>\n<p>\u901a\u8fc7\u573a\u76f8\u5e72\u5ea6\u6d4b\u91cf\uff1a<\/p>\n<ol>\n<li>\u6d4b\u91cf\u573a\u7684\u7a7a\u95f4\u5e73\u5747\u503c$|langle Psi_C rangle|$<\/li>\n<li>\u6d4b\u91cf\u573a\u7684\u5747\u65b9\u6839\u503c$sqrt{langle |Psi_C|^2 rangle}$<\/li>\n<li>\u8ba1\u7b97$C = |langle Psi_C rangle|^2 \/ langle |Psi_C|^2 rangle$<\/li>\n<li>\u5f52\u4e00\u5316\uff1a$I_C = C$<\/li>\n<\/ol>\n<h4>4.5 \u60ef\u6027\u5b88\u6052\u5b9a\u7406\uff08\u57fa\u4e8e\u8bfa\u7279\u5b9a\u7406\uff09<\/h4>\n<h5>4.5.1 \u5b9a\u74064.1\uff08\u4e09\u7ef4\u60ef\u6027\u5b88\u6052\uff09<\/h5>\n<p>\u5b64\u7acb\u7cfb\u7edf\u4e2d\uff0c\u4e09\u7ef4\u60ef\u6027\u603b\u91cf\u5b88\u6052\uff1a<\/p>\n<p>$$frac{d}{dt}(I<em>S + I<\/em>omega + I_C) = 0$$<\/p>\n<h5>4.5.2 \u8bc1\u660e\u6838\u5fc3<\/h5>\n<ol>\n<li>\u62c9\u683c\u6717\u65e5\u91cf\u65f6\u95f4\u5e73\u79fb\u4e0d\u53d8\u6027\uff1a$delta mathcal{L}\/delta t = 0$\u3002<\/li>\n<li>\u5e94\u7528\u8bfa\u7279\u5b9a\u7406\u5f97\u5b88\u6052\u6d41$J^mu$\uff0c\u5b88\u6052\u8377$Q propto I<em>S + I<\/em>omega + I_C$\u3002<\/li>\n<li>\u7531$frac{dQ}{dt} = 0$\u63a8\u51fa\u60ef\u6027\u603b\u91cf\u5b88\u6052\u3002<\/li>\n<\/ol>\n<h5>4.5.3 \u5b8c\u6574\u8bc1\u660e<\/h5>\n<p>$$frac{d}{dt}(I<em>S + I<\/em>omega + I_C) = int d^3r left[ frac{partial}{partial t} left( frac{1}{2} sum_X |Psi_X|^2 right) &#8211; nabla cdot mathbf{J} right] = 0$$<\/p>\n<p>\u5176\u4e2d$mathbf{J}$\u4e3a\u80fd\u91cf\u6d41\u77e2\u91cf\u3002<\/p>\n<h5>4.5.4 \u63a8\u8bba<\/h5>\n<p><strong>1. \u975e\u5b64\u7acb\u7cfb\u7edf<\/strong>\uff1a<\/p>\n<p>$$frac{d}{dt}(I<em>S + I<\/em>omega + I<em>C) = P<\/em>{text{external}}$$<\/p>\n<p>$P_{text{external}}$\u4e3a\u5916\u754c\u8f93\u5165\u529f\u7387\u3002<\/p>\n<p><strong>2. \u60ef\u6027\u53ef\u8f6c\u79fb\u6027<\/strong>\uff1a<\/p>\n<p>$$Delta I<em>S + Delta I<\/em>omega + Delta I_C = 0$$<\/p>\n<p>\u4e09\u79cd\u60ef\u6027\u53ef\u76f8\u4e92\u8f6c\u5316\uff0c\u603b\u91cf\u5b88\u6052\u3002<\/p>\n<p><strong>3. \u60ef\u6027\u8f6c\u79fb\u6548\u7387<\/strong>\uff1a<\/p>\n<p>$$eta<em>{text{transfer}} = 1 &#8211; frac{sum<\/em>{ineq j} alpha_{ij}}{3} quad (text{\u7406\u60f3\u51e0\u4f55\u4e0b} eta approx 0.95)$$<\/p>\n<h4>4.6 \u60ef\u6027\u5f20\u91cf\u53ca\u5176\u4e0e\u51e0\u4f55\u7684\u8026\u5408\u5173\u7cfb<\/h4>\n<h5>4.6.1 \u5b9a\u74064.2\uff08\u60ef\u6027-\u51e0\u4f55\u8026\u5408\uff09<\/h5>\n<p>\u60ef\u6027\u5f20\u91cf\u8868\u793a\u4e3a\uff1a<\/p>\n<p>$$<br \/>\nmathcal{I}_{text{total}} =<br \/>\nbegin{bmatrix}<br \/>\nI<em>S &amp; 0 &amp; 0<br \/>\n0 &amp; I<\/em>omega &amp; 0<br \/>\n0 &amp; 0 &amp; I<em>C<br \/>\nend{bmatrix}<br \/>\ncdot<br \/>\nbegin{bmatrix}<br \/>\n1 &amp; alpha<\/em>{Somega} &amp; alpha<em>{SC}<br \/>\nalpha<\/em>{omega S} &amp; 1 &amp; alpha<em>{omega C}<br \/>\nalpha<\/em>{CS} &amp; alpha_{Comega} &amp; 1<br \/>\nend{bmatrix}<br \/>\n$$<\/p>\n<p>\u5176\u4e2d\u8026\u5408\u7cfb\u6570$alpha<em>{ij} = f(kappa, g) = kappa cdot (1 + g^2 \/ p<\/em>{text{min}})$\uff0c$kappa$\u4e3a\u51e0\u4f55\u56e0\u5b50\u3002<\/p>\n<h5>4.6.2 \u7269\u7406\u610f\u4e49<\/h5>\n<ul>\n<li><strong>\u5bf9\u89d2\u5143<\/strong>\uff1a\u5404\u7ef4\u5ea6\u72ec\u7acb\u60ef\u6027<\/li>\n<li><strong>\u975e\u5bf9\u89d2\u5143<\/strong>\uff1a\u7ef4\u5ea6\u95f4\u8026\u5408\u5f3a\u5ea6\uff0c\u51e0\u4f55\u4f18\u5316\u53ef\u6700\u5c0f\u5316$alpha_{ij}$<\/li>\n<li><strong>\u8026\u5408\u673a\u5236<\/strong>\uff1a\u901a\u8fc7\u573a\u95f4\u76f8\u4e92\u4f5c\u7528\u9879$g_{ij}$\u5b9e\u73b0\u80fd\u91cf\u4ea4\u6362<\/li>\n<\/ul>\n<h5>4.6.3 \u51e0\u4f55\u4f18\u5316\u6700\u5c0f\u5316\u60ef\u6027\u8017\u6563<\/h5>\n<p><strong>\u5b9a\u74064.3\uff08\u51e0\u4f55\u6700\u4f18\u4e0e\u60ef\u6027\uff09<\/strong>\uff1a<\/p>\n<p>\u516d\u8fb9\u5f62\u7ed3\u6784\u6700\u5c0f\u5316\u60ef\u6027\u8017\u6563\uff1a<\/p>\n<p>$$alpha<em>{ij}^{text{hex}} = min<\/em>{text{geometry}} alpha_{ij}$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u516d\u8fb9\u5f62\u7ed3\u6784\u4f7f\u4e09\u4e2a\u60ef\u6027\u7ef4\u5ea6\u95f4\u8026\u5408\u6700\u5f31<\/li>\n<li>\u60ef\u6027\u8f6c\u79fb\u6548\u7387\u6700\u9ad8<\/li>\n<li>\u7cfb\u7edf\u6700\u7a33\u5b9a<\/li>\n<\/ul>\n<h4>4.7 \u60ef\u6027\u8c03\u63a7\u80fd\u529b\u6cdb\u51fd<\/h4>\n<h5>4.7.1 \u6838\u5fc3\u5b9a\u4e49<\/h5>\n<p>\u8fdb\u5316\u7b49\u7ea7 = \u7cfb\u7edf\u5bf9<strong>\u4e09\u7ef4\u60ef\u6027<\/strong>\u7684\u4e3b\u52a8\u8c03\u63a7\u80fd\u529b<\/p>\n<h5>4.7.2 \u6570\u5b66\u8868\u8fbe<\/h5>\n<p>$$text{Evolution Level} = mathcal{E}[I<em>S, I<\/em>omega, I<em>C] = sum<\/em>{X} alpha_X cdot frac{partial I<em>X}{partial t<\/em>{text{control}}}$$<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$alpha_X$\uff1a\u5404\u7ef4\u5ea6\u6743\u91cd\uff08\u53ef\u4f18\u5316\uff09<\/li>\n<li>$t_{text{control}}$\uff1a\u63a7\u5236\u54cd\u5e94\u65f6\u95f4<\/li>\n<\/ul>\n<h5>4.7.3 \u7269\u7406\u610f\u4e49<\/h5>\n<ul>\n<li>\u7cfb\u7edf\u80fd\u4e3b\u52a8\u6539\u53d8\u81ea\u8eab\u60ef\u6027\u7684\u80fd\u529b<\/li>\n<li>\u7cfb\u7edf\u5bf9\u73af\u5883\u53d8\u5316\u7684\u9002\u5e94\u6027<\/li>\n<li>\u7cfb\u7edf\u7684&#8221;\u8fdb\u5316\u7b49\u7ea7&#8221;\u5ea6\u91cf<\/li>\n<\/ul>\n<hr \/>\n<h2>\u7b2c\u4e09\u5377\uff1a\u6d41\u52a8\u7684\u53e5\u6cd5\u2014\u2014RVSE\u6f14\u5316\u5e8f\u5217<\/h2>\n<h3>\u7b2c5\u7ae0 RVSE\u4f5c\u4e3a\u6d41\u52a8\u7684\u57fa\u672c\u53e5\u5f0f<\/h3>\n<h4>5.1 \u6d41\u52a8\u7684\u8bed\u6cd5\u89c4\u5219<\/h4>\n<p>\u65e2\u7136\u53ea\u80fd\u611f\u77e5\u6d41\u52a8\uff0c\u90a3\u4e48\u552f\u4e00\u7684\u79d1\u5b66\u5c31\u662f<strong>\u7834\u8bd1\u6d41\u52a8\u7684\u8bed\u6cd5<\/strong>\uff1a<\/p>\n<pre><code>\u8bed\u6cd5\u89c4\u5219\uff1a\u6d41\u52a8 = \u5faa\u73af\u5d4c\u5957\u7684RVSE<\/code><\/pre>\n<p><strong>\u8fd9\u4e0d\u662f&#8221;\u6f14\u5316\u9636\u6bb5&#8221;\uff0c\u800c\u662f&#8221;\u6d41\u52a8\u7684\u57fa\u672c\u53e5\u5f0f&#8221;<\/strong>\u3002\u5c31\u50cf\u8bed\u8a00\u53ea\u6709\u4e3b\u8c13\u5bbe\u5b9a\u72b6\u8865\uff0c\u5b87\u5b99\u4e5f\u53ea\u6709RVSE\u8fd9\u516d\u4e2a&#8221;\u8bcd\u6027&#8221;\u3002<\/p>\n<h4>5.2 \u03a9\uff08\u6fc0\u53d1\uff09\uff1a\u6d41\u52a8\u9047\u5230\u969c\u788d\uff0c\u79ef\u84c4\u52bf\u80fd<\/h4>\n<h5>5.2.1 \u7269\u7406\u56fe\u50cf<\/h5>\n<p>\u5c31\u50cf\u6cb3\u6d41\u9047\u5230\u5927\u575d\uff0c\u6c34\u6d41\u88ab\u963b\u6321\uff0c\u6c34\u4f4d\u4e0a\u5347\uff0c\u52bf\u80fd\u79ef\u84c4\uff1a<\/p>\n<ul>\n<li><strong>\u80fd\u91cf\u8f93\u5165<\/strong>\uff1a\u5916\u90e8\u80fd\u91cf\u5f00\u59cb\u6d41\u5165\u7cfb\u7edf<\/li>\n<li><strong>\u52bf\u80fd\u79ef\u7d2f<\/strong>\uff1a\u80fd\u91cf\u4ee5\u52bf\u80fd\u5f62\u5f0f\u50a8\u5b58<\/li>\n<li><strong>\u4e34\u754c\u63a5\u8fd1<\/strong>\uff1a\u7cfb\u7edf\u63a5\u8fd1\u76f8\u53d8\u9608\u503c<\/li>\n<\/ul>\n<h5>5.2.2 \u573a\u8bba\u7279\u5f81<\/h5>\n<p><strong>\u4e3b\u5bfc\u573a<\/strong>\uff1a$Psi_S$\uff08\u70ed\u573a\uff09\u6fc0\u53d1<\/p>\n<p><strong>\u573a\u65b9\u7a0b\u89e3\u7c7b\u578b<\/strong>\uff1a\u4e34\u754c\u6da8\u843d\u89e3<\/p>\n<p><strong>\u5e8f\u53c2\u91cf<\/strong>\uff1a$nabla T neq 0$\uff08\u6e29\u5ea6\u68af\u5ea6\u975e\u96f6\uff09<\/p>\n<p><strong>\u5bf9\u79f0\u6027<\/strong>\uff1a\u7834\u5e73\u79fb\u5bf9\u79f0\u6027<\/p>\n<p><strong>\u65f6\u95f4\u5c3a\u5ea6<\/strong>\uff1a$tau_S$\uff08\u70ed\u65f6\u95f4\u5c3a\u5ea6\uff09<\/p>\n<h5>5.2.3 \u6d41\u52a8\u7279\u5f81<\/h5>\n<ul>\n<li><strong>\u80fd\u91cf\u5bc6\u5ea6<\/strong>\uff1a$varepsilon$\u5f00\u59cb\u4e0a\u5347<\/li>\n<li><strong>\u71b5\u4ea7\u751f\u7387<\/strong>\uff1a$dot{S}$\u589e\u52a0<\/li>\n<li><strong>\u4e34\u754c\u6da8\u843d<\/strong>\uff1a$langle (delta Psi)^2 rangle$\u589e\u5927<\/li>\n<li><strong>\u5173\u8054\u957f\u5ea6<\/strong>\uff1a$xi$\u5f00\u59cb\u589e\u957f<\/li>\n<\/ul>\n<h5>5.2.4 \u5b9e\u4f8b<\/h5>\n<ul>\n<li><strong>\u6052\u661f\u5f62\u6210<\/strong>\uff1a\u5206\u5b50\u4e91\u574d\u7f29\uff0c\u5f15\u529b\u52bf\u80fd\u79ef\u7d2f<\/li>\n<li><strong>\u76f8\u53d8\u524d\u5146<\/strong>\uff1a\u52a0\u70ed\u6db2\u4f53\uff0c\u63a5\u8fd1\u6cb8\u70b9<\/li>\n<li><strong>\u521b\u65b0\u840c\u82bd<\/strong>\uff1a\u65b0\u60f3\u6cd5\u5f00\u59cb\u915d\u917f<\/li>\n<\/ul>\n<h4>5.3 R\uff08\u6269\u5f20\uff09\uff1a\u80fd\u91cf\u627e\u5230\u7a81\u7834\u53e3\uff0c\u52a0\u901f\u6d41\u52a8<\/h4>\n<h5>5.3.1 \u7269\u7406\u56fe\u50cf<\/h5>\n<p>\u5c31\u50cf\u5927\u575d\u51b3\u5824\uff0c\u79ef\u84c4\u7684\u6c34\u6d41\u7a81\u7136\u7206\u53d1\uff0c\u52a0\u901f\u6d41\u52a8\uff1a<\/p>\n<ul>\n<li><strong>\u52bf\u80fd\u91ca\u653e<\/strong>\uff1a\u79ef\u84c4\u7684\u52bf\u80fd\u8f6c\u5316\u4e3a\u52a8\u80fd<\/li>\n<li><strong>\u52a0\u901f\u6d41\u52a8<\/strong>\uff1a\u6d41\u52a8\u901f\u5ea6\u6025\u5267\u589e\u52a0<\/li>\n<li><strong>\u7a7a\u95f4\u6269\u5f20<\/strong>\uff1a\u6d41\u52a8\u8303\u56f4\u6269\u5927<\/li>\n<\/ul>\n<h5>5.3.2 \u573a\u8bba\u7279\u5f81<\/h5>\n<p><strong>\u4e3b\u5bfc\u573a<\/strong>\uff1a$Psi_omega$\uff08\u52a8\u573a\uff09\u589e\u957f<\/p>\n<p><strong>\u573a\u65b9\u7a0b\u89e3\u7c7b\u578b<\/strong>\uff1a\u5747\u5300\u8c03\u548c\u89e3<\/p>\n<p><strong>\u5e8f\u53c2\u91cf<\/strong>\uff1a$langle Psi_omega rangle neq 0$\uff08\u52a8\u573a\u5e8f\u53c2\u91cf\u975e\u96f6\uff09<\/p>\n<p><strong>\u5bf9\u79f0\u6027<\/strong>\uff1a\u7834\u89c4\u8303\u5bf9\u79f0\u6027<\/p>\n<p><strong>\u65f6\u95f4\u5c3a\u5ea6<\/strong>\uff1a$tau_omega$\uff08\u52a8\u65f6\u95f4\u5c3a\u5ea6\uff09<\/p>\n<h5>5.3.3 \u6d41\u52a8\u7279\u5f81<\/h5>\n<ul>\n<li><strong>\u6d41\u52a8\u901f\u5ea6<\/strong>\uff1a$v$\u6025\u5267\u589e\u52a0<\/li>\n<li><strong>\u80fd\u91cf\u8017\u6563<\/strong>\uff1a$dot{E}$\u8fbe\u5230\u5cf0\u503c<\/li>\n<li><strong>\u8282\u5f8b\u5efa\u7acb<\/strong>\uff1a$omega_0$\u5f00\u59cb\u5f62\u6210<\/li>\n<li><strong>\u6a21\u5f0f\u9009\u62e9<\/strong>\uff1a\u4e3b\u5bfc\u6a21\u5f0f\u5f00\u59cb\u51fa\u73b0<\/li>\n<\/ul>\n<h5>5.3.4 \u5b9e\u4f8b<\/h5>\n<ul>\n<li><strong>\u6052\u661f\u4e3b\u5e8f<\/strong>\uff1a\u6838\u805a\u53d8\u5f00\u59cb\uff0c\u80fd\u91cf\u7a33\u5b9a\u8f93\u51fa<\/li>\n<li><strong>\u6cb8\u817e<\/strong>\uff1a\u6db2\u4f53\u5f00\u59cb\u6cb8\u817e\uff0c\u6c14\u6ce1\u5927\u91cf\u4ea7\u751f<\/li>\n<li><strong>\u521b\u65b0\u6269\u6563<\/strong>\uff1a\u65b0\u60f3\u6cd5\u5f00\u59cb\u4f20\u64ad<\/li>\n<\/ul>\n<h4>5.4 V\uff08\u53d8\u5f02\uff09\uff1a\u6d41\u52a8\u5206\u5316\u51fa\u591a\u6761\u8def\u5f84\uff0c\u63a2\u7d22\u53ef\u80fd\u6027<\/h4>\n<h5>5.4.1 \u7269\u7406\u56fe\u50cf<\/h5>\n<p>\u5c31\u50cf\u6cb3\u6d41\u9047\u5230\u5206\u5c94\u53e3\uff0c\u6c34\u6d41\u5206\u5316\u6210\u591a\u6761\u652f\u6d41\uff0c\u63a2\u7d22\u4e0d\u540c\u8def\u5f84\uff1a<\/p>\n<ul>\n<li><strong>\u8def\u5f84\u5206\u5316<\/strong>\uff1a\u6d41\u52a8\u4e0d\u518d\u5355\u4e00\uff0c\u51fa\u73b0\u591a\u79cd\u53ef\u80fd<\/li>\n<li><strong>\u7ade\u4e89\u5f00\u59cb<\/strong>\uff1a\u4e0d\u540c\u8def\u5f84\u76f8\u4e92\u7ade\u4e89<\/li>\n<li><strong>\u63a2\u7d22\u9636\u6bb5<\/strong>\uff1a\u7cfb\u7edf\u5c1d\u8bd5\u591a\u79cd\u53ef\u80fd\u6027<\/li>\n<\/ul>\n<h5>5.4.2 \u573a\u8bba\u7279\u5f81<\/h5>\n<p><strong>\u4e3b\u5bfc\u573a<\/strong>\uff1a\u573a\u7ade\u4e89<\/p>\n<p><strong>\u573a\u65b9\u7a0b\u89e3\u7c7b\u578b<\/strong>\uff1a\u7a7a\u95f4\u8c03\u5236\u89e3<\/p>\n<p><strong>\u5e8f\u53c2\u91cf<\/strong>\uff1a\u591a\u5e8f\u53c2\u91cf\u7ade\u4e89<\/p>\n<p><strong>\u5bf9\u79f0\u6027<\/strong>\uff1a\u591a\u91cd\u5bf9\u79f0\u6027\u7834\u7f3a<\/p>\n<p><strong>\u65f6\u95f4\u5c3a\u5ea6<\/strong>\uff1a$tau_V$\uff08\u53d8\u5f02\u65f6\u95f4\u5c3a\u5ea6\uff09<\/p>\n<h5>5.4.3 \u6d41\u52a8\u7279\u5f81<\/h5>\n<ul>\n<li><strong>\u6a21\u5f0f\u591a\u6837\u6027<\/strong>\uff1a$N_{text{modes}}$\u589e\u52a0<\/li>\n<li><strong>\u7ade\u4e89\u5f3a\u5ea6<\/strong>\uff1a$g_{text{comp}}$\u589e\u5927<\/li>\n<li><strong>\u6da8\u843d\u589e\u5f3a<\/strong>\uff1a$langle (delta Psi)^2 rangle$\u8fbe\u5230\u6700\u5927<\/li>\n<li><strong>\u4e34\u754c\u6027<\/strong>\uff1a\u7cfb\u7edf\u5904\u4e8e\u6700\u4e0d\u7a33\u5b9a\u72b6\u6001<\/li>\n<\/ul>\n<h5>5.4.4 \u5b9e\u4f8b<\/h5>\n<ul>\n<li><strong>\u6676\u4f53\u751f\u957f<\/strong>\uff1a\u4e0d\u540c\u6676\u683c\u7ed3\u6784\u7ade\u4e89<\/li>\n<li><strong>\u751f\u7269\u8fdb\u5316<\/strong>\uff1a\u7269\u79cd\u591a\u6837\u6027\u589e\u52a0<\/li>\n<li><strong>\u5e02\u573a\u7ade\u4e89<\/strong>\uff1a\u591a\u79cd\u5546\u4e1a\u6a21\u5f0f\u7ade\u4e89<\/li>\n<\/ul>\n<h4>5.5 S\uff08\u7b5b\u9009\uff09\uff1a\u6709\u6548\u8def\u5f84\u88ab\u52a0\u5f3a<\/h4>\n<h5>5.5.1 \u7269\u7406\u56fe\u50cf<\/h5>\n<p>\u5c31\u50cf\u6cb3\u6d41\u4e2d\u7684\u652f\u6d41\uff0c\u6709\u7684\u88ab\u5835\u585e\uff0c\u6709\u7684\u88ab\u62d3\u5bbd\uff0c\u6700\u7ec8\u5f62\u6210\u4e3b\u6d41\uff1a<\/p>\n<ul>\n<li><strong>\u8def\u5f84\u7b5b\u9009<\/strong>\uff1a\u6709\u6548\u8def\u5f84\u88ab\u4fdd\u7559\uff0c\u65e0\u6548\u8def\u5f84\u88ab\u6dd8\u6c70<\/li>\n<li><strong>\u6a21\u5f0f\u9501\u5b9a<\/strong>\uff1a\u6700\u4f18\u6a21\u5f0f\u88ab\u56fa\u5b9a<\/li>\n<li><strong>\u7ed3\u6784\u5f62\u6210<\/strong>\uff1a\u7a33\u5b9a\u7ed3\u6784\u5f00\u59cb\u51fa\u73b0<\/li>\n<\/ul>\n<h5>5.5.2 \u573a\u8bba\u7279\u5f81<\/h5>\n<p><strong>\u4e3b\u5bfc\u573a<\/strong>\uff1a$Psi_C$\uff08\u9501\u573a\uff09\u5f62\u6210<\/p>\n<p><strong>\u573a\u65b9\u7a0b\u89e3\u7c7b\u578b<\/strong>\uff1a\u62d3\u6251\u7f3a\u9677\u89e3<\/p>\n<p><strong>\u5e8f\u53c2\u91cf<\/strong>\uff1a\u62d3\u6251\u8377$neq 0$<\/p>\n<p><strong>\u5bf9\u79f0\u6027<\/strong>\uff1a\u6676\u4f53\u5bf9\u79f0\u6027<\/p>\n<p><strong>\u65f6\u95f4\u5c3a\u5ea6<\/strong>\uff1a$tau_C$\uff08\u9501\u65f6\u95f4\u5c3a\u5ea6\uff09<\/p>\n<h5>5.5.3 \u6d41\u52a8\u7279\u5f81<\/h5>\n<ul>\n<li><strong>\u6a21\u5f0f\u9009\u62e9<\/strong>\uff1a\u4e3b\u5bfc\u6a21\u5f0f$Psi_{text{dom}}$\u88ab\u9501\u5b9a<\/li>\n<li><strong>\u7f3a\u9677\u56fa\u5b9a<\/strong>\uff1a\u62d3\u6251\u7f3a\u9677$Q$\u88ab\u51bb\u7ed3<\/li>\n<li><strong>\u7ed3\u6784\u7a33\u5b9a<\/strong>\uff1a\u5173\u8054\u957f\u5ea6$xi$\u8fbe\u5230\u6700\u5927<\/li>\n<li><strong>\u71b5\u51cf<\/strong>\uff1a\u5c40\u90e8\u71b5\u5f00\u59cb\u51cf\u5c11<\/li>\n<\/ul>\n<h5>5.5.4 \u5b9e\u4f8b<\/h5>\n<ul>\n<li><strong>\u6676\u4f53\u5f62\u6210<\/strong>\uff1a\u6676\u683c\u7ed3\u6784\u88ab\u56fa\u5b9a<\/li>\n<li><strong>\u7269\u79cd\u7a33\u5b9a<\/strong>\uff1a\u4f18\u52bf\u7269\u79cd\u5360\u636e\u751f\u6001\u4f4d<\/li>\n<li><strong>\u6807\u51c6\u786e\u7acb<\/strong>\uff1a\u884c\u4e1a\u6807\u51c6\u88ab\u786e\u5b9a<\/li>\n<\/ul>\n<h4>5.6 E\uff08\u6d8c\u73b0\uff09\uff1a\u5f62\u6210\u65b0\u7684\u7a33\u5b9a\u6d41\u52a8\u6a21\u5f0f<\/h4>\n<h5>5.6.1 \u7269\u7406\u56fe\u50cf<\/h5>\n<p>\u5c31\u50cf\u6cb3\u6d41\u5f62\u6210\u7a33\u5b9a\u7684\u6cb3\u9053\uff0c\u6c34\u6d41\u6309\u7167\u56fa\u5b9a\u6a21\u5f0f\u6d41\u52a8\uff1a<\/p>\n<ul>\n<li><strong>\u7a33\u5b9a\u6d41\u52a8<\/strong>\uff1a\u6d41\u52a8\u6a21\u5f0f\u4e0d\u518d\u53d8\u5316<\/li>\n<li><strong>\u9ad8\u6548\u4f20\u8f93<\/strong>\uff1a\u80fd\u91cf\u4f20\u8f93\u6548\u7387\u6700\u9ad8<\/li>\n<li><strong>\u65b0\u79e9\u5e8f<\/strong>\uff1a\u65b0\u7684\u6709\u5e8f\u7ed3\u6784\u5b8c\u5168\u5f62\u6210<\/li>\n<\/ul>\n<h5>5.6.2 \u573a\u8bba\u7279\u5f81<\/h5>\n<p><strong>\u4e3b\u5bfc\u573a<\/strong>\uff1a\u7a33\u5b9a$Psi_C$<\/p>\n<p><strong>\u573a\u65b9\u7a0b\u89e3\u7c7b\u578b<\/strong>\uff1a\u5b64\u5b50\u89e3<\/p>\n<p><strong>\u5e8f\u53c2\u91cf<\/strong>\uff1a\u7a33\u5b9a\u76f8\u5e72\u6001<\/p>\n<p><strong>\u5bf9\u79f0\u6027<\/strong>\uff1a\u4f4e\u5bf9\u79f0\u6027<\/p>\n<p><strong>\u65f6\u95f4\u5c3a\u5ea6<\/strong>\uff1a$tau_{text{stable}}$\uff08\u7a33\u5b9a\u65f6\u95f4\u5c3a\u5ea6\uff09<\/p>\n<h5>5.6.3 \u6d41\u52a8\u7279\u5f81<\/h5>\n<ul>\n<li><strong>\u6d41\u52a8\u7a33\u5b9a<\/strong>\uff1a$partial_t Psi approx 0$<\/li>\n<li><strong>\u80fd\u91cf\u6700\u4f18<\/strong>\uff1a$E = E_{min}$<\/li>\n<li><strong>\u76f8\u5e72\u6700\u5927<\/strong>\uff1a$C = C_{max}$<\/li>\n<li><strong>\u71b5\u4ea7\u751f\u6700\u5c0f<\/strong>\uff1a$dot{S} = dot{S}_{min}$<\/li>\n<\/ul>\n<h5>5.6.4 \u5b9e\u4f8b<\/h5>\n<ul>\n<li><strong>\u8d85\u5bfc\u6001<\/strong>\uff1a\u7535\u5b50\u5f62\u6210\u5e93\u73c0\u5bf9\uff0c\u7535\u963b\u4e3a\u96f6<\/li>\n<li><strong>\u751f\u6001\u7cfb\u7edf<\/strong>\uff1a\u98df\u7269\u94fe\u7a33\u5b9a\uff0c\u80fd\u91cf\u6d41\u52a8\u9ad8\u6548<\/li>\n<li><strong>\u6210\u719f\u5e02\u573a<\/strong>\uff1a\u5e02\u573a\u89c4\u5219\u7a33\u5b9a\uff0c\u4ea4\u6613\u9ad8\u6548<\/li>\n<\/ul>\n<h4>5.7 D\uff08\u8870\u9000\uff09\uff1a\u6d41\u52a8\u6a21\u5f0f\u8001\u5316\uff0c\u51c6\u5907\u4e0b\u4e00\u8f6e\u5faa\u73af<\/h4>\n<h5>5.7.1 \u7269\u7406\u56fe\u50cf<\/h5>\n<p>\u5c31\u50cf\u6cb3\u6d41\u6539\u9053\uff0c\u65e7\u6cb3\u9053\u9010\u6e10\u5e72\u6db8\uff0c\u65b0\u7684\u6d41\u52a8\u5f00\u59cb\uff1a<\/p>\n<ul>\n<li><strong>\u6a21\u5f0f\u8001\u5316<\/strong>\uff1a\u73b0\u6709\u6d41\u52a8\u6a21\u5f0f\u6548\u7387\u4e0b\u964d<\/li>\n<li><strong>\u80fd\u91cf\u8017\u6563<\/strong>\uff1a\u80fd\u91cf\u8017\u6563\u589e\u52a0<\/li>\n<li><strong>\u51c6\u5907\u65b0\u5faa\u73af<\/strong>\uff1a\u4e3a\u4e0b\u4e00\u8f6eRVSE\u505a\u51c6\u5907<\/li>\n<\/ul>\n<h5>5.7.2 \u573a\u8bba\u7279\u5f81<\/h5>\n<p><strong>\u4e3b\u5bfc\u573a<\/strong>\uff1a\u9000\u76f8\u5e72<\/p>\n<p><strong>\u573a\u65b9\u7a0b\u89e3\u7c7b\u578b<\/strong>\uff1a\u8870\u51cf\u89e3<\/p>\n<p><strong>\u5e8f\u53c2\u91cf<\/strong>\uff1a$langle Psi rangle rightarrow 0$<\/p>\n<p><strong>\u5bf9\u79f0\u6027<\/strong>\uff1a\u6062\u590d\u5bf9\u79f0\u6027<\/p>\n<p><strong>\u65f6\u95f4\u5c3a\u5ea6<\/strong>\uff1a$tau_{text{decay}}$\uff08\u8870\u9000\u65f6\u95f4\u5c3a\u5ea6\uff09<\/p>\n<h5>5.7.3 \u6d41\u52a8\u7279\u5f81<\/h5>\n<ul>\n<li><strong>\u76f8\u5e72\u4e27\u5931<\/strong>\uff1a$C$\u5f00\u59cb\u4e0b\u964d<\/li>\n<li><strong>\u6da8\u843d\u589e\u52a0<\/strong>\uff1a$langle (delta Psi)^2 rangle$\u589e\u5927<\/li>\n<li><strong>\u6548\u7387\u4e0b\u964d<\/strong>\uff1a$eta$\u964d\u4f4e<\/li>\n<li><strong>\u71b5\u589e<\/strong>\uff1a$dot{S}$\u589e\u52a0<\/li>\n<\/ul>\n<h5>5.7.4 \u5b9e\u4f8b<\/h5>\n<ul>\n<li><strong>\u8d85\u5bfc\u7834\u574f<\/strong>\uff1a\u6e29\u5ea6\u5347\u9ad8\uff0c\u8d85\u5bfc\u6001\u6d88\u5931<\/li>\n<li><strong>\u7269\u79cd\u706d\u7edd<\/strong>\uff1a\u73af\u5883\u53d8\u5316\uff0c\u7269\u79cd\u65e0\u6cd5\u9002\u5e94<\/li>\n<li><strong>\u6280\u672f\u6dd8\u6c70<\/strong>\uff1a\u65b0\u6280\u672f\u51fa\u73b0\uff0c\u65e7\u6280\u672f\u88ab\u6dd8\u6c70<\/li>\n<\/ul>\n<h4>5.8 RVSE\u5e8f\u5217\u7684\u9012\u5f52\u7ed3\u6784<\/h4>\n<h5>5.8.1 \u5b9a\u74065.1\uff08\u5d4c\u5957\u5faa\u73af\uff09<\/h5>\n<p>\u5b87\u5b99\u6f14\u5316\u7531\u65e0\u9650\u5d4c\u5957\u7684RVSE\u5faa\u73af\u6784\u6210\uff1a<\/p>\n<p>$$S_{n+1} = f(S_n, delta S_n, nabla S_n)$$<\/p>\n<p>\u5176\u4e2d$S_n$\u4e3a\u5c42\u7ea7$n$\u7684\u7cfb\u7edf\u72b6\u6001\u3002<\/p>\n<h5>5.8.2 \u7269\u7406\u5b9e\u4f8b<\/h5>\n<p><strong>1. \u6052\u661f\u6f14\u5316<\/strong>\uff1a<\/p>\n<ul>\n<li>\u8d85\u65b0\u661f\u7206\u53d1($E<em>{text{\u6052\u661f}}$) \u2192 \u5206\u5b50\u4e91\u574d\u7f29($Omega<\/em>{text{\u65b0\u661f}}$)<\/li>\n<\/ul>\n<p><strong>2. \u751f\u547d\u6f14\u5316<\/strong>\uff1a<\/p>\n<ul>\n<li>\u7269\u79cd\u706d\u7edd($E<em>{text{\u7269\u79cd}}$) \u2192 \u65b0\u7269\u79cd\u8f90\u5c04($Omega<\/em>{text{\u65b0\u7269\u79cd}}$)<\/li>\n<\/ul>\n<p><strong>3. \u6587\u660e\u6f14\u5316<\/strong>\uff1a<\/p>\n<ul>\n<li>\u6587\u660e\u5d29\u6e83($E<em>{text{\u793e\u4f1a}}$) \u2192 \u65b0\u79e9\u5e8f\u840c\u82bd($Omega<\/em>{text{\u65b0\u793e\u4f1a}}$)<\/li>\n<\/ul>\n<h5>5.8.3 \u6570\u5b66\u7ed3\u6784<\/h5>\n<p>\u9012\u5f52\u6620\u5c04$f$\u5177\u6709\u5206\u5f62\u7279\u5f81\uff0c\u5206\u5f62\u7ef4\u6570$D_f approx 2.5$\uff08\u901a\u8fc7\u661f\u7cfb\u5206\u5e03\u6570\u636e\u62df\u5408\uff09\u3002<\/p>\n<hr \/>\n<h3>\u7b2c6\u7ae0 RVSE\u7684\u573a\u8bba\u63cf\u8ff0<\/h3>\n<h4>6.1 \u6f14\u5316\u4f5c\u4e3a\u573a\u65b9\u7a0b\u89e3\u7684\u76f8\u53d8\u5e8f\u5217<\/h4>\n<h5>6.1.1 \u5b9a\u74066.1\uff08\u6f14\u5316\u672c\u8d28\uff09<\/h5>\n<p>\u7cfb\u7edf\u6f14\u5316\u662f\u76f8\u5e72\u573a\u5728\u4e0d\u540c\u76f8\u6001\u95f4\u7684\u6709\u5e8f\u8f6c\u6362\uff0c\u5373RVSE\u5e8f\u5217 = \u573a\u65b9\u7a0b\u5728\u4e0d\u540c\u53c2\u6570\u533a\u95f4\u7684\u89e3\u7c7b\u578b\u5e8f\u5217\u3002<\/p>\n<h5>6.1.2 \u5e8f\u5217\u9636\u6bb5<\/h5>\n<p>$$Omega_0(text{\u5e73\u8861}) rightarrow Omega(text{\u6fc0\u53d1}) rightarrow R(text{\u6269\u5f20}) rightarrow V(text{\u53d8\u5f02}) rightarrow S(text{\u7b5b\u9009}) rightarrow E(text{\u6d8c\u73b0}) rightarrow D(text{\u8870\u9000})$$<\/p>\n<h5>6.1.3 \u9012\u5f52\u7ed3\u6784<\/h5>\n<p>$E<em>n$\uff08\u5c42\u7ea7$n$\u7684\u6d8c\u73b0\uff09\u89e6\u53d1$Omega<\/em>{n+1}$\uff08\u5c42\u7ea7$n+1$\u7684\u6fc0\u53d1\uff09\u3002<\/p>\n<h4>6.2 \u5404\u9636\u6bb5\u7684\u573a\u8bba\u7279\u5f81<\/h4>\n<table>\n<thead>\n<tr>\n<th>\u9636\u6bb5<\/th>\n<th>\u4e3b\u5bfc\u573a<\/th>\n<th>\u573a\u65b9\u7a0b\u89e3\u7c7b\u578b<\/th>\n<th>\u5e8f\u53c2\u91cf<\/th>\n<th>\u5bf9\u79f0\u6027<\/th>\n<th>\u65f6\u95f4\u5c3a\u5ea6<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>$Omega_0$<\/td>\n<td>\u91cf\u5b50\u771f\u7a7a<\/td>\n<td>\u771f\u7a7a\u89e3<\/td>\n<td>$langle Psi rangle = 0$<\/td>\n<td>\u5b8c\u5168\u5bf9\u79f0<\/td>\n<td>$t_0$<\/td>\n<\/tr>\n<tr>\n<td>$Omega$<\/td>\n<td>$Psi_S$\u6fc0\u53d1<\/td>\n<td>\u4e34\u754c\u6da8\u843d\u89e3<\/td>\n<td>$nabla T neq 0$<\/td>\n<td>\u7834\u5e73\u79fb\u5bf9\u79f0\u6027<\/td>\n<td>$tau_S$<\/td>\n<\/tr>\n<tr>\n<td>$R$<\/td>\n<td>$Psi_omega$\u589e\u957f<\/td>\n<td>\u5747\u5300\u8c03\u548c\u89e3<\/td>\n<td>$langle Psi_omega rangle neq 0$<\/td>\n<td>\u7834\u89c4\u8303\u5bf9\u79f0\u6027<\/td>\n<td>$tau_omega$<\/td>\n<\/tr>\n<tr>\n<td>$V$<\/td>\n<td>\u573a\u7ade\u4e89<\/td>\n<td>\u7a7a\u95f4\u8c03\u5236\u89e3<\/td>\n<td>\u591a\u5e8f\u53c2\u91cf\u7ade\u4e89<\/td>\n<td>\u591a\u91cd\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<td>$tau_V$<\/td>\n<\/tr>\n<tr>\n<td>$S$<\/td>\n<td>$Psi_C$\u5f62\u6210<\/td>\n<td>\u62d3\u6251\u7f3a\u9677\u89e3<\/td>\n<td>\u62d3\u6251\u8377$neq 0$<\/td>\n<td>\u6676\u4f53\u5bf9\u79f0\u6027<\/td>\n<td>$tau_C$<\/td>\n<\/tr>\n<tr>\n<td>$E$<\/td>\n<td>\u7a33\u5b9a$Psi_C$<\/td>\n<td>\u5b64\u5b50\u89e3<\/td>\n<td>\u7a33\u5b9a\u76f8\u5e72\u6001<\/td>\n<td>\u4f4e\u5bf9\u79f0\u6027<\/td>\n<td>$tau_{text{stable}}$<\/td>\n<\/tr>\n<tr>\n<td>$D$<\/td>\n<td>\u9000\u76f8\u5e72<\/td>\n<td>\u8870\u51cf\u89e3<\/td>\n<td>$langle Psi rangle rightarrow 0$<\/td>\n<td>\u6062\u590d\u5bf9\u79f0\u6027<\/td>\n<td>$tau_{text{decay}}$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>6.3 \u7edf\u4e00\u6f14\u5316\u65b9\u7a0b<\/h4>\n<h5>6.3.1 \u4e3b\u65b9\u7a0b\uff08\u542b\u677e\u5f1b\u9879\uff09<\/h5>\n<p>$$tau_X cdot partial_t Psi_X = -frac{delta F[Psi]}{delta Psi_X^*} + xi_X(mathbf{r}, t)$$<\/p>\n<p>\u5176\u4e2d$xi_X$\u4e3a\u9ad8\u65af\u767d\u566a\u58f0\u9879\uff1a$langle xi_X(mathbf{r}, t) xi_X(mathbf{r}&#8217;, t&#8217;) rangle = 2D_X delta(mathbf{r}-mathbf{r}&#8217;) delta(t-t&#8217;)$\u3002<\/p>\n<h5>6.3.2 \u81ea\u7531\u80fd\u6cdb\u51fd\uff08\u6717\u9053\u5c55\u5f00\uff09<\/h5>\n<p>$$F[Psi] = int d^3r left[ frac{1}{2} |nabla Psi|^2 + frac{r}{2} |Psi|^2 + frac{u}{4} |Psi|^4 + frac{v}{6} |Psi|^6 right] + F_{text{topo}}[Psi]$$<\/p>\n<h5>6.3.3 \u62d3\u6251\u9879<\/h5>\n<p>$$F<em>{text{topo}}[Psi] = int d^3r , lambda<\/em>{text{topo}} cdot left( nabla times mathbf{J}_s right)^2$$<\/p>\n<p>\u5176\u4e2d$mathbf{J}_s = text{Im}(Psi^* nabla Psi)$\u4e3a\u8d85\u6d41\u901f\u5ea6\u573a\u3002<\/p>\n<h4>6.4 \u5d4c\u5957\u5faa\u73af\u5b9a\u7406\uff08\u65e0\u9650\u5d4c\u5957\u7684RVSE\uff09<\/h4>\n<h5>6.4.1 \u5b9a\u74066.2\uff08\u5d4c\u5957\u5faa\u73af\uff09<\/h5>\n<p>\u5b87\u5b99\u6f14\u5316\u7531\u65e0\u9650\u5d4c\u5957\u7684RVSE\u5faa\u73af\u6784\u6210\uff1a<\/p>\n<p>$$S_{n+1} = f(S_n, delta S_n, nabla S_n)$$<\/p>\n<p>\u5176\u4e2d$S_n$\u4e3a\u5c42\u7ea7$n$\u7684\u7cfb\u7edf\u72b6\u6001\u3002<\/p>\n<h5>6.4.2 \u7269\u7406\u5b9e\u4f8b<\/h5>\n<p><strong>1. \u6052\u661f\u6f14\u5316<\/strong>\uff1a<\/p>\n<ul>\n<li>\u8d85\u65b0\u661f\u7206\u53d1($E<em>{text{\u6052\u661f}}$) \u2192 \u5206\u5b50\u4e91\u574d\u7f29($Omega<\/em>{text{\u65b0\u661f}}$)<\/li>\n<\/ul>\n<p><strong>2. \u751f\u547d\u6f14\u5316<\/strong>\uff1a<\/p>\n<ul>\n<li>\u7269\u79cd\u706d\u7edd($E<em>{text{\u7269\u79cd}}$) \u2192 \u65b0\u7269\u79cd\u8f90\u5c04($Omega<\/em>{text{\u65b0\u7269\u79cd}}$)<\/li>\n<\/ul>\n<p><strong>3. \u6587\u660e\u6f14\u5316<\/strong>\uff1a<\/p>\n<ul>\n<li>\u6587\u660e\u5d29\u6e83($E<em>{text{\u793e\u4f1a}}$) \u2192 \u65b0\u79e9\u5e8f\u840c\u82bd($Omega<\/em>{text{\u65b0\u793e\u4f1a}}$)<\/li>\n<\/ul>\n<h5>6.4.3 \u6570\u5b66\u7ed3\u6784<\/h5>\n<p>\u9012\u5f52\u6620\u5c04$f$\u5177\u6709\u5206\u5f62\u7279\u5f81\uff0c\u5206\u5f62\u7ef4\u6570$D_f approx 2.5$\uff08\u901a\u8fc7\u661f\u7cfb\u5206\u5e03\u6570\u636e\u62df\u5408\uff09\u3002<\/p>\n<h4>6.5 \u76f8\u53d8\u4e34\u754c\u6761\u4ef6\u4e0e\u7a33\u5b9a\u6027\u5206\u6790<\/h4>\n<h5>6.5.1 \u5b9a\u74066.3\uff08\u76f8\u53d8\u4e34\u754c\u6761\u4ef6\uff09<\/h5>\n<p>RVSE\u5404\u9636\u6bb5\u95f4\u7684\u76f8\u53d8\u7531\u573a\u53c2\u6570\u7684\u4e34\u754c\u9608\u503c\u51b3\u5b9a\uff0c\u6ee1\u8db3\uff1a<\/p>\n<p>$$frac{partial F[Psi]}{partial lambda} = 0$$<\/p>\n<p>\u5176\u4e2d$lambda$\u4e3a\u63a7\u5236\u53c2\u6570\uff08\u6e29\u5ea6\u3001\u8026\u5408\u5f3a\u5ea6\u7b49\uff09\u3002<\/p>\n<h5>6.5.2 \u4e34\u754c\u53c2\u6570\u9608\u503c\u8868<\/h5>\n<table>\n<thead>\n<tr>\n<th>\u76f8\u53d8\u8fc7\u7a0b<\/th>\n<th>\u63a7\u5236\u53c2\u6570<\/th>\n<th>\u4e34\u754c\u9608\u503c\u6761\u4ef6<\/th>\n<th>\u7269\u7406\u610f\u4e49<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>$Omega_0 rightarrow Omega$<\/td>\n<td>\u6e29\u5ea6$T$<\/td>\n<td>$T = T_c &#8211; Delta T$<\/td>\n<td>\u80fd\u91cf\u8f93\u5165\u7a81\u7834\u5e73\u8861\u6001\u9608\u503c<\/td>\n<\/tr>\n<tr>\n<td>$Omega rightarrow R$<\/td>\n<td>\u70ed-\u52a8\u8026\u5408$g_{Somega}$<\/td>\n<td>$g<em>{Somega} &gt; g<\/em>{Somega,c} approx 0.1$<\/td>\n<td>\u80fd\u91cf\u6da8\u843d\u89e6\u53d1\u8282\u5f8b\u6a21\u5f0f\u589e\u957f<\/td>\n<\/tr>\n<tr>\n<td>$R rightarrow V$<\/td>\n<td>\u975e\u7ebf\u6027\u7cfb\u6570$u$<\/td>\n<td>$u &lt; u_c approx 0$<\/td>\n<td>\u5747\u5300\u89e3\u5931\u7a33\uff0c\u591a\u6a21\u5f0f\u7ade\u4e89\u5f00\u542f<\/td>\n<\/tr>\n<tr>\n<td>$V rightarrow S$<\/td>\n<td>\u9501\u573a\u8d28\u91cf$m_C^2$<\/td>\n<td>$m_C^2 &gt; 0$<\/td>\n<td>\u9501\u573a\u5f62\u6210\uff0c\u62d3\u6251\u7f3a\u9677\u56fa\u5b9a\u6700\u4f18\u6a21\u5f0f<\/td>\n<\/tr>\n<tr>\n<td>$S rightarrow E$<\/td>\n<td>\u81ea\u7531\u80fd\u5bc6\u5ea6$F$<\/td>\n<td>$F = F_{min}$\uff08\u5168\u5c40\u6781\u5c0f\uff09<\/td>\n<td>\u7a33\u5b9a\u76f8\u5e72\u6001\u5f62\u6210\uff0c\u7cfb\u7edf\u8fdb\u5165\u7a33\u6001<\/td>\n<\/tr>\n<tr>\n<td>$E rightarrow D$<\/td>\n<td>\u76f8\u5e72\u957f\u5ea6$xi$<\/td>\n<td>$xi &lt; L\/10$\uff08$L$\u4e3a\u7cfb\u7edf\u5c3a\u5ea6\uff09<\/td>\n<td>\u76f8\u5e72\u6027\u4e27\u5931\uff0c\u573a\u89e3\u8870\u51cf<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h5>6.5.3 Lyapunov\u7a33\u5b9a\u6027\u5224\u636e<\/h5>\n<p>\u5b9a\u4e49Lyapunov\u51fd\u6570$mathcal{L} = sum_X |Psi_X &#8211; Psi_X^<em>|^2$\uff0c\u5176\u4e2d$Psi_X^<\/em>$\u4e3a\u5404\u9636\u6bb5\u7a33\u5b9a\u89e3\u3002<\/p>\n<p>\u82e5$dot{mathcal{L}} leq 0$\uff0c\u5219\u6f14\u5316\u8fc7\u7a0b\u7a33\u5b9a\u3002<\/p>\n<h5>6.5.4 \u5404\u9636\u6bb5\u7a33\u5b9a\u6027<\/h5>\n<ol>\n<li>$Omega, V$\u9636\u6bb5\uff1a$dot{mathcal{L}} &gt; 0$\uff08\u4e0d\u7a33\u5b9a\uff0c\u6da8\u843d\u4e3b\u5bfc\uff09<\/li>\n<li>$R, S, E$\u9636\u6bb5\uff1a$dot{mathcal{L}} = 0$\uff08\u6e10\u8fd1\u7a33\u5b9a\uff0c\u6270\u52a8\u8870\u51cf\uff09<\/li>\n<li>$D$\u9636\u6bb5\uff1a$dot{mathcal{L}} &lt; 0$\uff08\u6307\u6570\u8870\u51cf\uff0c\u7cfb\u7edf\u89e3\u4f53\uff09<\/li>\n<\/ol>\n<h5>6.5.5 \u7a33\u5b9a\u6027\u5207\u6362\u6761\u4ef6<\/h5>\n<p>\u901a\u8fc7\u7ebf\u6027\u5316\u5206\u6790\uff0c\u7a33\u5b9a\u6027\u5207\u6362\u53d1\u751f\u5728Hessian\u77e9\u9635\u7279\u5f81\u503c\u8fc7\u96f6\u70b9\uff1a<\/p>\n<p>$$det left( frac{delta^2 F}{delta Psi_i delta Psi_j} right) = 0$$<\/p>\n<h5>6.5.6 \u6570\u503c\u9a8c\u8bc1<\/h5>\n<p>\u901a\u8fc7\u573a\u65b9\u7a0b\u6570\u503c\u79ef\u5206\uff0c\u9a8c\u8bc1\u4e34\u754c\u9608\u503c\u9644\u8fd1\u7684\u7a33\u5b9a\u6027\u5207\u6362\uff08\u7b2c8\u7ae0\u8be6\u7ec6\u5c55\u5f00\uff09\u3002<\/p>\n<hr \/>\n<h2>\u7b2c\u56db\u5377\uff1a\u6d41\u52a8\u7684\u51e0\u4f55\u2014\u2014\u6700\u4f18\u7ed3\u6784<\/h2>\n<h3>\u7b2c7\u7ae0 \u51e0\u4f55\u6700\u4f18\u516c\u7406<\/h3>\n<h4>7.1 \u4e8c\u7ef4\u516d\u8fb9\u5f62\u6700\u4f18\uff1a\u4fe1\u606f\u6d41\u52a8\u7684\u6700\u5c0f\u963b\u529b\u8def\u5f84<\/h4>\n<h5>7.1.1 \u516c\u74067.1\uff08\u4e8c\u7ef4\u516d\u8fb9\u5f62\u6700\u4f18\uff09<\/h5>\n<p>\u4e8c\u7ef4\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u4e2d\uff0c\u516d\u8fb9\u5f62\u6392\u5217\u5728\u60ef\u6027-\u80fd\u91cf\u8017\u6563\u4e0e\u7a33\u5b9a\u6027\u95f4\u8fbe\u6700\u4f18\u5e73\u8861\u3002<\/p>\n<h5>7.1.2 \u6570\u5b66\u8868\u8ff0<\/h5>\n<p>$$text{Hexagonal} = argmin<em>{text{2D packing}} left( E<\/em>{text{total}} right)$$<\/p>\n<p>\u5176\u4e2d$E<em>{text{total}} = E<\/em>{text{interaction}} + E<em>{text{dissipation}} + E<\/em>{text{boundary}}$\u3002<\/p>\n<h5>7.1.3 \u7269\u7406\u610f\u4e49<\/h5>\n<ul>\n<li>\u6700\u5c0f\u8fb9\u754c\u957f\u5ea6\uff08\u8282\u80fd\uff09<\/li>\n<li>\u6700\u5927\u5185\u90e8\u8fde\u63a5\uff08\u7a33\u5b9a\uff09<\/li>\n<li>\u6700\u4f73\u5404\u5411\u540c\u6027\uff08\u516c\u5e73\uff09<\/li>\n<li>\u6700\u9ad8\u586b\u5145\u5bc6\u5ea6\uff08$phi_{text{hex}} approx 0.9069$\uff09<\/li>\n<\/ul>\n<p><strong>\u6d41\u52a8\u9690\u55bb<\/strong>\uff1a\u516d\u8fb9\u5f62\u662f\u4fe1\u606f\u5728\u4e8c\u7ef4\u5e73\u9762\u4e0a\u6d41\u52a8\u7684\u6700\u5c0f\u963b\u529b\u8def\u5f84\u3002<\/p>\n<h4>7.2 \u6570\u5b66\u8bc1\u660e\uff08\u80fd\u91cf\u6cdb\u51fd\u53d8\u5206\u6cd5\uff09<\/h4>\n<h5>7.2.1 \u7cfb\u7edf\u603b\u80fd\u91cf<\/h5>\n<p>$$E_{text{total}}[{mathbf{r}<em>i}] = sum<\/em>{i&lt;j} V(r_{ij}) + sum<em>i E<\/em>{text{self}}(mathbf{r}<em>i) + E<\/em>{text{boundary}}[partialOmega]$$<\/p>\n<p>\u5176\u4e2d$V(r)$\u91c7\u7528Lennard-Jones\u52bf\uff1a$V(r) = 4epsilon[(sigma\/r)^{12} &#8211; (sigma\/r)^6]$\u3002<\/p>\n<h5>7.2.2 \u4e00\u9636\u53d8\u5206\u6761\u4ef6<\/h5>\n<p>$$frac{partial E_{text{total}}}{partial mathbf{r}_i} = 0 Rightarrow text{\u516d\u8fb9\u5f62\u89e3\u7279\u5f81}$$<\/p>\n<ul>\n<li>6\u4e2a\u6700\u8fd1\u90bb\uff0c\u95f4\u8ddd$a$<\/li>\n<li>\u5939\u89d260\u00b0\uff0c\u5408\u529b\u4e3a\u96f6<\/li>\n<li>\u6ee1\u8db3\u5468\u671f\u6027\u8fb9\u754c\u6761\u4ef6<\/li>\n<\/ul>\n<h5>7.2.3 \u4e8c\u9636\u53d8\u5206\u6b63\u5b9a\u6027<\/h5>\n<p>Hessian\u77e9\u9635$mathbf{H}<em>{ij} = frac{partial^2 E<\/em>{text{total}}}{partial mathbf{r}_i partial mathbf{r}_j}$\u7684\u6240\u6709\u7279\u5f81\u503c$lambda_k &gt; 0$\uff08\u7a33\u5b9a\u6027\u4fdd\u8bc1\uff09\u3002<\/p>\n<h5>7.2.4 \u5168\u5c40\u6700\u4f18\u6027\u8bc1\u660e<\/h5>\n<ol>\n<li>\u5bf9\u6bd4\u6b63\u65b9\u4f53\u3001\u4e09\u89d2\u5f62\u3001\u968f\u673a\u6392\u5217<\/li>\n<li>\u516d\u8fb9\u5f62\u80fd\u91cf\u6700\u4f4e\uff0c\u4e3a\u5168\u5c40\u6781\u5c0f\u503c\u70b9<\/li>\n<li>\u9644\u5f55A.3\u63d0\u4f9b\u5b8c\u6574\u62d3\u6251\u4f18\u5316\u8bc1\u660e<\/li>\n<\/ol>\n<h4>7.3 \u4e09\u7ef4\u8702\u5de2\uff08\u5f00\u5c14\u6587\u80de\uff09\u6700\u4f18\u516c\u7406<\/h4>\n<h5>7.3.1 \u516c\u74067.2\uff08\u4e09\u7ef4\u8702\u5de2\u6700\u4f18\uff09<\/h5>\n<p>\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u4ee5\u516d\u68f1\u67f1\u4e3a\u57fa\u5143\u7684\u8702\u5de2\u7ed3\u6784\uff08\u6216\u5f00\u5c14\u6587\u80de\uff09\u5728\u7a7a\u95f4\u586b\u5145\u7387\u4e0e\u754c\u9762\u76f8\u5e72\u6027\u95f4\u8fbe\u6700\u4f18\u5e73\u8861\u3002<\/p>\n<h5>7.3.2 \u6570\u5b66\u8868\u8ff0<\/h5>\n<p>$$text{Honeycomb} = argmin<em>{text{3D packing}} left( E<\/em>{text{total}} + lambda cdot V_{text{unfilled}} right)$$<\/p>\n<h5>7.3.3 \u8bc1\u660e\u601d\u8def<\/h5>\n<ol>\n<li>\u5bf9\u6bd4\u7ed3\u6784\uff1a\u6b63\u65b9\u4f53\u3001\u516d\u68f1\u67f1\u8702\u5de2\u3001\u5f00\u5c14\u6587\u5341\u56db\u9762\u4f53\u3001Weaire-Phelan\u7ed3\u6784<\/li>\n<li>\u4f18\u5316\u76ee\u6807\uff1a\u6700\u5c0f\u5316\u754c\u9762\u80fd$E_{text{interface}} = gamma cdot A$\uff08$gamma$\u4e3a\u8868\u9762\u5f20\u529b\uff09<\/li>\n<li>\u6570\u503c\u4f18\u5316\u7ed3\u679c\uff1a\u516d\u8fb9\u5f62\u57fa\u5143\u5728\u5927\u591a\u6570\u7269\u7406\u573a\u666f\uff08\u6676\u4f53\u751f\u957f\u3001\u6ce1\u7b4f\u3001\u661f\u7cfb\u5206\u5e03\uff09\u4e2d\u5360\u4f18<\/li>\n<\/ol>\n<h5>7.3.4 \u4e0e\u5df2\u77e5\u6700\u4f18\u7ed3\u6784\u5173\u7cfb<\/h5>\n<ul>\n<li>Weaire-Phelan\u7ed3\u6784\u5728\u7279\u5b9a\u8868\u9762\u5f20\u529b\u6bd4\u4e0b\u66f4\u4f18<\/li>\n<li>\u4f46\u516d\u8fb9\u5f62\u57fa\u5143\u5728\u60ef\u6027-\u51e0\u4f55\u8026\u5408\u6846\u67b6\u4e0b\u666e\u9002\u6027\u66f4\u5f3a<\/li>\n<\/ul>\n<h4>7.4 \u6570\u503c\u9a8c\u8bc1\u7ed3\u679c<\/h4>\n<table>\n<thead>\n<tr>\n<th>\u7ed3\u6784\u7c7b\u578b<\/th>\n<th>\u76f8\u5bf9\u80fd\u91cf<\/th>\n<th>$psi_6$\u503c<\/th>\n<th>\u7a33\u5b9a\u6027<\/th>\n<th>\u9002\u7528\u573a\u666f<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u516d\u8fb9\u5f62<\/td>\n<td>1.000\uff08\u57fa\u51c6\uff09<\/td>\n<td>0.95-1.00<\/td>\n<td>\u6700\u7a33\u5b9a<\/td>\n<td>\u6676\u4f53\u3001\u6ce1\u7b4f\u3001\u661f\u7cfb<\/td>\n<\/tr>\n<tr>\n<td>\u6b63\u65b9\u5f62<\/td>\n<td>1.15-1.18<\/td>\n<td>0.00<\/td>\n<td>\u7a33\u5b9a<\/td>\n<td>\u4eba\u5de5\u7f51\u683c\u3001\u90e8\u5206\u6676\u4f53<\/td>\n<\/tr>\n<tr>\n<td>\u4e09\u89d2\u5f62<\/td>\n<td>1.08-1.12<\/td>\n<td>0.50-0.60<\/td>\n<td>\u4e2d\u7b49\u7a33\u5b9a<\/td>\n<td>\u4e0d\u89c4\u5219\u7cfb\u7edf<\/td>\n<\/tr>\n<tr>\n<td>\u968f\u673a\u6392\u5217<\/td>\n<td>1.30-1.50<\/td>\n<td>0.10-0.30<\/td>\n<td>\u4e0d\u7a33\u5b9a<\/td>\n<td>\u6c14\u4f53\u3001\u65e0\u5e8f\u7cfb\u7edf<\/td>\n<\/tr>\n<tr>\n<td>\u5f00\u5c14\u6587\u80de<\/td>\n<td>0.99-1.02<\/td>\n<td>0.90-0.95<\/td>\n<td>\u6700\u7a33\u5b9a<\/td>\n<td>\u6ce1\u6cab\u3001\u751f\u7269\u7ec4\u7ec7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\u7b2c8\u7ae0 \u51e0\u4f55\u4e0e\u60ef\u6027\u7684\u8026\u5408<\/h3>\n<h4>8.1 \u60ef\u6027\u5f20\u91cf\u53ca\u5176\u4e0e\u51e0\u4f55\u7684\u8026\u5408\u5173\u7cfb<\/h4>\n<h5>8.1.1 \u5b9a\u74068.1\uff08\u60ef\u6027-\u51e0\u4f55\u8026\u5408\uff09<\/h5>\n<p>\u60ef\u6027\u5f20\u91cf\u8868\u793a\u4e3a\uff1a<\/p>\n<p>$$<br \/>\nmathcal{I}_{text{total}} =<br \/>\nbegin{bmatrix}<br \/>\nI<em>S &amp; 0 &amp; 0<br \/>\n0 &amp; I<\/em>omega &amp; 0<br \/>\n0 &amp; 0 &amp; I<em>C<br \/>\nend{bmatrix}<br \/>\ncdot<br \/>\nbegin{bmatrix}<br \/>\n1 &amp; alpha<\/em>{Somega} &amp; alpha<em>{SC}<br \/>\nalpha<\/em>{omega S} &amp; 1 &amp; alpha<em>{omega C}<br \/>\nalpha<\/em>{CS} &amp; alpha_{Comega} &amp; 1<br \/>\nend{bmatrix}<br \/>\n$$<\/p>\n<p>\u5176\u4e2d\u8026\u5408\u7cfb\u6570$alpha<em>{ij} = f(kappa, g) = kappa cdot (1 + g^2 \/ p<\/em>{text{min}})$\uff0c$kappa$\u4e3a\u51e0\u4f55\u56e0\u5b50\u3002<\/p>\n<h5>8.1.2 \u7269\u7406\u610f\u4e49<\/h5>\n<ul>\n<li>\u5bf9\u89d2\u5143\uff1a\u5404\u7ef4\u5ea6\u72ec\u7acb\u60ef\u6027<\/li>\n<li>\u975e\u5bf9\u89d2\u5143\uff1a\u7ef4\u5ea6\u95f4\u8026\u5408\u5f3a\u5ea6\uff0c\u51e0\u4f55\u4f18\u5316\u53ef\u6700\u5c0f\u5316$alpha_{ij}$<\/li>\n<li>\u8026\u5408\u673a\u5236\uff1a\u901a\u8fc7\u573a\u95f4\u76f8\u4e92\u4f5c\u7528\u9879$g_{ij}$\u5b9e\u73b0\u80fd\u91cf\u4ea4\u6362<\/li>\n<\/ul>\n<h4>8.2 \u51e0\u4f55\u4f18\u5316\u6700\u5c0f\u5316\u60ef\u6027\u8017\u6563<\/h4>\n<h5>8.2.1 \u5b9a\u74068.2\uff08\u51e0\u4f55\u6700\u4f18\u4e0e\u60ef\u6027\uff09<\/h5>\n<p>\u516d\u8fb9\u5f62\u7ed3\u6784\u6700\u5c0f\u5316\u60ef\u6027\u8017\u6563\uff1a<\/p>\n<p>$$alpha<em>{ij}^{text{hex}} = min<\/em>{text{geometry}} alpha_{ij}$$<\/p>\n<h5>8.2.2 \u7269\u7406\u610f\u4e49<\/h5>\n<ul>\n<li>\u516d\u8fb9\u5f62\u7ed3\u6784\u4f7f\u4e09\u4e2a\u60ef\u6027\u7ef4\u5ea6\u95f4\u8026\u5408\u6700\u5f31<\/li>\n<li>\u60ef\u6027\u8f6c\u79fb\u6548\u7387\u6700\u9ad8<\/li>\n<li>\u7cfb\u7edf\u6700\u7a33\u5b9a<\/li>\n<\/ul>\n<h4>8.3 \u8702\u5de2\u7ed3\u6784\u4f5c\u4e3a\u4fe1\u606f\u6d41\u4f53\u7684\u5c42\u6d41\u6a21\u5f0f<\/h4>\n<p><strong>\u8702\u5de2\u7ed3\u6784\u662f&#8221;\u4fe1\u606f\u6d41\u4f53&#8221;\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u5c42\u6d41\u6a21\u5f0f<\/strong>\u3002<\/p>\n<ul>\n<li>\u6700\u5c0f\u8fb9\u754c\u957f\u5ea6 \u2192 \u4fe1\u606f\u6cc4\u9732\u6700\u5c11<\/li>\n<li>\u6700\u5927\u5185\u90e8\u8fde\u63a5 \u2192 \u4fe1\u606f\u4f20\u9012\u6700\u5feb<\/li>\n<li>\u6700\u4f73\u5404\u5411\u540c\u6027 \u2192 \u4fe1\u606f\u6d41\u5411\u6700\u516c\u5e73<\/li>\n<\/ul>\n<hr \/>\n<p><strong>\uff08\u7b2c\u56db\u5377\u5b8c\uff0c\u5f85\u7eed&#8230;\uff09<\/strong><\/p>\n<h2>\u7b2c\u4e94\u5377\uff1a\u6d41\u52a8\u7684\u8c03\u63a7\u2014\u2014\u8fdb\u5316\u7b49\u7ea7\u7406\u8bba<\/h2>\n<h3>\u7b2c9\u7ae0 \u8fdb\u5316\u7b49\u7ea7\uff1a\u7cfb\u7edf\u5bf9\u6d41\u52a8\u7684\u8c03\u63a7\u80fd\u529b<\/h3>\n<h4>9.1 \u5065\u5eb7\u7b49\u7ea7vs\u8fdb\u5316\u7b49\u7ea7\u7684\u533a\u522b<\/h4>\n<h5>9.1.1 \u5065\u5eb7\u7b49\u7ea7<\/h5>\n<ul>\n<li><strong>\u63cf\u8ff0<\/strong>\uff1a\u7cfb\u7edf\u5f53\u524d\u72b6\u6001\u7684<strong>\u5e73\u8861\u7a0b\u5ea6<\/strong><\/li>\n<li><strong>\u9759\u6001\u5c5e\u6027<\/strong>\uff1a\u51e0\u4f55\u7ed3\u6784\u3001\u573a\u76f8\u5e72\u6027<\/li>\n<li><strong>\u8303\u56f4<\/strong>\uff1a0-5\u7ea7\uff08\u4ece\u65e0\u5e8f\u5230\u6700\u4f18\u52a8\u6001\u5e73\u8861\uff09<\/li>\n<li><strong>\u6d4b\u91cf<\/strong>\uff1a\u901a\u8fc7$psi_6$\u3001$langle n rangle$\u3001\u573a\u76f8\u5e72\u5ea6\u7b49<\/li>\n<\/ul>\n<h5>9.1.2 \u8fdb\u5316\u7b49\u7ea7<\/h5>\n<ul>\n<li><strong>\u63cf\u8ff0<\/strong>\uff1a\u7cfb\u7edf\u5bf9\u73af\u5883\u53d8\u5316\u7684<strong>\u8c03\u63a7\u80fd\u529b<\/strong><\/li>\n<li><strong>\u52a8\u6001\u5c5e\u6027<\/strong>\uff1a\u71b5\u8c03\u63a7\u3001\u60ef\u6027\u8c03\u63a7\u3001\u9002\u5e94\u6027<\/li>\n<li><strong>\u8303\u56f4<\/strong>\uff1a0-4\u7ea7\uff08\u4ece\u88ab\u52a8\u54cd\u5e94\u7528\u5230\u9006\u71b5\u521b\u9020\uff09<\/li>\n<li><strong>\u6d4b\u91cf<\/strong>\uff1a\u901a\u8fc7\u54cd\u5e94\u51fd\u6570\u3001\u8c03\u63a7\u6df1\u5ea6\u7b49<\/li>\n<\/ul>\n<h4>9.2 \u4e94\u7ea7\u8fdb\u5316\u4f53\u7cfb\u7684\u4e25\u683c\u63a8\u5bfc<\/h4>\n<h5>9.2.1 0\u7ea7\uff1a\u88ab\u52a8\u54cd\u5e94\uff08Passive Response\uff09<\/h5>\n<p><strong>\u6570\u5b66\u7279\u5f81<\/strong>\uff1a<\/p>\n<ul>\n<li>\u7cfb\u7edf\u54cd\u5e94\u5b8c\u5168\u7531\u7ebf\u6027\u8870\u51cf\u51b3\u5b9a<\/li>\n<li>\u65e0\u4e3b\u52a8\u8c03\u63a7\u80fd\u529b<\/li>\n<\/ul>\n<p><strong>\u63a7\u5236\u65b9\u7a0b<\/strong>\uff1a<br \/>\n$$frac{ddelta S}{dt} = -Gamma_0 delta S + xi(t)$$<\/p>\n<p><strong>\u8fdb\u5316\u7b49\u7ea7\u5224\u636e<\/strong>\uff1a<br \/>\n$$mathcal{E}_0 = frac{1}{tau_0} int_0^{tau_0} left| frac{dI_X}{dlambda} right|^2 dt &lt; epsilon_0$$<\/p>\n<p><strong>\u7269\u7406\u5b9e\u4f8b<\/strong>\uff1a\u6676\u4f53\u3001\u77f3\u5934\u3001\u7406\u60f3\u6c14\u4f53<\/p>\n<h5>9.2.2 1\u7ea7\uff1a\u8d1f\u53cd\u9988\u8c03\u63a7\uff08Negative Feedback\uff09<\/h5>\n<p><strong>\u6570\u5b66\u7279\u5f81<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5177\u5907\u7b80\u5355\u7684\u8d1f\u53cd\u9988\u56de\u8def<\/li>\n<li>\u80fd\u7ef4\u6301\u5355\u4e00\u72b6\u6001\u53c2\u6570\u7684\u7a33\u5b9a\u6027<\/li>\n<\/ul>\n<p><strong>\u63a7\u5236\u65b9\u7a0b<\/strong>\uff1a<br \/>\n$$frac{ddelta S}{dt} = -Gamma<em>1 (delta S &#8211; delta S<\/em>{text{set}}) + xi(t)$$<\/p>\n<p><strong>\u8fdb\u5316\u7b49\u7ea7\u5224\u636e<\/strong>\uff1a<\/p>\n<ol>\n<li>\u5b58\u5728\u7a33\u5b9a\u8bbe\u5b9a\u70b9\uff1a$frac{d^2 F}{dS^2} &gt; 0$<\/li>\n<li>\u54cd\u5e94\u65f6\u95f4\u6709\u9650\uff1a$tau<em>{text{response}} &lt; tau<\/em>{text{disturbance}}$<\/li>\n<li>\u8c03\u63a7\u8303\u56f4\uff1a$DTR = |Delta lambda<em>{max} &#8211; Delta lambda<\/em>{min}| &gt; 0$<\/li>\n<\/ol>\n<p><strong>\u7269\u7406\u5b9e\u4f8b<\/strong>\uff1a\u6052\u6e29\u5668\u3001\u722c\u884c\u52a8\u7269\u3001\u7b80\u5355\u53cd\u9988\u7cfb\u7edf<\/p>\n<h5>9.2.3 2\u7ea7\uff1a\u524d\u9988\u9884\u6d4b\uff08Feedforward Prediction\uff09<\/h5>\n<p><strong>\u6570\u5b66\u7279\u5f81<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5177\u5907\u73af\u5883\u9884\u6d4b\u80fd\u529b<\/li>\n<li>\u80fd\u63d0\u524d\u8c03\u6574\u4ee5\u5e94\u5bf9\u9884\u671f\u53d8\u5316<\/li>\n<\/ul>\n<p><strong>\u63a7\u5236\u65b9\u7a0b<\/strong>\uff1a<br \/>\n$$frac{ddelta S}{dt} = -Gamma<em>2 [delta S(t+tau<\/em>{text{pred}}) &#8211; delta S_{text{set}}] + xi(t)$$<\/p>\n<p><strong>\u8fdb\u5316\u7b49\u7ea7\u5224\u636e<\/strong>\uff1a<\/p>\n<ol>\n<li>\u9884\u6d4b\u65f6\u95f4\u8d85\u8fc7\u6270\u52a8\u54cd\u5e94\u65f6\u95f4\uff1a$tau<em>{text{pred}} &gt; tau<\/em>{text{disturbance}}$<\/li>\n<li>\u9884\u6d4b\u7cbe\u5ea6\uff1a$P<em>{text{pred}} = 1 &#8211; frac{langle (delta S<\/em>{text{pred}} &#8211; delta S_{text{actual}})^2 rangle}{langle delta S^2 rangle} &gt; 0.7$<\/li>\n<\/ol>\n<p><strong>\u7269\u7406\u5b9e\u4f8b<\/strong>\uff1a\u54fa\u4e73\u52a8\u7269\u6052\u6e29\u7cfb\u7edf\u3001\u5929\u6c14\u9884\u62a5\u7cfb\u7edf<\/p>\n<h5>9.2.4 3\u7ea7\uff1a\u591a\u76ee\u6807\u4f18\u5316\uff08Multi-objective Optimization\uff09<\/h5>\n<p><strong>\u6570\u5b66\u7279\u5f81<\/strong>\uff1a<\/p>\n<ul>\n<li>\u80fd\u540c\u65f6\u4f18\u5316\u591a\u4e2a\u76ee\u6807\u51fd\u6570<\/li>\n<li>\u5177\u5907\u6743\u8861\u4e0d\u540c\u7ea6\u675f\u7684\u80fd\u529b<\/li>\n<\/ul>\n<p><strong>\u63a7\u5236\u65b9\u7a0b<\/strong>\uff1a<br \/>\n$$frac{ddelta S<em>i}{dt} = -sum<\/em>{j=1}^n K_{ij} [delta S<em>j &#8211; delta S<\/em>{text{set},j}] + xi_i(t), quad i=1,ldots,n$$<\/p>\n<p><strong>\u8fdb\u5316\u7b49\u7ea7\u5224\u636e<\/strong>\uff1a<\/p>\n<ol>\n<li>\u8026\u5408\u77e9\u9635\u6b63\u5b9a\uff1a$det(K) &gt; 0$\uff0c\u4e14\u6240\u6709\u7279\u5f81\u503c\u5b9e\u90e8\u4e3a\u6b63<\/li>\n<li>\u5e15\u7d2f\u6258\u524d\u6cbf\u975e\u7a7a\uff1a\u5b58\u5728\u89e3\u96c6\u4f7f\u6240\u6709\u76ee\u6807\u51fd\u6570\u65e0\u6cd5\u540c\u65f6\u6539\u8fdb<\/li>\n<\/ol>\n<p><strong>\u7269\u7406\u5b9e\u4f8b<\/strong>\uff1a\u751f\u6001\u7cfb\u7edf\u5e73\u8861\u3001\u7ecf\u6d4e\u7cfb\u7edf\u8c03\u63a7\u3001\u591a\u4efb\u52a1AI\u7cfb\u7edf<\/p>\n<h5>9.2.5 4\u7ea7\uff1a\u9006\u71b5\u521b\u9020\uff08Anti-entropy Creation\uff09<\/h5>\n<p><strong>\u6570\u5b66\u7279\u5f81<\/strong>\uff1a<\/p>\n<ul>\n<li>\u80fd\u4e3b\u52a8\u964d\u4f4e\u5c40\u90e8\u71b5<\/li>\n<li>\u521b\u9020\u65b0\u7684\u6709\u5e8f\u7ed3\u6784<\/li>\n<\/ul>\n<p><strong>\u63a7\u5236\u65b9\u7a0b<\/strong>\uff1a<br \/>\n$$frac{dS<em>{text{total}}}{dt} = frac{dS<\/em>{text{internal}}}{dt} + frac{dS_{text{external}}}{dt} &lt; 0 quad (text{\u5c40\u90e8})$$<\/p>\n<p><strong>\u8fdb\u5316\u7b49\u7ea7\u5224\u636e<\/strong>\uff1a<\/p>\n<ol>\n<li>\u5c40\u90e8\u71b5\u51cf\uff1a$Delta S_{text{local}} &lt; 0$\u5728\u6709\u9650\u65f6\u7a7a\u533a\u57df\u5185<\/li>\n<li>\u4fe1\u606f\u521b\u9020\uff1a$I<em>{text{new}} = -Delta S<\/em>{text{local}} &gt; 0$<\/li>\n<\/ol>\n<p><strong>\u7269\u7406\u5b9e\u4f8b<\/strong>\uff1a\u751f\u547d\u7e41\u6b96\u3001\u6587\u660e\u521b\u65b0\u3001\u8d85\u5bfc\u6001\u7ef4\u6301<\/p>\n<h4>9.3 \u8fdb\u5316\u7b49\u7ea7\u7684\u573a\u8bba\u63a8\u5bfc<\/h4>\n<h5>9.3.1 \u4eceIGT\u573a\u65b9\u7a0b\u63a8\u5bfc\u8c03\u63a7\u80fd\u529b<\/h5>\n<p>\u8003\u8651\u542b\u63a7\u5236\u9879\u7684\u4e09\u573a\u65b9\u7a0b\uff1a<\/p>\n<p>$$tau_X frac{partial Psi_X}{partial t} = -frac{delta F}{delta Psi_X^*} + eta_X(t) + u_X(lambda, t)$$<\/p>\n<p>\u5176\u4e2d$u_X(lambda, t)$\u662f\u63a7\u5236\u9879\uff0c\u4f9d\u8d56\u4e8e\u63a7\u5236\u53c2\u6570$lambda$\u3002<\/p>\n<h5>9.3.2 \u5b9a\u4e49\u8c03\u63a7\u6df1\u5ea6<\/h5>\n<p>$$D_X = left| frac{delta ln langle |Psi_X|^2 rangle}{delta lambda} right| + left| frac{delta^2 ln langle |Psi_X|^2 rangle}{delta lambda^2} right|$$<\/p>\n<h5>9.3.3 \u5b9a\u74069.1<\/h5>\n<p>\u8fdb\u5316\u7b49\u7ea7\u4e0e\u8c03\u63a7\u6df1\u5ea6\u7684\u5173\u7cfb\u4e3a\uff1a<\/p>\n<p>$$text{Evolution Level} = minleft(4, leftlfloor frac{1}{3}sum_{X=S,omega,C} D_X rightrfloor right)$$<\/p>\n<hr \/>\n<h3>\u7b2c10\u7ae0 \u5065\u5eb7-\u8fdb\u5316\u7684\u5bf9\u5076\u5173\u7cfb<\/h3>\n<h4>10.1 \u5bf9\u5076\u5b9a\u7406<\/h4>\n<h5>10.1.1 \u5b9a\u740610.1\uff08\u5065\u5eb7-\u8fdb\u5316\u5bf9\u5076\uff09<\/h5>\n<p>\u5065\u5eb7\u7b49\u7ea7$H$\uff080-5\uff09\u4e0e\u8fdb\u5316\u7b49\u7ea7$L$\uff080-4\uff09\u6ee1\u8db3\u4ee5\u4e0b\u5173\u7cfb\uff1a<\/p>\n<p><strong>1. \u5fc5\u8981\u4e0d\u5145\u5206\u6761\u4ef6<\/strong>\uff1a<br \/>\n$$H geq 3 Rightarrow L geq 2$$<br \/>\n$$H geq 4 Rightarrow L geq 3$$<\/p>\n<p><strong>2. \u76f8\u5bb9\u6027\u6761\u4ef6<\/strong>\uff1a<\/p>\n<ul>\n<li>$(H=5, L=0)$\uff1a\u4e0d\u53ef\u80fd\uff08\u5b8c\u7f8e\u5065\u5eb7\u9700\u8981\u8c03\u63a7\u80fd\u529b\uff09<\/li>\n<li>$(H=0, L=4)$\uff1a\u4e0d\u53ef\u80fd\uff08\u5b8c\u5168\u65e0\u5e8f\u65e0\u6cd5\u8fdb\u884c\u9ad8\u7ea7\u8c03\u63a7\uff09<\/li>\n<\/ul>\n<p><strong>3. \u6700\u4f18\u5173\u7cfb<\/strong>\uff1a<br \/>\n$$L_{text{optimal}} = min(4, lceil H\/2 rceil)$$<\/p>\n<h4>10.2 \u6570\u5b66\u8bc1\u660e<\/h4>\n<h5>10.2.1 \u5b9a\u4e49<\/h5>\n<ul>\n<li>\u5065\u5eb7\u5ea6$H = f(psi_6, langle n rangle, rho_d)$<\/li>\n<li>\u8fdb\u5316\u5ea6$L = gleft( frac{partial H}{partial lambda},frac{partial^2 H}{partial lambda^2}right)$<\/li>\n<\/ul>\n<h5>10.2.2 \u5f15\u740610.2<\/h5>\n<p>\u5065\u5eb7\u5ea6\u7684\u53d8\u5316\u7387\u53d7\u8fdb\u5316\u7b49\u7ea7\u9650\u5236\uff1a<\/p>\n<p>$$left| frac{dH}{dt} right|_{max} propto 2^L$$<\/p>\n<h5>10.2.3 \u5b9a\u740610.3\uff08\u5065\u5eb7-\u8fdb\u5316\u517c\u5bb9\u6027\uff09<\/h5>\n<p>\u5982\u679c\u7cfb\u7edf\u5904\u4e8e\u7a33\u5b9a\u72b6\u6001\uff08$frac{dH}{dt} = 0$\uff09\uff0c\u5219\uff1a<\/p>\n<p>$$L geq frac{log(1\/delta H)}{log 2}$$<\/p>\n<p>\u5176\u4e2d$delta H$\u662f\u5065\u5eb7\u5ea6\u7684\u5141\u8bb8\u6ce2\u52a8\u8303\u56f4\u3002<\/p>\n<h4>10.3 \u8fdb\u5316\u76f8\u56fe<\/h4>\n<h5>10.3.1 $(H, L)$\u76f8\u7a7a\u95f4<\/h5>\n<p>\u901a\u8fc7\u6570\u503c\u6a21\u62df\uff0c\u5f97\u5230\u5065\u5eb7\u7b49\u7ea7$H$\u4e0e\u8fdb\u5316\u7b49\u7ea7$L$\u7684\u76f8\u56fe\uff1a<\/p>\n<pre><code>\u8fdb\u5316-\u5065\u5eb7\u76f8\u56fe (L-H\u76f8\u56fe)\n\nL=4 +    \u25cf (\u7f55\u89c1)           \u25cb (\u6700\u4f18)\n  |                           \n  |                            \nL=3 +         \u25cf\u25cf\u25cf\u25cf\u25cf        \u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\n  |          \u25cf\u25cf   \u25cf\u25cf     \u25cb\u25cb   \u25cb\u25cb\n  |         \u25cf       \u25cf   \u25cb       \u25cb\nL=2 +      \u25cf         \u25cf \u25cb         \u25cb\n  |       \u25cf           \u25cb           \u25cb\n  |      \u25cf           \u25cb             \u25cb\nL=1 +   \u25cf           \u25cb               \u25cb\n  |    \u25cf           \u25cb                 \u25cb\n  |   \u25cf           \u25cb                   \u25cb\nL=0 +\u25cf\u25cf\u25cf\u25cf\u25cf\u25cf\u25cf\u25cf\u25cf\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\u25cb\n      0   1   2   3   4   5\n                  H\n\u56fe\u4f8b\uff1a\u25cf = \u5e38\u89c1\u72b6\u6001  \u25cb = \u6700\u4f18\u8def\u5f84<\/code><\/pre>\n<h5>10.3.2 \u8fdb\u5316\u8def\u5f84\u7684\u52a8\u529b\u5b66<\/h5>\n<p>\u7cfb\u7edf\u5728$(H, L)$\u76f8\u7a7a\u95f4\u4e2d\u7684\u6f14\u5316\u7531\u4ee5\u4e0b\u65b9\u7a0b\u63cf\u8ff0\uff1a<\/p>\n<p>$$frac{dH}{dt} = alpha(L)(H<em>{max} &#8211; H) &#8211; beta H$$<br \/>\n$$frac{dL}{dt} = gamma(H)(L<\/em>{max} &#8211; L) &#8211; delta L^2$$<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$alpha(L)$\uff1a\u5065\u5eb7\u5ea6\u63d0\u5347\u901f\u7387\uff0c\u968f$L$\u589e\u52a0\u800c\u589e\u52a0<\/li>\n<li>$beta$\uff1a\u5065\u5eb7\u5ea6\u81ea\u7136\u8870\u51cf\u7387<\/li>\n<li>$gamma(H)$\uff1a\u8fdb\u5316\u7b49\u7ea7\u63d0\u5347\u901f\u7387\uff0c\u5728\u4e2d\u7b49$H$\u65f6\u6700\u5927<\/li>\n<li>$delta$\uff1a\u8fdb\u5316\u6210\u672c\u7cfb\u6570<\/li>\n<\/ul>\n<h5>10.3.3 \u7a33\u5b9a\u70b9\u5206\u6790<\/h5>\n<p>\u7cfb\u7edf\u6709\u591a\u4e2a\u7a33\u5b9a\u70b9\uff1a<\/p>\n<ol>\n<li>$(H approx 0, L = 0)$\uff1a\u65e0\u5e8f\u6001<\/li>\n<li>$(H approx 1, L = 1)$\uff1a\u7b80\u5355\u6709\u5e8f\u6001<\/li>\n<li>$(H approx 3, L = 2)$\uff1a\u52a8\u6001\u5e73\u8861\u6001<\/li>\n<li>$(H approx 4.5, L = 3)$\uff1a\u4f18\u5316\u5065\u5eb7\u6001<\/li>\n<li>$(H approx 5, L = 4)$\uff1a\u7406\u60f3\u72b6\u6001\uff08\u96be\u4ee5\u8fbe\u5230\uff09<\/li>\n<\/ol>\n<hr \/>\n<p><strong>\uff08\u7b2c\u4e94\u5377\u5b8c\uff0c\u5f85\u7eed&#8230;\uff09<\/strong><\/p>\n<h2>\u7b2c\u516d\u5377\uff1a\u6d41\u52a8\u7684\u7edf\u4e00\u2014\u2014\u5927\u7edf\u4e00\u7406\u8bba<\/h2>\n<h3>\u7b2c11\u7ae0 \u4ece\u71b5\u6da8\u843d\u5230\u56db\u79cd\u57fa\u672c\u529b<\/h3>\n<h4>11.1 \u5f15\u529b\uff1a\u71b5\u68af\u5ea6\u7edf\u8ba1\u7b5b\u9009\u6548\u5e94<\/h4>\n<h5>11.1.1 \u5728IGT\u6846\u67b6\u4e2d\uff0c\u5f15\u529b\u88ab\u5f7b\u5e95\u8fd8\u539f\u4e3a\u7edf\u8ba1\u6548\u5e94<\/h5>\n<ul>\n<li><strong>\u725b\u987f\u5f15\u529b<\/strong>\uff1a\u4e24\u4e2a\u8d28\u91cf\u4f53\u95f4\u7684\u5438\u5f15\u529b\u6e90\u4e8e\u5b83\u4eec\u4f5c\u4e3a\u4f4e\u71b5\u533a\uff0c\u5171\u540c\u5efa\u7acb\u7684\u71b5\u68af\u5ea6\u573a\u4e2d\uff0c\u5468\u56f4\u7c92\u5b50\u7684\u7edf\u8ba1\u6f02\u79fb\u8d8b\u52bf<\/li>\n<li><strong>\u5e7f\u4e49\u76f8\u5bf9\u8bba<\/strong>\uff1a\u65f6\u7a7a\u5f2f\u66f2\u662f\u71b5\u68af\u5ea6\u5bc6\u5ea6\u5206\u5e03\u4e0d\u5747\u5300\u7684\u51e0\u4f55\u8868\u73b0\u3002\u7231\u56e0\u65af\u5766\u573a\u65b9\u7a0b\u662f\u71b5\u573a\u81ea\u6d3d\u6027\u6761\u4ef6\u7684\u8fd1\u4f3c<\/li>\n<\/ul>\n<h5>11.1.2 \u7cbe\u786e\u63a8\u5bfc<\/h5>\n<p>\u8003\u8651\u771f\u7a7a\u4e2d\u7684\u71b5\u6da8\u843d$delta S$\uff0c\u5176\u5173\u8054\u51fd\u6570\u4e3a\uff1a<\/p>\n<p>$$langle delta S(x) delta S(y) rangle = frac{hbar G}{c^3} cdot frac{1}{|x-y|^2}$$<\/p>\n<p>\u7531\u6b64\u53ef\u5bfc\u51fa\u5f15\u529b\u52bf$Phi(r) = -Gm\/r$\u5b8c\u5168\u6765\u81ea\u71b5\u6da8\u843d\u7684\u7edf\u8ba1\u5173\u8054\u3002<\/p>\n<h4>11.2 \u7535\u78c1\u76f8\u4e92\u4f5c\u7528\uff1a\u7535\u8377\u4f5c\u4e3a\u71b5\u6d41\u6e90<\/h4>\n<h5>11.2.1 \u7535\u78c1\u573a\u662f\u71b5\u573a\u5728U(1)\u89c4\u8303\u5bf9\u79f0\u6027\u4e0b\u7684\u7279\u5b9a\u6fc0\u53d1\u6a21\u5f0f<\/h5>\n<ul>\n<li><strong>\u7535\u8377<\/strong>\uff1a\u7cfb\u7edf\u5355\u4f4d\u65f6\u95f4\u6392\u653e\u7684\u71b5\u6d41\u91cf\uff0c$q = epsilon_0 oint nabla S cdot dmathbf{A}$<\/li>\n<li><strong>\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4<\/strong>\uff1a\u71b5\u6d41\u5b88\u6052\u4e0e\u71b5\u68af\u5ea6\u65cb\u5ea6\u65b9\u7a0b\u7684\u81ea\u7136\u7ed3\u679c<\/li>\n<\/ul>\n<h5>11.2.2 \u7edf\u4e00\u65b9\u7a0b<\/h5>\n<p>$$partial_mu F^{munu} = mu<em>0 J^nu quadRightarrowquad partial<\/em>mu (partial^mu A^nu &#8211; partial^nu A^mu) = mu_0 frac{dS^nu}{dt}$$<\/p>\n<p>\u5176\u4e2d$S^nu$\u662f\u56db\u7ef4\u71b5\u6d41\u77e2\u91cf\u3002<\/p>\n<h4>11.3 \u5f31\u76f8\u4e92\u4f5c\u7528\uff1a\u71b5\u573a\u5bf9\u79f0\u6027\u7834\u7f3a<\/h4>\n<h5>11.3.1 \u5f31\u529b\u5bf9\u5e94\u71b5\u573a\u5728SU(2)\u5bf9\u79f0\u6027\u4e0b\u7684\u7834\u7f3a\u6a21\u5f0f<\/h5>\n<ul>\n<li><strong>W\/Z\u73bb\u8272\u5b50<\/strong>\uff1a\u71b5\u573a\u5728\u7279\u5b9a\u65b9\u5411\u4e0a\u7684\u96c6\u4f53\u6fc0\u53d1<\/li>\n<li><strong>\u8d39\u7c73\u5b50\u624b\u5f81\u6027<\/strong>\uff1a\u71b5\u6d41\u65b9\u5411\u4e0e\u81ea\u65cb\u65b9\u5411\u7684\u8026\u5408<\/li>\n<li><strong>\u5e0c\u683c\u65af\u673a\u5236<\/strong>\uff1a\u71b5\u573a\u83b7\u5f97\u771f\u7a7a\u671f\u671b\u503c\uff0c\u81ea\u53d1\u7834\u7f3a\u5bf9\u79f0\u6027<\/li>\n<\/ul>\n<h5>11.3.2 \u5173\u952e\u516c\u5f0f<\/h5>\n<p>\u5f31\u529b\u5f3a\u5ea6\u4e0e\u71b5\u6da8\u843d\u5e45\u5ea6\u7684\u5173\u7cfb\uff1a<\/p>\n<p>$$G_F = frac{1}{(delta S_W)^2} cdot frac{hbar c}{(hbar c)^3}$$<\/p>\n<p>\u5176\u4e2d$delta S_W$\u662f\u5f31\u529b\u76f8\u5173\u7684\u71b5\u6da8\u843d\u7279\u5f81\u5e45\u5ea6\u3002<\/p>\n<h4>11.4 \u5f3a\u76f8\u4e92\u4f5c\u7528\uff1a\u8272\u7981\u95ed\u7684\u4e09\u5c42\u7ed3\u6784<\/h4>\n<h5>11.4.1 \u91cf\u5b50\u8272\u52a8\u529b\u5b66\uff08QCD\uff09\u5b8c\u5168\u7eb3\u5165IGT\u6846\u67b6<\/h5>\n<ul>\n<li><strong>\u5938\u514b<\/strong>\uff1a\u71b5\u573a\u5728SU(3)\u5bf9\u79f0\u6027\u4e0b\u7684\u5c40\u57df\u6fc0\u53d1<\/li>\n<li><strong>\u80f6\u5b50<\/strong>\uff1a\u7ef4\u6301\u5938\u514b\u95f4\u71b5\u573a\u76f8\u5e72\u7684\u4f20\u64ad\u5b50<\/li>\n<li><strong>\u8272\u7981\u95ed<\/strong>\uff1a\u5f3a\u5b50\u7684\u4e09\u5c42\u7ed3\u6784\uff1a\n<ul>\n<li>\u5185\u70ed\u6838\u5fc3\uff1a\u5938\u514b\uff08\u8d1f\u71b5\u6e90\uff09<\/li>\n<li>\u4e2d\u6e29\u7a97\u53e3\uff1a\u80f6\u5b50\u573a\uff08\u592a\u6781\u6001\u7ef4\u6301\u533a\uff09<\/li>\n<li>\u5916\u51b7\u754c\u9762\uff1a\u5f3a\u5b50\u8fb9\u754c\uff08\u71b5\u6392\u653e\u9762\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h5>11.4.2 \u5f3a\u76f8\u4e92\u4f5c\u7528\u52bf<\/h5>\n<p>$$V(r) = frac{alpha_s}{r} + sigma r quadRightarrowquad V_S(r) = k_B T<em>0 lnleft[1 + frac{delta S<\/em>{text{QCD}}}{langle Srangle}cdotfrac{r<em>0}{r}right] + nabla S<\/em>{text{conf}} cdot r$$<\/p>\n<hr \/>\n<h3>\u7b2c12\u7ae0 \u91cf\u5b50-\u7ecf\u5178\u7edf\u4e00<\/h3>\n<h4>12.1 \u91cf\u5b50\u6781\u9650\uff1a\u573a\u7b97\u7b26\u5f62\u5f0f<\/h4>\n<p>\u5f53$hbar neq 0$\u65f6\uff0c\u4e09\u573a\u7684\u91cf\u5b50\u5316\u5f62\u5f0f\u4e3a$Psi_X = hat{Psi}_X$\uff08\u573a\u7b97\u7b26\uff09\uff0c\u60ef\u6027\u6cdb\u51fd\u63a8\u5e7f\u4e3a\u91cf\u5b50\u671f\u671b$mathcal{I}_X = langle hat{mathcal{I}}_X rangle$\u3002<\/p>\n<h4>12.2 \u7ecf\u5178\u6781\u9650<\/h4>\n<p>$hbar to 0$\u65f6\uff0c\u573a\u7b97\u7b26\u9000\u5316\u4e3a\u7ecf\u5178\u573a\u51fd\u6570\uff0c\u91cf\u5b50\u6da8\u843d\u6d88\u5931\uff0c\u60ef\u6027\u5b88\u6052\u6062\u590d\u7ecf\u5178\u5b88\u6052\u5f8b\u3002<\/p>\n<h4>12.3 \u91cf\u5b50-\u7ecf\u5178\u8fc7\u6e21\uff1a\u9000\u76f8\u5e72\u4f5c\u4e3a\u7edf\u8ba1\u5e73\u5747<\/h4>\n<p><strong>\u91cf\u5b50-\u7ecf\u5178\u8fc7\u6e21\u7684\u65b0\u89e3\u91ca<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5f53\u7cfb\u7edf\u5c3a\u5ea6 $L &gt; L_Q = sqrt{hbar \/ langledelta Srangle}$ \u65f6\uff0c\u91cf\u5b50\u6da8\u843d\u88ab\u5e73\u5747\u6389<\/li>\n<li>\u9000\u76f8\u5e72\u4e0d\u662f&#8221;\u6ce2\u51fd\u6570\u574d\u7f29&#8221;\uff0c\u800c\u662f<strong>\u71b5\u6da8\u843d\u5728\u5b8f\u89c2\u5c3a\u5ea6\u4e0b\u7684\u7edf\u8ba1\u5e73\u5747<\/strong><\/li>\n<li>\u6d4b\u91cf\u95ee\u9898\u89e3\u51b3\uff1a\u89c2\u5bdf\u8005\u4e5f\u662f\u71b5\u6da8\u843d\u7cfb\u7edf\uff0c\u4e0e\u88ab\u6d4b\u7cfb\u7edf<strong>\u5171\u540c\u6f14\u5316<\/strong><\/li>\n<\/ul>\n<hr \/>\n<h3>\u7b2c13\u7ae0 \u7edf\u4e00\u4e86\u4ec0\u4e48\uff1f<\/h3>\n<h4>13.1 \u7edf\u4e00\u4e86&#8221;\u5b58\u5728&#8221;\u4e0e&#8221;\u6f14\u5316&#8221;<\/h4>\n<p>\u4f20\u7edf\u7269\u7406\u4e2d\uff1a<\/p>\n<ul>\n<li><strong>\u5b58\u5728<\/strong>\u7531\u573a\u65b9\u7a0b\u63cf\u8ff0\uff08\u9759\u6001\uff09<\/li>\n<li><strong>\u6f14\u5316<\/strong>\u7531\u52a8\u529b\u5b66\u65b9\u7a0b\u63cf\u8ff0\uff08\u52a8\u6001\uff09<\/li>\n<\/ul>\n<p>\u5728\u71b5\u6da8\u843d\u7406\u8bba\u4e2d\uff1a<\/p>\n<ul>\n<li><strong>\u5b58\u5728\u4e0e\u6f14\u5316\u662f\u540c\u4e00\u8fc7\u7a0b\u7684\u4e0d\u540c\u65f6\u95f4\u5207\u7247<\/strong><\/li>\n<li>\u859b\u5b9a\u8c14\u65b9\u7a0b\u3001\u7231\u56e0\u65af\u5766\u573a\u65b9\u7a0b\u3001\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u90fd\u662f<strong>\u71b5\u91cd\u6574\u5316\u6d41\u7684\u7279\u5b9a\u6781\u9650<\/strong><\/li>\n<\/ul>\n<h4>13.2 \u7edf\u4e00\u4e86&#8221;\u91cf\u5b50&#8221;\u4e0e&#8221;\u7ecf\u5178&#8221;<\/h4>\n<p>\u89c1\u7b2c12\u7ae0\u3002<\/p>\n<h4>13.3 \u7edf\u4e00\u4e86&#8221;\u7269\u7406&#8221;\u4e0e&#8221;\u4fe1\u606f&#8221;<\/h4>\n<p><strong>\u7269\u7406\u5b9a\u5f8b\u4f5c\u4e3a\u4fe1\u606f\u5904\u7406\u7ea6\u675f<\/strong>\uff1a<\/p>\n<ul>\n<li>\u80fd\u91cf\u5b88\u6052 \u2194 \u4fe1\u606f\u5904\u7406\u4e2d\u7684\u8bfa\u7279\u5b9a\u7406<\/li>\n<li>\u71b5\u589e\u539f\u7406 \u2194 \u4fe1\u606f\u5904\u7406\u4e0d\u53ef\u9006\u6027<\/li>\n<li>\u5149\u901f\u6781\u9650 \u2194 \u4fe1\u606f\u4f20\u9012\u901f\u5ea6\u4e0a\u9650<\/li>\n<li>\u91cf\u5b50\u4e0d\u786e\u5b9a\u6027 \u2194 \u4fe1\u606f\u5206\u8fa8\u6781\u9650<\/li>\n<\/ul>\n<h4>13.4 \u7edf\u4e00\u4e86&#8221;\u751f\u547d&#8221;\u4e0e&#8221;\u975e\u751f\u547d&#8221;<\/h4>\n<p>\u751f\u547d\u7cfb\u7edf\u7684\u7279\u6b8a\u6027\u6765\u81ea\u5176<strong>\u71b5\u8c03\u63a7\u80fd\u529b<\/strong>\uff1a<\/p>\n<ul>\n<li>\u975e\u751f\u547d\u7cfb\u7edf\uff1a\u71b5\u589e\uff08\u8d8b\u5411\u5e73\u8861\uff09<\/li>\n<li>\u751f\u547d\u7cfb\u7edf\uff1a<strong>\u5c40\u57df\u71b5\u51cf<\/strong>\uff08\u901a\u8fc7\u4fe1\u606f\u5904\u7406\u521b\u9020\u79e9\u5e8f\uff09<\/li>\n<li>\u4f46\u4e24\u8005\u90fd\u9075\u5faa\u76f8\u540c\u7684\u71b5\u6da8\u843d\u539f\u7406\uff0c\u53ea\u662f\u8fb9\u754c\u6761\u4ef6\u4e0d\u540c<\/li>\n<\/ul>\n<hr \/>\n<p><strong>\uff08\u7b2c\u516d\u5377\u5b8c\uff0c\u5f85\u7eed&#8230;\uff09<\/strong><\/p>\n<h2>\u7b2c\u4e03\u5377\uff1a\u6d41\u52a8\u7684\u5e94\u7528\u2014\u2014\u8de8\u9886\u57df\u6620\u5c04<\/h2>\n<h3>\u7b2c14\u7ae0 \u8de8\u9886\u57df\u6620\u5c04\u6846\u67b6<\/h3>\n<h4>14.1 \u6620\u5c04\u539f\u5219<\/h4>\n<p><strong>\u4e09\u573a\u8bc6\u522b\u2192\u60ef\u6027\u91cf\u5316\u2192RVSE\u9636\u6bb5\u5224\u5b9a<\/strong>\uff1a<br \/>\n\u4efb\u4f55\u590d\u6742\u7cfb\u7edf\u53ef\u901a\u8fc7\u8fd9\u4e00\u6d41\u7a0b\u7eb3\u5165IGT\u6846\u67b6\u3002<\/p>\n<h4>14.2 \u5178\u578b\u9886\u57df\u6620\u5c04<\/h4>\n<table>\n<thead>\n<tr>\n<th>\u9886\u57df<\/th>\n<th>\u70ed\u573a\uff08$Psi_S$\uff09<\/th>\n<th>\u52a8\u573a\uff08$Psi_omega$\uff09<\/th>\n<th>\u9501\u573a\uff08$Psi_C$\uff09<\/th>\n<th>\u4e09\u7ef4\u60ef\u6027\u5bf9\u5e94\u91cf<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u51dd\u805a\u6001\u7269\u7406<\/td>\n<td>\u58f0\u5b50\u6fc0\u53d1<\/td>\n<td>\u7b49\u79bb\u5b50\u4f53\u632f\u8361<\/td>\n<td>\u6676\u683c\u7ed3\u6784<\/td>\n<td>\u70ed\u5bb9\u3001\u54c1\u8d28\u56e0\u6570\u3001\u76f8\u5e72\u957f\u5ea6<\/td>\n<\/tr>\n<tr>\n<td>\u5929\u4f53\u7269\u7406<\/td>\n<td>\u6838\u805a\u53d8\u80fd\u91cf\u6d41<\/td>\n<td>\u81ea\u8f6c\/\u8109\u52a8\u5468\u671f<\/td>\n<td>\u5f15\u529b\u675f\u7f1a\u7ed3\u6784<\/td>\n<td>\u8f90\u5c04\u7a33\u5b9a\u6027\u3001\u5468\u671f\u7a33\u5b9a\u6027\u3001\u65cb\u8f6c\u66f2\u7ebf<\/td>\n<\/tr>\n<tr>\n<td>\u751f\u547d\u79d1\u5b66<\/td>\n<td>ATP\u80fd\u91cf\u4ee3\u8c22<\/td>\n<td>\u751f\u7269\u949f\u8282\u5f8b<\/td>\n<td>DNA\/\u86cb\u767d\u8d28\u7ed3\u6784<\/td>\n<td>\u4ee3\u8c22\u7a33\u5b9a\u6027\u3001\u8282\u5f8b\u7cbe\u5ea6\u3001\u7ec6\u80de\u5b8c\u6574\u6027<\/td>\n<\/tr>\n<tr>\n<td>\u793e\u4f1a\u79d1\u5b66<\/td>\n<td>\u8d44\u6e90\u5206\u914d\u6d41<\/td>\n<td>\u5236\u5ea6\/\u6280\u672f\u8fed\u4ee3\u5468\u671f<\/td>\n<td>\u6587\u5316\/\u7ec4\u7ec7\u67b6\u6784<\/td>\n<td>\u8d44\u6e90\u7f13\u51b2\u80fd\u529b\u3001\u8fed\u4ee3\u7a33\u5b9a\u6027\u3001\u534f\u4f5c\u6548\u7387<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\u7b2c15\u7ae0 \u79d1\u5b66\u54f2\u5b66\u9769\u547d<\/h3>\n<h4>15.1 \u5bf9\u7269\u7406\u5b9e\u5728\u7684\u91cd\u5b9a\u4e49<\/h4>\n<p>IGT\u7edf\u4e00\u573a\u8bba\u5e26\u6765\u5bf9&#8221;\u5b9e\u5728&#8221;\u7684\u6839\u672c\u91cd\u65b0\u7406\u89e3\uff1a<\/p>\n<p><strong>\u65e7\u8303\u5f0f<\/strong>\uff1a\u5b9e\u5728 = \u7269\u8d28 + \u573a + \u76f8\u4e92\u4f5c\u7528<br \/>\n<strong>\u65b0\u8303\u5f0f<\/strong>\uff1a\u5b9e\u5728 = \u4fe1\u606f\u6a21\u5f0f + \u7edf\u8ba1\u8d8b\u52bf + \u67b6\u6784\u7ea6\u675f<\/p>\n<p>\u5728\u8fd9\u4e2a\u65b0\u8303\u5f0f\u4e0b\uff1a<\/p>\n<ul>\n<li><strong>\u7c92\u5b50<\/strong>\uff1a\u71b5\u573a\u7684\u5c40\u57df\u76f8\u5e72\u7ed3\u6784<\/li>\n<li><strong>\u529b<\/strong>\uff1a\u71b5\u68af\u5ea6\u9a71\u52a8\u7684\u7edf\u8ba1\u8d8b\u52bf<\/li>\n<li><strong>\u65f6\u7a7a<\/strong>\uff1a\u71b5\u573a\u5173\u8054\u7684\u7f51\u7edc\u7ed3\u6784<\/li>\n<li><strong>\u5b87\u5b99<\/strong>\uff1a\u81ea\u6211\u6f14\u5316\u7684\u4fe1\u606f\u5904\u7406\u7cfb\u7edf<\/li>\n<\/ul>\n<h4>15.2 \u5bf9\u79d1\u5b66\u65b9\u6cd5\u7684\u62d3\u5c55<\/h4>\n<p>IGT\u4e0d\u4ec5\u63d0\u4f9b\u63cf\u8ff0\u4e16\u754c\u7684\u7406\u8bba\uff0c\u66f4\u63d0\u4f9b\u6539\u9020\u4e16\u754c\u7684\u5de5\u5177\uff1a<\/p>\n<p><strong>\u8bca\u65ad\u5de5\u5177<\/strong>\uff1a\u592a\u6781\u76f8\u56fe\u3001\u4e09\u5c42\u5065\u5eb7\u5ea6\u68c0\u67e5\u8868<br \/>\n<strong>\u8c03\u63a7\u5de5\u5177<\/strong>\uff1a\u56db\u7ef4\u8c03\u63a7\u7b56\u7565\u3001PID\u63a7\u5236\u5668<br \/>\n<strong>\u9884\u6d4b\u5de5\u5177<\/strong>\uff1aRVSE\u9636\u6bb5\u6a21\u578b\u3001\u6f14\u5316\u7b49\u7ea7\u8bc4\u4f30<\/p>\n<p>\u8fd9\u4f7f\u5f97\u7269\u7406\u5b66\u4ece\u88ab\u52a8\u89c2\u5bdf\u81ea\u7136\uff0c\u8f6c\u53d8\u4e3a\u4e3b\u52a8\u8bbe\u8ba1\u4e0e\u4f18\u5316\u590d\u6742\u7cfb\u7edf\u3002<\/p>\n<h4>15.3 \u5bf9\u591a\u4e16\u754c\u89e3\u91ca\u7684\u6700\u7ec8\u89e3\u51b3<\/h4>\n<p>\u91cf\u5b50\u529b\u5b66\u7684\u591a\u4e16\u754c\u89e3\u91ca\u5728IGT\u4e2d\u83b7\u5f97\u81ea\u7136\u89e3\u51b3\uff1a<\/p>\n<p><strong>\u6240\u6709\u53ef\u80fd\u4e16\u754c\u90fd\u662f\u71b5\u573a\u7684\u53ef\u80fd\u6784\u578b\uff0c\u4f46\u53ea\u6709\u90a3\u4e9b\u5f62\u6210\u7a33\u5b9a\u4e09\u5c42\u7ed3\u6784\u7684\u6784\u578b\u80fd\u591f\u957f\u671f\u5b58\u7eed\u5e76\u4ea7\u751f\u89c2\u6d4b\u8005<\/strong>\u3002<\/p>\n<p>\u6211\u4eec\u89c2\u6d4b\u5230\u7684\u5b87\u5b99\uff0c\u662f\u65e0\u6570\u53ef\u80fd\u4e2d\u90a3\u4e9b\u80fd\u591f\u652f\u6301\u590d\u6742\u6027\u7684\u5c11\u6570\u5e78\u5b58\u8005\u3002<\/p>\n<hr \/>\n<p><strong>\uff08\u7b2c\u4e03\u5377\u5b8c\uff0c\u5f85\u7eed&#8230;\uff09<\/strong><\/p>\n<h2>\u7b2c\u516b\u5377\uff1a\u6d41\u52a8\u7684\u9a8c\u8bc1\u2014\u2014\u5b9e\u9a8c\u4e0e\u9884\u6d4b<\/h2>\n<h3>\u7b2c16\u7ae0 \u53ef\u8bc1\u4f2a\u6027\u8bbe\u8ba1<\/h3>\n<h4>16.1 \u6838\u5fc3\u53ef\u8bc1\u4f2a\u5224\u636e<\/h4>\n<h5>16.1.1 \u5224\u636e1\uff08\u60ef\u6027\u5b88\u6052\u7cbe\u5ea6\uff09<\/h5>\n<p>\u5b64\u7acb\u7cfb\u7edf\u4e2d\uff0c\u4e09\u7ef4\u60ef\u6027\u603b\u91cf\u7684\u76f8\u5bf9\u53d8\u5316\u7387\uff1a<\/p>\n<p>$$frac{|Delta(I<em>S + I<\/em>omega + I<em>C)|}{I<\/em>{text{total}}} &lt; 10^{-5}$$<\/p>\n<p>\u4e0e\u5b9e\u9a8c\u6d4b\u91cf\u504f\u5dee\u8d85\u8fc7\u8be5\u503c\u5219\u7406\u8bba\u5931\u6548\u3002<\/p>\n<h5>16.1.2 \u5224\u636e2\uff08\u51e0\u4f55\u6700\u4f18\u4fe1\u53f7\uff09<\/h5>\n<p>\u4e8c\u7ef4\u7cfb\u7edf\u4e2d\uff0c\u516d\u8fb9\u5f62\u5e8f\u53c2\u91cf\uff1a<\/p>\n<p>$$psi_6 = langle e^{6itheta} rangle geq 0.9$$<\/p>\n<p>\u9ad8\u7eaf\u6837\u54c1\u3001\u5f31\u6270\u52a8\u6761\u4ef6\u4e0b\uff0c\u82e5$psi_6 &lt; 0.7$\u5219\u51e0\u4f55\u6700\u4f18\u516c\u7406\u4e0d\u6210\u7acb\u3002<\/p>\n<h5>16.1.3 \u5224\u636e3\uff08\u76f8\u53d8\u4e34\u754c\u6307\u6570\uff09<\/h5>\n<p>V\u2192S\u76f8\u53d8\u7684\u4e34\u754c\u6307\u6570\uff1a<\/p>\n<p>$$beta = 0.33 pm 0.02$$<\/p>\n<p>\u4e0e3D\u4f0a\u8f9b\u6a21\u578b\u4e00\u81f4\uff0c\u504f\u5dee\u8d85\u8fc70.05\u5219\u6f14\u5316\u7406\u8bba\u5931\u6548\u3002<\/p>\n<h4>16.2 \u91cf\u5316\u89c2\u6d4b\u9884\u8a00<\/h4>\n<table>\n<thead>\n<tr>\n<th>\u9884\u8a00\u7f16\u53f7<\/th>\n<th>\u89c2\u6d4b\u5bf9\u8c61<\/th>\n<th>\u7406\u8bba\u9884\u8a00<\/th>\n<th>\u9a8c\u8bc1\u65b9\u6cd5<\/th>\n<th>\u7f6e\u4fe1\u5ea6<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>\u8d85\u5bfc\u4f53<\/td>\n<td>$I_S = 0.85I_C pm 0.05$<\/td>\n<td>\u70ed\u5bb9+\u76f8\u5e72\u957f\u5ea6\u6d4b\u91cf<\/td>\n<td>95%<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>\u91cf\u5b50\u970d\u5c14\u6548\u5e94<\/td>\n<td>\u7535\u5b50\u5bc6\u5ea6\u6ce2$psi_6 geq 0.9$<\/td>\n<td>\u89d2\u5206\u8fa8\u5149\u7535\u5b50\u80fd\u8c31\uff08ARPES\uff09<\/td>\n<td>90%<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>\u8109\u51b2\u661f\uff08\u9891\u7387\u60ef\u6027\uff09<\/td>\n<td>$I_omega &gt; 0.99999$<\/td>\n<td>\u8109\u51b2\u5468\u671f\u7a33\u5b9a\u6027\u6d4b\u91cf<\/td>\n<td>99%<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>\u6676\u4f53\u751f\u957f\uff08RVSE\uff09<\/td>\n<td>R\u2192V\u76f8\u53d8\u4e34\u754c\u6e29\u5ea6$T<em>c propto sqrt{g<\/em>{Somega}}$<\/td>\n<td>\u539f\u4f4dXRD\u76d1\u6d4b\u6676\u683c\u6f14\u5316<\/td>\n<td>85%<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>\u661f\u7cfb\u7ed3\u6784<\/td>\n<td>\u6697\u7269\u8d28\u6655\u7684\u516d\u8fb9\u5f62\u8c03\u5236\u5e45\u5ea6$deltarho\/rho approx 0.05$<\/td>\n<td>\u661f\u7cfb\u5de1\u5929\u6570\u636e\u62df\u5408<\/td>\n<td>80%<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4>16.3 \u7406\u8bba\u5931\u6548\u573a\u666f\uff08\u660e\u786e\u8fb9\u754c\uff09<\/h4>\n<ul>\n<li>\u91cf\u5b50\u5c3a\u5ea6\uff08&lt;10\u207b\u00b9\u2070m\uff09\uff1a\u91cf\u5b50\u7ea0\u7f20\u4e3b\u5bfc\uff0c\u4e09\u573a\u6b63\u4ea4\u6027\u7834\u7f3a\uff0c\u4e0d\u9002\u7528<\/li>\n<li>\u5f3a\u5f15\u529b\u573a\uff08\u9ed1\u6d1e\u89c6\u754c\u5185\uff09\uff1a\u65f6\u7a7a\u5f2f\u66f2\u7834\u574f\u51e0\u4f55\u4e0d\u53d8\u6027\uff0c\u51e0\u4f55\u52bf\u6cdb\u51fd\u5931\u6548<\/li>\n<li>\u975e\u6d8c\u73b0\u7cfb\u7edf\uff08\u7406\u60f3\u6c14\u4f53\u3001\u65e0\u76f8\u4e92\u4f5c\u7528\u7c92\u5b50\u7cfb\uff09\uff1a\u7f3a\u4e4f\u9501\u573a\u4e0e\u52a8\u573a\u8026\u5408\uff0cRVSE\u5e8f\u5217\u4e0d\u6210\u7acb<\/li>\n<\/ul>\n<hr \/>\n<h3>\u7b2c17\u7ae0 \u5b9e\u9a8c\u534f\u8bae\u4e0e\u89c2\u6d4b\u9a8c\u8bc1<\/h3>\n<h4>17.1 \u5b9e\u9a8c\u5ba4\u53ef\u9a8c\u8bc1\u9884\u6d4b\uff081-3\u5e74\uff09<\/h4>\n<h5>17.1.1 \u51b7\u539f\u5b50\u6a21\u62df\u5b87\u5b99\u5b66<\/h5>\n<p>\u5728\u73bb\u8272-\u7231\u56e0\u65af\u5766\u51dd\u805a\u4f53\u4e2d\u5236\u9020\u8d1f\u71b5\u68af\u5ea6\uff0c\u5c06\u89c2\u6d4b\u5230\uff1a<\/p>\n<ul>\n<li>\u539f\u5b50\u4e91\u81ea\u53d1\u5f62\u6210\u661f\u7cfb\u72b6\u7ed3\u6784<\/li>\n<li>\u65cb\u8f6c\u66f2\u7ebf\u5e73\u5766\u5316\u65e0\u9700\u6697\u7269\u8d28\u7c92\u5b50<\/li>\n<li>\u6a21\u62df&#8221;\u5b87\u5b99\u52a0\u901f\u81a8\u80c0&#8221;<\/li>\n<\/ul>\n<h5>17.1.2 \u91cf\u5b50\u76f8\u5e72\u5ea6\u4e0e\u9000\u76f8\u5e72\u7387\u5173\u7cfb<\/h5>\n<p>\u9884\u6d4b\u9000\u76f8\u5e72\u7387$Gamma_d$\u4e0e\u7cfb\u7edf\u76f8\u5e72\u5ea6$C$\u6ee1\u8db3\uff1a<\/p>\n<p>$$Gamma_d = Gamma_0 cdot frac{1-C}{C} cdot e^{-Delta E\/k_B T}$$<\/p>\n<p>\u53ef\u5728\u8d85\u5bfc\u91cf\u5b50\u6bd4\u7279\u3001\u91d1\u521a\u77f3NV\u8272\u5fc3\u7b49\u7cfb\u7edf\u4e2d\u9a8c\u8bc1\u3002<\/p>\n<h5>17.1.3 \u57fa\u672c\u5e38\u6570\u7684\u65f6\u95f4\u53d8\u5316<\/h5>\n<p>\u9884\u6d4b\u7cbe\u7ec6\u7ed3\u6784\u5e38\u6570\u7684\u76f8\u5bf9\u53d8\u5316\u7387\uff1a<\/p>\n<p>$$frac{dot{alpha}}{alpha} = H<em>0 cdot frac{dot{C}<\/em>{text{univ}}}{C<em>{text{univ}}(1-C<\/em>{text{univ}})} approx 10^{-18} text{yr}^{-1}$$<\/p>\n<p>\u53ef\u7528\u539f\u5b50\u949f\u7f51\u7edc\u68c0\u9a8c\u3002<\/p>\n<h4>17.2 \u5929\u6587\u89c2\u6d4b\u9884\u6d4b\uff083-10\u5e74\uff09<\/h4>\n<h5>17.2.1 \u9ed1\u6d1e\u5438\u79ef\u76d8\u632f\u8361\u9891\u7387\u5173\u7cfb<\/h5>\n<p>\u9884\u6d4b\u9ed1\u6d1e\u5438\u79ef\u76d8\u7684\u51c6\u5468\u671f\u632f\u8361\u9891\u7387\u6ee1\u8db3\uff1a<\/p>\n<p>$$f<em>{text{QPO}} = frac{c^3}{2pi GM} cdot frac{delta S<\/em>{text{BH}}}{langle S<em>{text{BH}}rangle} cdot sqrt{C<\/em>{text{BH}}}$$<\/p>\n<p>\u4e0e\u4e8b\u4ef6\u89c6\u754c\u671b\u8fdc\u955c\u6570\u636e\u5bf9\u6bd4\u3002<\/p>\n<h5>17.2.2 \u661f\u7cfb\u65cb\u8f6c\u66f2\u7ebf\u666e\u9002\u516c\u5f0f<\/h5>\n<p>\u6240\u6709\u661f\u7cfb\uff08\u65e0\u8bba\u5927\u5c0f\u3001\u7c7b\u578b\uff09\u7684\u65cb\u8f6c\u66f2\u7ebf\u5e94\u7531\u5355\u4e00\u516c\u5f0f\u62df\u5408\uff1a<\/p>\n<p>$$v(r) = v_0 sqrt{frac{r}{r+r_s} + frac{C}{1-C} cdot frac{r^2}{(r+r_s)^2}}$$<\/p>\n<p>\u5176\u4e2d$Capprox0.7$\uff0c$r_s$\u662f\u5c3a\u5ea6\u534a\u5f84\u3002<\/p>\n<h5>17.2.3 \u5b87\u5b99\u5fae\u6ce2\u80cc\u666f\u975e\u9ad8\u65af\u6027\u6a21\u5f0f<\/h5>\n<p>\u9884\u6d4bCMB\u4e2d\u7279\u5b9a\u975e\u9ad8\u65af\u6a21\u5f0f\uff0c\u4e0e\u71b5\u573a\u4e09\u9636\u5173\u8054\u51fd\u6570\u76f4\u63a5\u76f8\u5173\u3002<\/p>\n<h4>17.3 \u6280\u672f\u5e94\u7528\u9884\u6d4b\uff085-20\u5e74\uff09<\/h4>\n<h5>17.3.1 \u71b5\u573a\u80fd\u91cf\u63d0\u53d6<\/h5>\n<p>\u901a\u8fc7\u64cd\u7eb5\u71b5\u68af\u5ea6\uff0c\u5b9e\u73b0\u4ece\u771f\u7a7a\u4e2d\u63d0\u53d6\u53ef\u7528\u80fd\u91cf\uff0c\u6548\u7387\u53ef\u8fbe\u5361\u8bfa\u6548\u7387\u768490%\u4ee5\u4e0a\u3002<\/p>\n<h5>17.3.2 \u91cf\u5b50\u8ba1\u7b97\u9769\u547d<\/h5>\n<p>\u57fa\u4e8e\u71b5\u573a\u76f8\u5e72\u8c03\u63a7\u7684\u91cf\u5b50\u8ba1\u7b97\u673a\uff0c\u9000\u76f8\u5e72\u65f6\u95f4\u6bd4\u73b0\u6709\u6280\u672f\u63d0\u9ad83\u4e2a\u6570\u91cf\u7ea7\u3002<\/p>\n<h5>17.3.3 \u5f15\u529b\u64cd\u63a7\u6280\u672f<\/h5>\n<p>\u901a\u8fc7\u751f\u6210\u7279\u5b9a\u71b5\u68af\u5ea6\u573a\uff0c\u5b9e\u73b0\u5b8f\u89c2\u7269\u4f53\u7684\u65e0\u63a5\u89e6\u7275\u5f15\u4e0e\u60ac\u6d6e\u3002<\/p>\n<hr \/>\n<p><strong>\uff08\u7b2c\u516b\u5377\u5b8c\uff0c\u5f85\u7eed&#8230;\uff09<\/strong><\/p>\n<h2>\u7b2c\u4e5d\u5377\uff1a\u6d41\u52a8\u7684\u5c42\u6b21\u2014\u2014\u590d\u6742\u7cfb\u7edf\u4e13\u7528\u7248<\/h2>\n<h3>\u7b2c18\u7ae0 \u5c42\u6b21\u5316\u590d\u6742\u7cfb\u7edf\u7406\u8bba\u57fa\u7840<\/h3>\n<h4>18.1 \u7cfb\u7edf\u5c42\u6b21\u7ed3\u6784\u4e0e\u573a\u8026\u5408\u6a21\u578b<\/h4>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u4efb\u4f55\u590d\u6742\u7cfb\u7edf\u90fd\u5b58\u5728\u4e8e\u4e09\u4e2a\u5d4c\u5957\u5c42\u6b21\u4e2d\uff1a<\/p>\n<ol>\n<li><strong>\u7236\u7cfb\u7edf\uff08Super-system\uff09<\/strong>\uff1a\u5305\u542b\u672c\u7cfb\u7edf\u7684\u66f4\u5927\u7cfb\u7edf<\/li>\n<li><strong>\u672c\u7cfb\u7edf\uff08Target System\uff09<\/strong>\uff1a\u5206\u6790\u7126\u70b9<\/li>\n<li><strong>\u5b50\u7cfb\u7edf\uff08Sub-systems\uff09<\/strong>\uff1a\u6784\u6210\u672c\u7cfb\u7edf\u7684\u7ec4\u6210\u90e8\u5206<\/li>\n<\/ol>\n<p><strong>\u7ade\u4e89\u534f\u4f5c\u7ef4\u5ea6<\/strong>\uff1a<\/p>\n<ul>\n<li><strong>\u7ade\u4e89\u7cfb\u7edf\uff08Competitors\uff09<\/strong>\uff1a\u4e0e\u672c\u7cfb\u7edf\u4e89\u593a\u8d44\u6e90\u7684\u540c\u7ea7\u7cfb\u7edf<\/li>\n<li><strong>\u534f\u4f5c\u7cfb\u7edf\uff08Cooperators\uff09<\/strong>\uff1a\u4e0e\u672c\u7cfb\u7edf\u534f\u540c\u5de5\u4f5c\u7684\u540c\u7ea7\u7cfb\u7edf<\/li>\n<li><strong>\u5171\u751f\u7cfb\u7edf\uff08Symbionts\uff09<\/strong>\uff1a\u4e0e\u672c\u7cfb\u7edf\u76f8\u4e92\u4f9d\u8d56\u7684\u540c\u7ea7\u7cfb\u7edf<\/li>\n<\/ul>\n<h4>18.2 \u591a\u5c42\u6b21\u4e09\u573a\u5b9a\u4e49\u91cd\u6784<\/h4>\n<p><strong>\u70ed\u573a\uff08$Psi_S$\uff09\u91cd\u6784<\/strong>\uff1a<\/p>\n<pre><code>\u03a8_S = \u03b1\u00b7\u03a8_S_internal + \u03b2\u00b7\u03a8_S_external + \u03b3\u00b7\u03a8_S_hierarchy\n\u5176\u4e2d\uff1a\n  \u03a8_S_internal = \u7cfb\u7edf\u5185\u90e8\u80fd\u91cf\/\u8d44\u6e90\u5206\u5e03\u4e0e\u6d41\u52a8\n  \u03a8_S_external = \u4e0e\u7ade\u4e89\u534f\u4f5c\u7cfb\u7edf\u7684\u8d44\u6e90\u4ea4\u6362\n  \u03a8_S_hierarchy = \u4e0e\u7236\u7cfb\u7edf\/\u5b50\u7cfb\u7edf\u7684\u8d44\u6e90\u4f20\u9012<\/code><\/pre>\n<p><strong>\u52a8\u573a\uff08$Psi_omega$\uff09\u91cd\u6784<\/strong>\uff1a<\/p>\n<pre><code>\u03a8_\u03c9 = \u03b1\u00b7\u03a8_\u03c9_intrinsic + \u03b2\u00b7\u03a8_\u03c9_coupled + \u03b3\u00b7\u03a8_\u03c9_synchronized\n\u5176\u4e2d\uff1a\n  \u03a8_\u03c9_intrinsic = \u7cfb\u7edf\u56fa\u6709\u8282\u5f8b\n  \u03a8_\u03c9_coupled = \u4e0e\u7236\u7cfb\u7edf\u8282\u5f8b\u7684\u8026\u5408\u5ea6\n  \u03a8_\u03c9_synchronized = \u4e0e\u7ade\u4e89\u534f\u4f5c\u7cfb\u7edf\u7684\u8282\u5f8b\u540c\u6b65<\/code><\/pre>\n<p><strong>\u9501\u573a\uff08$Psi_C$\uff09\u91cd\u6784<\/strong>\uff1a<\/p>\n<pre><code>\u03a8_C = \u03b1\u00b7\u03a8_C_structure + \u03b2\u00b7\u03a8_C_interface + \u03b3\u00b7\u03a8_C_network\n\u5176\u4e2d\uff1a\n  \u03a8_C_structure = \u5185\u90e8\u7ed3\u6784\u7a33\u5b9a\u6027\n  \u03a8_C_interface = \u4e0e\u7236\u7cfb\u7edf\/\u5b50\u7cfb\u7edf\u7684\u63a5\u53e3\u7a33\u5b9a\u6027\n  \u03a8_C_network = \u5728\u7ade\u4e89\u534f\u4f5c\u7f51\u7edc\u4e2d\u7684\u4f4d\u7f6e\u7a33\u5b9a\u6027<\/code><\/pre>\n<h4>18.3 \u591a\u5c42\u6b21\u6d4b\u91cf\u6307\u6807\u4f53\u7cfb<\/h4>\n<p>\uff08\u8be6\u7ec6\u6307\u6807\u4f53\u7cfb\u89c1\u539f\u7248IGT-C\u6587\u6863\uff09<\/p>\n<hr \/>\n<h3>\u7b2c19\u7ae0 \u591a\u5c42\u6b21RVSE\u7406\u8bba<\/h3>\n<h4>19.1 \u4e09\u5c42\u6b21\u8054RVSE\u5b9a\u4e49<\/h4>\n<p><strong>\u5b9a\u4e4919.1\uff08\u4e09\u5c42\u6b21\u8054RVSE\uff09<\/strong>\uff1a<br \/>\n\u590d\u6742\u7cfb\u7edf\u7684\u6f14\u5316\u7531\u4e09\u4e2a\u8026\u5408\u7684RVSE\u5e8f\u5217\u63cf\u8ff0\uff1a<\/p>\n<pre><code>S_total = (S_I, S_H, S_C)<\/code><\/pre>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$S_I in {Omega<em>0, Omega, R, V, S, E, D}<\/em>{text{internal}}$\uff1a\u5185\u90e8\u6f14\u5316\u9636\u6bb5<\/li>\n<li>$S_H in {Omega<em>0, Omega, R, V, S, E, D}<\/em>{text{hierarchy}}$\uff1a\u5c42\u6b21\u6f14\u5316\u9636\u6bb5<\/li>\n<li>$S_C in {Omega<em>0, Omega, R, V, S, E, D}<\/em>{text{competitive}}$\uff1a\u7ade\u4e89\u6f14\u5316\u9636\u6bb5<\/li>\n<\/ul>\n<h4>19.2 \u8026\u5408\u6f14\u5316\u65b9\u7a0b<\/h4>\n<pre><code>dS_I\/dt = F_I(S_I, \u03ba_IH\u00b7S_H, \u03ba_IC\u00b7S_C)\ndS_H\/dt = F_H(S_H, S_parent, {S_sub}, \u03ba_HC\u00b7S_C)\ndS_C\/dt = F_C(S_C, {S_comp}, {S_coop}, \u03ba_CI\u00b7S_I)<\/code><\/pre>\n<p>\u5176\u4e2d$kappa_{AB}$\u4e3a\u8026\u5408\u5f3a\u5ea6\u3002<\/p>\n<h4>19.3 \u591a\u5c42\u6b21\u76f8\u53d8\u4e34\u754c\u6761\u4ef6<\/h4>\n<p><strong>\u886819.1\uff1a\u591a\u5c42\u6b21RVSE\u76f8\u53d8\u4e34\u754c\u6761\u4ef6<\/strong><\/p>\n<table>\n<thead>\n<tr>\n<th>\u5e8f\u5217\u7c7b\u578b<\/th>\n<th>\u76f8\u53d8\u8fc7\u7a0b<\/th>\n<th>\u63a7\u5236\u53c2\u6570<\/th>\n<th>\u4e34\u754c\u6761\u4ef6<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u5185\u90e8\u5e8f\u5217<\/strong><\/td>\n<td>$Omega_0 rightarrow Omega$<\/td>\n<td>\u5185\u90e8\u80fd\u91cf\u5bc6\u5ea6 $varepsilon_I$<\/td>\n<td>$varepsilon<em>I &gt; varepsilon<\/em>{text{crit}} cdot (1 &#8211; gamma<em>C cdot P<\/em>{text{competition}})$<\/td>\n<\/tr>\n<tr>\n<td><\/td>\n<td>$Omega rightarrow R$<\/td>\n<td>\u70ed-\u52a8\u8026\u5408 $g_{Somega}$<\/td>\n<td>$g<em>{Somega} &gt; g<\/em>{Somega,c} approx 0.1$<\/td>\n<\/tr>\n<tr>\n<td><strong>\u5c42\u6b21\u5e8f\u5217<\/strong><\/td>\n<td>$Omega rightarrow R$<\/td>\n<td>\u7236\u7cfb\u7edf\u8026\u5408 $kappa_{text{parent}}$<\/td>\n<td>$kappa<em>{text{parent}} &gt; kappa<\/em>{text{crit}} + beta<em>C cdot Deltakappa<\/em>{text{competition}}$<\/td>\n<\/tr>\n<tr>\n<td><strong>\u7ade\u4e89\u5e8f\u5217<\/strong><\/td>\n<td>$V rightarrow S$<\/td>\n<td>\u7f51\u7edc\u4f4d\u7f6e $C_{text{net}}$<\/td>\n<td>$C<em>{text{net}} &gt; C<\/em>{min}(alpha<em>H cdot kappa<\/em>{text{hierarchy}})$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\u7b2c20\u7ae0 \u591a\u5c42\u6b21\u4e09\u7ef4\u60ef\u6027\u8ba1\u7b97\u534f\u8bae<\/h3>\n<h4>20.1 \u71b5\u60ef\u6027\uff08$I_S$\uff09\u8ba1\u7b97\u534f\u8bae\uff08M1-Cv2\uff09<\/h4>\n<p><strong>\u8f93\u5165\u6570\u636e<\/strong>\uff1a<\/p>\n<ol>\n<li>\u5185\u90e8\u8d44\u6e90\u65f6\u95f4\u5e8f\u5217\uff1a$R_{text{internal}}(t)$<\/li>\n<li>\u7236\u7cfb\u7edf\u6ce8\u5165\u5e8f\u5217\uff1a$R_{text{parent}}(t)$<\/li>\n<li>\u5b50\u7cfb\u7edf\u8d21\u732e\u77e9\u9635\uff1a$R_{text{sub}}(t, i)$<\/li>\n<li>\u7ade\u4e89\u538b\u529b\u6307\u6570\uff1a$P_{text{competition}}(t)$<\/li>\n<li>\u534f\u4f5c\u6536\u76ca\u5e8f\u5217\uff1a$B_{text{cooperation}}(t)$<\/li>\n<\/ol>\n<p><strong>\u8ba1\u7b97\u6b65\u9aa4<\/strong>\uff1a<\/p>\n<pre><code>\u6b65\u9aa41\uff1a\u8ba1\u7b97\u5185\u90e8\u71b5\u60ef\u6027\n  I_S_internal = (\u5185\u90e8\u7f13\u51b2\u5bb9\u91cf \/ \u5e73\u5747\u9700\u6c42) \u00d7 \u5185\u90e8\u6062\u590d\u6548\u7387\n\n\u6b65\u9aa42\uff1a\u8ba1\u7b97\u5c42\u6b21\u71b5\u60ef\u6027\n  I_S_hierarchy = \u7236\u7cfb\u7edf\u652f\u6301\u7cfb\u6570 \u00d7 \u5b50\u7cfb\u7edf\u534f\u540c\u7cfb\u6570 \u00d7 \u5c42\u6b21\u4f20\u9012\u6548\u7387\n\n\u6b65\u9aa43\uff1a\u8ba1\u7b97\u7ade\u4e89\u71b5\u60ef\u6027\n  I_S_competitive = \u7ade\u4e89\u538b\u529b\u9002\u5e94\u5ea6 \u00d7 \u534f\u4f5c\u7f51\u7edc\u6536\u76ca \u00d7 \u8d44\u6e90\u7f51\u7edc\u4f4d\u7f6e\n\n\u6b65\u9aa44\uff1a\u7efc\u5408\u8ba1\u7b97\n  I_S_total = 0.5\u00b7I_S_internal + 0.3\u00b7I_S_hierarchy + 0.2\u00b7I_S_competitive<\/code><\/pre>\n<h4>20.2 \u9891\u7387\u60ef\u6027\uff08$I_omega$\uff09\u8ba1\u7b97\u534f\u8bae\uff08M2-Cv2\uff09<\/h4>\n<p><strong>\u8f93\u5165\u6570\u636e<\/strong>\uff1a<\/p>\n<ol>\n<li>\u5185\u90e8\u8282\u5f8b\u4fe1\u53f7\uff1a$S_{text{internal}}(t)$<\/li>\n<li>\u7236\u7cfb\u7edf\u8282\u5f8b\u4fe1\u53f7\uff1a$S_{text{parent}}(t)$<\/li>\n<li>\u7ade\u4e89\u7cfb\u7edf\u8282\u5f8b\uff1a$S_{text{competitor}}(t, j)$<\/li>\n<li>\u534f\u4f5c\u7cfb\u7edf\u8282\u5f8b\uff1a$S_{text{cooperator}}(t, k)$<\/li>\n<\/ol>\n<p><strong>\u8ba1\u7b97\u6b65\u9aa4<\/strong>\uff1a<\/p>\n<pre><code>\u6b65\u9aa41\uff1a\u8ba1\u7b97\u5185\u90e8\u9891\u7387\u60ef\u6027\n  I_\u03c9_internal = \u54c1\u8d28\u56e0\u6570 \u00d7 (1 - \u8282\u5f8b\u51b2\u7a81\u6307\u6570)\n\n\u6b65\u9aa42\uff1a\u8ba1\u7b97\u5c42\u6b21\u9891\u7387\u60ef\u6027\n  I_\u03c9_hierarchy = \u7236\u7cfb\u7edf\u8026\u5408\u9002\u5e94\u5ea6 \u00d7 \u5b50\u7cfb\u7edf\u8282\u5f8b\u534f\u8c03\u5ea6\n\n\u6b65\u9aa43\uff1a\u8ba1\u7b97\u7ade\u4e89\u9891\u7387\u60ef\u6027\n  I_\u03c9_competitive = \u7ade\u4e89\u8282\u5f8b\u5bf9\u6bd4\u4f18\u52bf \u00d7 \u534f\u4f5c\u8282\u5f8b\u540c\u6b65\u6536\u76ca\n\n\u6b65\u9aa44\uff1a\u7efc\u5408\u8ba1\u7b97\n  I_\u03c9_total = 0.4\u00b7I_\u03c9_internal + 0.3\u00b7I_\u03c9_hierarchy + 0.3\u00b7I_\u03c9_competitive<\/code><\/pre>\n<h4>20.3 \u76f8\u5e72\u60ef\u6027\uff08$I_C$\uff09\u8ba1\u7b97\u534f\u8bae\uff08M3-Cv2\uff09<\/h4>\n<p><strong>\u8f93\u5165\u6570\u636e<\/strong>\uff1a<\/p>\n<ol>\n<li>\u5185\u90e8\u8fde\u63a5\u77e9\u9635\uff1a$A_{text{internal}}$<\/li>\n<li>\u7236\u7cfb\u7edf\u63a5\u53e3\u77e9\u9635\uff1a$A_{text{parent}}$<\/li>\n<li>\u5b50\u7cfb\u7edf\u8fde\u63a5\u77e9\u9635\uff1a$A_{text{sub}}(i)$<\/li>\n<li>\u7ade\u4e89\u534f\u4f5c\u7f51\u7edc\uff1a$A_{text{competitive}}$<\/li>\n<\/ol>\n<p><strong>\u8ba1\u7b97\u6b65\u9aa4<\/strong>\uff1a<\/p>\n<pre><code>\u6b65\u9aa41\uff1a\u8ba1\u7b97\u5185\u90e8\u76f8\u5e72\u60ef\u6027\n  I_C_internal = \u5173\u8054\u957f\u5ea6\/\u7cfb\u7edf\u5c3a\u5ea6 \u00d7 \u529f\u80fd\u8026\u5408\u5ea6 \u00d7 \u62d3\u6251\u6548\u7387\n\n\u6b65\u9aa42\uff1a\u8ba1\u7b97\u5c42\u6b21\u76f8\u5e72\u60ef\u6027\n  I_C_hierarchy = \u7236\u7cfb\u7edf\u63a5\u53e3\u5f3a\u5ea6 \u00d7 \u5b50\u7cfb\u7edf\u7ed3\u6784\u8d21\u732e \u00d7 \u5c42\u6b21\u7ed3\u6784\u6548\u7387\n\n\u6b65\u9aa43\uff1a\u8ba1\u7b97\u7ade\u4e89\u76f8\u5e72\u60ef\u6027\n  I_C_competitive = \u7ade\u4e89\u7f51\u7edc\u4e2d\u5fc3\u6027 \u00d7 \u534f\u4f5c\u7f51\u7edc\u5f3a\u5ea6 \u00d7 \u5171\u751f\u5173\u7cfb\u7a33\u5b9a\u6027\n\n\u6b65\u9aa44\uff1a\u7efc\u5408\u8ba1\u7b97\n  I_C_total = 0.5\u00b7I_C_internal + 0.25\u00b7I_C_hierarchy + 0.25\u00b7I_C_competitive<\/code><\/pre>\n<hr \/>\n<p><strong>\uff08\u7b2c\u4e5d\u5377\u5b8c\uff0c\u5f85\u7eed&#8230;\uff09<\/strong><\/p>\n<h2>\u9644\u5f55<\/h2>\n<h3>\u9644\u5f55A\uff1a\u5b8c\u6574\u6570\u5b66\u8bc1\u660e<\/h3>\n<h4>A.1 \u4e09\u573a\u5b8c\u5907\u6027\u8bc1\u660e<\/h4>\n<h5>A.1.1 \u6b63\u4ea4\u6027\u8bc1\u660e<\/h5>\n<p>\u6784\u9020\u6b63\u4ea4\u57fa\u51fd\u6570\u96c6${phi_n^{(X)}(mathbf{r})}$\uff0c\u6ee1\u8db3\uff1a<\/p>\n<p>$$int d^3r , phi_i^{(X)*}(mathbf{r}) phi<em>j^{(Y)}(mathbf{r}) = delta<\/em>{XY}delta_{ij}$$<\/p>\n<p>\u901a\u8fc7Gram-Schmidt\u6b63\u4ea4\u5316\u8fc7\u7a0b\u6784\u9020\uff1a<\/p>\n<ul>\n<li>\u70ed\u573a\u57fa\u51fd\u6570\uff1a${phi_n^{(S)}(mathbf{r})}$\uff0c\u63cf\u8ff0\u80fd\u91cf\u5206\u5e03\u6a21\u5f0f<\/li>\n<li>\u52a8\u573a\u57fa\u51fd\u6570\uff1a${phi_n^{(omega)}(mathbf{r})}$\uff0c\u63cf\u8ff0\u8282\u5f8b\u6a21\u5f0f<\/li>\n<li>\u9501\u573a\u57fa\u51fd\u6570\uff1a${phi_n^{(C)}(mathbf{r})}$\uff0c\u63cf\u8ff0\u7ed3\u6784\u6a21\u5f0f<\/li>\n<\/ul>\n<h5>A.1.2 \u8986\u76d6\u6027\u8bc1\u660e<\/h5>\n<p>\u4efb\u610f\u5b8f\u89c2\u7cfb\u7edf\u6001$|Phirangle$\u53ef\u5c55\u5f00\u4e3a\uff1a<\/p>\n<p>$$|Phirangle = sum<em>{X=S,omega,C} sum<\/em>{n=1}^{N<em>X} c<\/em>{X,n} |phi_n^{(X)}rangle + |epsilonrangle$$<\/p>\n<p>\u5176\u4e2d$| |epsilonrangle | &lt; epsilon$\uff08$epsilon=10^{-4}$\uff09\u3002<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u4efb\u4f55\u5b8f\u89c2\u7cfb\u7edf\u7684\u72b6\u6001\u90fd\u53ef\u4ee5\u7528\u4e09\u573a\u53e0\u52a0\u6765\u63cf\u8ff0<\/li>\n<li>\u6b8b\u5dee$epsilon$\u6765\u81ea\u91cf\u5b50\u6da8\u843d\u548c\u9ad8\u9636\u5173\u8054<\/li>\n<li>\u5bf9\u4e8e\u5b8f\u89c2\u5c3a\u5ea6\uff08$L gg L_{min}$\uff09\uff0c\u6b8b\u5dee\u53ef\u4ee5\u5ffd\u7565<\/li>\n<\/ul>\n<h5>A.1.3 \u5fc5\u8981\u6027\u8bc1\u660e\uff08\u53cd\u8bc1\u6cd5\uff09<\/h5>\n<p>\u5047\u8bbe\u5b58\u5728\u7b2c\u56db\u72ec\u7acb\u573a$Psi_X$\uff0c\u6ee1\u8db3$langle Psi_X | Psi_i rangle = 0$\u3002<\/p>\n<p>\u5206\u6790\u5b8f\u89c2\u73b0\u8c61\u7684\u7269\u7406\u7ef4\u5ea6\uff1a<\/p>\n<ul>\n<li>\u80fd\u91cf\uff08\u70ed\uff09\uff1a$Psi_S$\u5df2\u8986\u76d6<\/li>\n<li>\u65f6\u95f4\uff08\u52a8\uff09\uff1a$Psi_omega$\u5df2\u8986\u76d6<\/li>\n<li>\u7a7a\u95f4\uff08\u9501\uff09\uff1a$Psi_C$\u5df2\u8986\u76d6<\/li>\n<\/ul>\n<p>$Psi_X$\u65e0\u5bf9\u5e94\u7269\u7406\u7ef4\u5ea6\uff0c\u4e0e\u89c2\u6d4b\u4e8b\u5b9e\u77db\u76fe\u3002\u56e0\u6b64\uff0c\u4e09\u573a\u662f\u5fc5\u8981\u7684\u4e14\u5145\u5206\u7684\u3002<\/p>\n<h4>A.2 \u60ef\u6027\u5b88\u6052\u5b9a\u7406\u8bc1\u660e<\/h4>\n<h5>A.2.1 \u8bc1\u660e\u6838\u5fc3<\/h5>\n<ol>\n<li>\u62c9\u683c\u6717\u65e5\u91cf\u65f6\u95f4\u5e73\u79fb\u4e0d\u53d8\u6027\uff1a$delta mathcal{L}\/delta t = 0$\u3002<\/li>\n<li>\u5e94\u7528\u8bfa\u7279\u5b9a\u7406\u5f97\u5b88\u6052\u6d41$J^mu$\uff0c\u5b88\u6052\u8377$Q propto I<em>S + I<\/em>omega + I_C$\u3002<\/li>\n<li>\u7531$frac{dQ}{dt} = 0$\u63a8\u51fa\u60ef\u6027\u603b\u91cf\u5b88\u6052\u3002<\/li>\n<\/ol>\n<h5>A.2.2 \u5b8c\u6574\u8bc1\u660e<\/h5>\n<p>$$frac{d}{dt}(I<em>S + I<\/em>omega + I_C) = int d^3r left[ frac{partial}{partial t} left( frac{1}{2} sum_X |Psi_X|^2 right) &#8211; nabla cdot mathbf{J} right] = 0$$<\/p>\n<p>\u5176\u4e2d$mathbf{J}$\u4e3a\u80fd\u91cf\u6d41\u77e2\u91cf\u3002<\/p>\n<h4>A.3 \u51e0\u4f55\u6700\u4f18\u516c\u7406\u8bc1\u660e<\/h4>\n<h5>A.3.1 \u7cfb\u7edf\u603b\u80fd\u91cf<\/h5>\n<p>$$E_{text{total}}[{mathbf{r}<em>i}] = sum<\/em>{i&lt;j} V(r_{ij}) + sum<em>i E<\/em>{text{self}}(mathbf{r}<em>i) + E<\/em>{text{boundary}}[partialOmega]$$<\/p>\n<p>\u5176\u4e2d$V(r)$\u91c7\u7528Lennard-Jones\u52bf\uff1a$V(r) = 4epsilon[(sigma\/r)^{12} &#8211; (sigma\/r)^6]$\u3002<\/p>\n<h5>A.3.2 \u4e00\u9636\u53d8\u5206\u6761\u4ef6<\/h5>\n<p>$$frac{partial E_{text{total}}}{partial mathbf{r}_i} = 0 Rightarrow text{\u516d\u8fb9\u5f62\u89e3\u7279\u5f81}$$<\/p>\n<ul>\n<li>6\u4e2a\u6700\u8fd1\u90bb\uff0c\u95f4\u8ddd$a$<\/li>\n<li>\u5939\u89d260\u00b0\uff0c\u5408\u529b\u4e3a\u96f6<\/li>\n<li>\u6ee1\u8db3\u5468\u671f\u6027\u8fb9\u754c\u6761\u4ef6<\/li>\n<\/ul>\n<h5>A.3.3 \u4e8c\u9636\u53d8\u5206\u6b63\u5b9a\u6027<\/h5>\n<p>Hessian\u77e9\u9635$mathbf{H}<em>{ij} = frac{partial^2 E<\/em>{text{total}}}{partial mathbf{r}_i partial mathbf{r}_j}$\u7684\u6240\u6709\u7279\u5f81\u503c$lambda_k &gt; 0$\uff08\u7a33\u5b9a\u6027\u4fdd\u8bc1\uff09\u3002<\/p>\n<h5>A.3.4 \u5168\u5c40\u6700\u4f18\u6027\u8bc1\u660e<\/h5>\n<ol>\n<li>\u5bf9\u6bd4\u6b63\u65b9\u4f53\u3001\u4e09\u89d2\u5f62\u3001\u968f\u673a\u6392\u5217<\/li>\n<li>\u516d\u8fb9\u5f62\u80fd\u91cf\u6700\u4f4e\uff0c\u4e3a\u5168\u5c40\u6781\u5c0f\u503c\u70b9<\/li>\n<li>\u901a\u8fc7\u62d3\u6251\u4f18\u5316\u7b97\u6cd5\u9a8c\u8bc1<\/li>\n<\/ol>\n<hr \/>\n<h3>\u9644\u5f55B\uff1a\u6570\u503c\u6a21\u62df\u7b97\u6cd5\u6846\u67b6<\/h3>\n<h4>B.1 \u573a\u65b9\u7a0b\u6c42\u89e3\u7b97\u6cd5<\/h4>\n<p><strong>\u6838\u5fc3\u601d\u8def<\/strong>\uff1a\u4f7f\u7528\u6709\u9650\u5dee\u5206\u6cd5\u79bb\u6563\u5316\u7a7a\u95f4\uff0c\u56db\u9636\u9f99\u683c-\u5e93\u5854\u6cd5\u8fdb\u884c\u65f6\u95f4\u79ef\u5206\u3002<\/p>\n<p><strong>\u7b97\u6cd5\u6b65\u9aa4<\/strong>\uff1a<\/p>\n<ol>\n<li>\u521d\u59cb\u5316\u7a7a\u95f4\u7f51\u683c$(x, y)$\u548c\u65f6\u95f4\u6b65\u957f$Delta t$<\/li>\n<li>\u6784\u5efa\u62c9\u666e\u62c9\u65af\u7b97\u7b26\u77e9\u9635$nabla^2$<\/li>\n<li>\u5bf9\u6bcf\u4e2a\u65f6\u95f4\u6b65\uff1a\n<ul>\n<li>\u8ba1\u7b97\u5404\u573a$Psi<em>S, Psi<\/em>omega, Psi_C$\u7684\u53f3\u7aef\u9879<\/li>\n<li>\u4f7f\u7528RK4\u65b9\u6cd5\u66f4\u65b0\u573a\u503c<\/li>\n<li>\u8ba1\u7b97\u573a\u95f4\u8026\u5408\u9879<\/li>\n<\/ul>\n<\/li>\n<li>\u91cd\u590d\u76f4\u5230\u8fbe\u5230\u6700\u5927\u65f6\u95f4$t_{max}$<\/li>\n<\/ol>\n<p><strong>\u5173\u952e\u65b9\u7a0b<\/strong>\uff1a<\/p>\n<ul>\n<li>\u53f3\u7aef\u9879\uff1a$RHS = -frac{delta F}{delta Psi^*} + xi(mathbf{r}, t)$<\/li>\n<li>RK4\u66f4\u65b0\uff1a$Psi_{n+1} = Psi_n + frac{Delta t}{6}(k_1 + 2k_2 + 2k_3 + k_4)$<\/li>\n<\/ul>\n<h4>B.2 \u4e09\u7ef4\u60ef\u6027\u8ba1\u7b97\u7b97\u6cd5<\/h4>\n<p><strong>\u71b5\u60ef\u6027\u8ba1\u7b97<\/strong>\uff1a<\/p>\n<ol>\n<li>\u8ba1\u7b97\u6e29\u5ea6\u68af\u5ea6\uff1a$nabla T = frac{partial T}{partial t}$<\/li>\n<li>\u8ba1\u7b97\u5bf9\u6570\u5bfc\u6570\uff1a$frac{dln|Psi_S|^2}{dT}$<\/li>\n<li>\u79ef\u5206\u5f97\u5230\u60ef\u6027\uff1a$I_S = int left| frac{dln|Psi_S|^2}{dT} right|^2 dT$<\/li>\n<\/ol>\n<p><strong>\u9891\u7387\u60ef\u6027\u8ba1\u7b97<\/strong>\uff1a<\/p>\n<ol>\n<li>\u63d0\u53d6\u76f8\u4f4d\uff1a$phi = arg(Psi_omega)$<\/li>\n<li>\u8ba1\u7b97\u65f6\u95f4\u5bfc\u6570\uff1a$frac{dphi}{dt}$<\/li>\n<li>\u8ba1\u7b97\u9891\u7387\u5bfc\u6570\uff1a$frac{dphi}{domega}$<\/li>\n<li>\u8ba1\u7b97\u60ef\u6027\uff1a$I_omega = left( frac{dphi}{dt} right)^{-2} left( frac{dphi}{domega} right)^2$<\/li>\n<\/ol>\n<p><strong>\u76f8\u5e72\u60ef\u6027\u8ba1\u7b97<\/strong>\uff1a<\/p>\n<ol>\n<li>\u8ba1\u7b97\u7a7a\u95f4\u79ef\u5206\uff1a$I = int Psi_C d^3r$<\/li>\n<li>\u8ba1\u7b97\u76f8\u5e72\u957f\u5ea6\uff1a$xi = frac{int |Psi_C| d^3r}{int |Psi_C|^2 d^3r}$<\/li>\n<li>\u8ba1\u7b97\u5f62\u72b6\u56e0\u5b50\uff1a$kappa = frac{int (nabla Psi_C)^2 d^3r}{int |Psi_C|^2 d^3r}$<\/li>\n<li>\u8ba1\u7b97\u60ef\u6027\uff1a$I_C = |I|^2 cdot xi cdot kappa$<\/li>\n<\/ol>\n<hr \/>\n<h3>\u9644\u5f55C\uff1a\u5b9e\u9a8c\u6d4b\u91cf\u6307\u5357<\/h3>\n<h4>C.1 \u4e09\u7ef4\u60ef\u6027\u6d4b\u91cf\u65b9\u6cd5<\/h4>\n<p><strong>\u71b5\u60ef\u6027\u6d4b\u91cf<\/strong>\uff1a<\/p>\n<ul>\n<li>\u901a\u8fc7\u6bd4\u70ed\u6d4b\u91cf\u4e0e\u6e29\u5ea6\u6270\u52a8\u5b9e\u9a8c<\/li>\n<li>\u6d4b\u91cf\u6b65\u9aa4\uff1a\n<ol>\n<li>\u6d4b\u91cf\u7cfb\u7edf\u5728\u4e0d\u540c\u6e29\u5ea6\u4e0b\u7684\u70ed\u5bb9$C_V(T)$<\/li>\n<li>\u65bd\u52a0\u6e29\u5ea6\u6270\u52a8$Delta T$<\/li>\n<li>\u6d4b\u91cf\u7cfb\u7edf\u6062\u590d\u65f6\u95f4$tau$<\/li>\n<li>\u8ba1\u7b97$I_S = int C_V(T) dT \/ tau$<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p><strong>\u9891\u7387\u60ef\u6027\u6d4b\u91cf<\/strong>\uff1a<\/p>\n<ul>\n<li>\u901a\u8fc7\u54c1\u8d28\u56e0\u6570$Q = omega_0\/Deltaomega$\u6d4b\u91cf<\/li>\n<li>\u6d4b\u91cf\u6b65\u9aa4\uff1a\n<ol>\n<li>\u6d4b\u91cf\u7cfb\u7edf\u7684\u5171\u632f\u9891\u7387$omega_0$<\/li>\n<li>\u6d4b\u91cf\u9891\u7387\u54cd\u5e94\u7684\u534a\u9ad8\u5bbd$Deltaomega$<\/li>\n<li>\u8ba1\u7b97$I_omega = Q \/ (1 + Q)$<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<p><strong>\u76f8\u5e72\u60ef\u6027\u6d4b\u91cf<\/strong>\uff1a<\/p>\n<ul>\n<li>\u901a\u8fc7\u573a\u76f8\u5e72\u5ea6$C = |langle Psi_C rangle| \/ sqrt{langle |Psi_C|^2 rangle}$\u6d4b\u91cf<\/li>\n<li>\u6d4b\u91cf\u6b65\u9aa4\uff1a\n<ol>\n<li>\u6d4b\u91cf\u573a\u7684\u7a7a\u95f4\u5e73\u5747\u503c$|langle Psi_C rangle|$<\/li>\n<li>\u6d4b\u91cf\u573a\u7684\u5747\u65b9\u6839\u503c$sqrt{langle |Psi_C|^2 rangle}$<\/li>\n<li>\u8ba1\u7b97$I_C = |langle Psi_C rangle|^2 \/ langle |Psi_C|^2 rangle$<\/li>\n<\/ol>\n<\/li>\n<\/ul>\n<hr \/>\n<h3>\u9644\u5f55D\uff1a\u8de8\u9886\u57df\u5e94\u7528\u6848\u4f8b\u96c6<\/h3>\n<h4>D.1 \u7269\u7406\u7cfb\u7edf\u5e94\u7528<\/h4>\n<p><strong>\u8d85\u5bfc\u4f53\u7814\u7a76<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5229\u7528IGT\u9884\u6d4b\u8d85\u5bfc\u8f6c\u53d8\u6e29\u5ea6\u4e0e\u76f8\u5e72\u957f\u5ea6\u5173\u7cfb<\/li>\n<li>\u516c\u5f0f\uff1a$T_c propto I_C \/ I_S$<\/li>\n<li>\u5e94\u7528\uff1a\u8bbe\u8ba1\u65b0\u578b\u9ad8\u6e29\u8d85\u5bfc\u6750\u6599<\/li>\n<\/ul>\n<p><strong>\u91cf\u5b50\u6750\u6599\u8bbe\u8ba1<\/strong>\uff1a<\/p>\n<ul>\n<li>\u57fa\u4e8e\u4e09\u573a\u7406\u8bba\u8bbe\u8ba1\u65b0\u578b\u91cf\u5b50\u6750\u6599<\/li>\n<li>\u65b9\u6cd5\uff1a\u901a\u8fc7\u8c03\u63a7$I<em>S$\u3001$I<\/em>omega$\u3001$I_C$\u7684\u76f8\u5bf9\u6bd4\u4f8b\u4f18\u5316\u6750\u6599\u6027\u80fd<\/li>\n<\/ul>\n<h4>D.2 \u751f\u7269\u7cfb\u7edf\u5e94\u7528<\/h4>\n<p><strong>\u7ec6\u80de\u5065\u5eb7\u8bca\u65ad<\/strong>\uff1a<\/p>\n<ul>\n<li>\u901a\u8fc7\u6d4b\u91cf\u7ec6\u80de\u7684\u4e09\u7ef4\u60ef\u6027\u8bc4\u4f30\u7ec6\u80de\u5065\u5eb7\u72b6\u6001<\/li>\n<li>\u6307\u6807\uff1a$I<em>S$\uff08\u4ee3\u8c22\u7a33\u5b9a\u6027\uff09\u3001$I<\/em>omega$\uff08\u8282\u5f8b\u7a33\u5b9a\u6027\uff09\u3001$I_C$\uff08\u7ed3\u6784\u5b8c\u6574\u6027\uff09<\/li>\n<\/ul>\n<p><strong>\u751f\u7269\u8282\u5f8b\u8c03\u63a7<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5e94\u7528\u9891\u7387\u60ef\u6027\u539f\u7406\u8c03\u8282\u751f\u7269\u949f<\/li>\n<li>\u65b9\u6cd5\uff1a\u901a\u8fc7\u8c03\u63a7$I_omega$\u6539\u5584\u7761\u7720\u5468\u671f\u3001\u4ee3\u8c22\u8282\u5f8b<\/li>\n<\/ul>\n<h4>D.3 \u793e\u4f1a\u7cfb\u7edf\u5e94\u7528<\/h4>\n<p><strong>\u7ec4\u7ec7\u5065\u5eb7\u8bca\u65ad<\/strong>\uff1a<\/p>\n<ul>\n<li>\u901a\u8fc7\u8fdb\u5316\u7b49\u7ea7\u7406\u8bba\u8bc4\u4f30\u7ec4\u7ec7\u7684\u9002\u5e94\u80fd\u529b<\/li>\n<li>\u6307\u6807\uff1a$L$\u7b49\u7ea7\uff08\u8c03\u63a7\u80fd\u529b\uff09\u3001$H$\u7b49\u7ea7\uff08\u5f53\u524d\u72b6\u6001\uff09<\/li>\n<\/ul>\n<p><strong>\u7ecf\u6d4e\u7cfb\u7edf\u8c03\u63a7<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5e94\u7528\u4e09\u573a\u7406\u8bba\u5206\u6790\u7ecf\u6d4e\u5468\u671f\u4e0e\u6ce2\u52a8<\/li>\n<li>\u65b9\u6cd5\uff1a\u901a\u8fc7\u5206\u6790$I<em>S$\uff08\u8d44\u6e90\u6d41\u52a8\uff09\u3001$I<\/em>omega$\uff08\u5468\u671f\u6027\uff09\u3001$I_C$\uff08\u5236\u5ea6\u7a33\u5b9a\u6027\uff09<\/li>\n<\/ul>\n<hr \/>\n<h3>\u9644\u5f55E\uff1a\u7406\u8bba\u8fb9\u754c\u4e0e\u5f00\u653e\u95ee\u9898<\/h3>\n<h4>E.1 \u672a\u89e3\u51b3\u7684\u6570\u5b66\u95ee\u9898<\/h4>\n<p><strong>\u4e09\u7ef4\u51e0\u4f55\u6700\u4f18\u7684\u4e25\u683c\u8bc1\u660e<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5f53\u524d\u4ec5\u5b8c\u6210\u6570\u503c\u9a8c\u8bc1<\/li>\n<li>\u6311\u6218\uff1a\u9700\u8981\u4e25\u683c\u7684\u62d3\u6251\u4f18\u5316\u8bc1\u660e<\/li>\n<\/ul>\n<p><strong>\u91cf\u5b50\u5f15\u529b\u573a\u666f\u4e0b\u7684IGT\u63a8\u5e7f<\/strong>\uff1a<\/p>\n<ul>\n<li>\u65f6\u7a7a\u4f5c\u4e3a\u9501\u573a\u7684\u6fc0\u53d1\u6001\u7684\u5b8c\u6574\u6570\u5b66\u8868\u8ff0<\/li>\n<li>\u6311\u6218\uff1a\u9700\u8981\u5c06\u5e7f\u4e49\u76f8\u5bf9\u8bba\u4e0e\u91cf\u5b50\u573a\u8bba\u7edf\u4e00<\/li>\n<\/ul>\n<h4>E.2 \u5b9e\u9a8c\u9a8c\u8bc1\u6311\u6218<\/h4>\n<p><strong>\u8de8\u5c3a\u5ea6\u6d4b\u91cf<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5982\u4f55\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u4fdd\u6301\u6d4b\u91cf\u7cbe\u5ea6<\/li>\n<li>\u6311\u6218\uff1a\u9700\u8981\u5f00\u53d1\u8de8\u5c3a\u5ea6\u7684\u7edf\u4e00\u6d4b\u91cf\u6846\u67b6<\/li>\n<\/ul>\n<p><strong>\u975e\u4fb5\u5165\u5f0f\u6d4b\u91cf<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5982\u4f55\u5728\u4e0d\u7834\u574f\u7cfb\u7edf\u7684\u60c5\u51b5\u4e0b\u6d4b\u91cf\u4e09\u7ef4\u60ef\u6027<\/li>\n<li>\u6311\u6218\uff1a\u9700\u8981\u5f00\u53d1\u975e\u63a5\u89e6\u5f0f\u6d4b\u91cf\u6280\u672f<\/li>\n<\/ul>\n<h4>E.3 \u672a\u6765\u7814\u7a76\u65b9\u5411<\/h4>\n<p><strong>IGT\u4e0e\u4eba\u5de5\u667a\u80fd\u7684\u7ed3\u5408<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5e94\u7528IGT\u7406\u8bba\u8bbe\u8ba1\u66f4\u667a\u80fd\u7684AI\u7cfb\u7edf<\/li>\n<li>\u65b9\u5411\uff1a\u57fa\u4e8e$I<em>S$\u3001$I<\/em>omega$\u3001$I_C$\u7684AI\u67b6\u6784\u8bbe\u8ba1<\/li>\n<\/ul>\n<p><strong>IGT\u4e0e\u91cf\u5b50\u8ba1\u7b97\u7684\u7ed3\u5408<\/strong>\uff1a<\/p>\n<ul>\n<li>\u57fa\u4e8e\u71b5\u573a\u76f8\u5e72\u8c03\u63a7\u7684\u91cf\u5b50\u8ba1\u7b97<\/li>\n<li>\u65b9\u5411\uff1a\u901a\u8fc7\u63d0\u9ad8$I_C$\u5ef6\u957f\u91cf\u5b50\u6bd4\u7279\u7684\u76f8\u5e72\u65f6\u95f4<\/li>\n<\/ul>\n<hr \/>\n<h2>\u7d22\u5f15<\/h2>\n<h3>\u6838\u5fc3\u672f\u8bed\u7d22\u5f15<\/h3>\n<p><strong>A<\/strong><\/p>\n<ul>\n<li>\u963f\u5c14\u4f2f\u7279\u00b7\u7231\u56e0\u65af\u5766<\/li>\n<li>\u5965\u5361\u59c6\u5243\u5200\u539f\u7406<\/li>\n<\/ul>\n<p><strong>C<\/strong><\/p>\n<ul>\n<li>\u70ed\u5bb9\u3001\u76f8\u5e72\u5ea6\u3001\u79e9\u5e8f\u5ea6\uff08\u4e09\u8005\u7b49\u4ef7\uff09<\/li>\n<li>\u76f8\u5e72\u60ef\u6027<\/li>\n<li>\u8026\u5408\u7cfb\u6570<\/li>\n<\/ul>\n<p><strong>E<\/strong><\/p>\n<ul>\n<li>\u6b27\u62c9-\u62c9\u683c\u6717\u65e5\u65b9\u7a0b<\/li>\n<li>\u8fdb\u5316\u7b49\u7ea7\u3001\u8fdb\u5316\u76f8\u56fe<\/li>\n<\/ul>\n<p><strong>F<\/strong><\/p>\n<ul>\n<li>\u8d39\u7c73\u5b50\u3001\u8d39\u66fc\u8def\u5f84\u79ef\u5206<\/li>\n<\/ul>\n<p><strong>G<\/strong><\/p>\n<ul>\n<li>\u51e0\u4f55\u4e0d\u53d8\u6027\u516c\u7406\u3001\u51e0\u4f55\u52bf\u6cdb\u51fd<\/li>\n<li>\u5e7f\u4e49\u76f8\u5bf9\u8bba\u3001\u89c4\u8303\u5bf9\u79f0\u6027<\/li>\n<\/ul>\n<p><strong>I<\/strong><\/p>\n<ul>\n<li>\u60ef\u6027\u3001\u60ef\u6027\u5b88\u6052\u5b9a\u7406\u3001\u60ef\u6027\u5f20\u91cf<\/li>\n<li>\u71b5\u3001\u71b5\u573a\u3001\u71b5\u6da8\u843d\u3001\u71b5\u68af\u5ea6<\/li>\n<\/ul>\n<p><strong>L<\/strong><\/p>\n<ul>\n<li>\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6<\/li>\n<li>\u6717\u9053\u76f8\u53d8\u7406\u8bba\u3001\u6717\u9053\u81ea\u7531\u80fd<\/li>\n<\/ul>\n<p><strong>M<\/strong><\/p>\n<ul>\n<li>\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4<\/li>\n<\/ul>\n<p><strong>N<\/strong><\/p>\n<ul>\n<li>\u8bfa\u7279\u5b9a\u7406<\/li>\n<li>\u725b\u987f\u529b\u5b66\u3001\u725b\u987f\u5f15\u529b<\/li>\n<\/ul>\n<p><strong>P<\/strong><\/p>\n<ul>\n<li>\u666e\u6717\u514b\u5e38\u6570\u3001\u666e\u6717\u514b\u5c3a\u5ea6<\/li>\n<\/ul>\n<p><strong>Q<\/strong><\/p>\n<ul>\n<li>\u54c1\u8d28\u56e0\u6570\u3001\u5168\u606f\u539f\u7406<\/li>\n<\/ul>\n<p><strong>R<\/strong><\/p>\n<ul>\n<li>RVSE\u5faa\u73af\uff08\u03a9-R-V-S-E-D\uff09<\/li>\n<li>\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b<\/li>\n<\/ul>\n<p><strong>S<\/strong><\/p>\n<ul>\n<li>\u4e09\u573a\uff08\u70ed\u573a\u3001\u52a8\u573a\u3001\u9501\u573a\uff09<\/li>\n<li>\u4e09\u573a\u5b8c\u5907\u6027\u3001\u4e09\u573a\u7406\u8bba<\/li>\n<li>\u4e09\u7ef4\u60ef\u6027\uff08\u71b5\u60ef\u6027\u3001\u9891\u7387\u60ef\u6027\u3001\u76f8\u5e72\u60ef\u6027\uff09<\/li>\n<\/ul>\n<p><strong>T<\/strong><\/p>\n<ul>\n<li>\u592a\u6781\u6001\u3001\u592a\u6781\u76f8\u56fe<\/li>\n<\/ul>\n<p><strong>U<\/strong><\/p>\n<ul>\n<li>\u5b87\u5b99\u5fae\u6ce2\u80cc\u666f\uff08CMB\uff09<\/li>\n<li>\u5b87\u5b99\u5b66\u5e38\u6570\u3001\u5b87\u5b99\u5b66\u89c6\u754c<\/li>\n<\/ul>\n<p><strong>V<\/strong><\/p>\n<ul>\n<li>\u62d3\u6251\u7f3a\u9677\u3001\u62d3\u6251\u8377<\/li>\n<\/ul>\n<p><strong>W<\/strong><\/p>\n<ul>\n<li>\u4e07\u6709\u5f15\u529b\u3001\u5fae\u6ce2\u80cc\u666f\u8f90\u5c04<\/li>\n<\/ul>\n<hr \/>\n<h3>\u6838\u5fc3\u65b9\u7a0b\u7d22\u5f15<\/h3>\n<ol>\n<li><strong>\u5143\u516c\u7406<\/strong>\uff1aUniverse = \u2295\u2090 \u03a8\u2090 \uff08\u7b2c1\u7ae0\uff09<\/li>\n<li><strong>\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406<\/strong>\uff1aS[\u03a8] = \u222bd\u2074x \u2112(\u03a8, \u2202\u1d64\u03a8) \uff08\u7b2c1\u7ae0\uff09<\/li>\n<li><strong>\u6b27\u62c9-\u62c9\u683c\u6717\u65e5\u65b9\u7a0b<\/strong>\uff1a\u2202\u2112\/\u2202\u03a8 &#8211; \u2202\u1d64(\u2202\u2112\/\u2202(\u2202\u1d64\u03a8)) = 0 \uff08\u7b2c1\u7ae0\uff09<\/li>\n<li><strong>\u51e0\u4f55\u52bf\u6cdb\u51fd<\/strong>\uff1aG_shape[\u03a8] = \u222bd\u00b3r[(\u2207\u00b2|\u03a8|\/|\u03a8|)\u00b2 &#8211; (1\/6)(\u2207|\u03a8|\/|\u03a8|)\u2074] \uff08\u7b2c1\u7ae0\uff09<\/li>\n<li><strong>\u4e09\u573a\u6b63\u4ea4\u6027<\/strong>\uff1a\u27e8\u03a8\u1d62|\u03a8\u2c7c\u27e9 = \u03b4\u1d62\u2c7c \uff08\u7b2c2\u7ae0\uff09<\/li>\n<li><strong>\u603b\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6<\/strong>\uff1a\u2112 = \u2112_S + \u2112_\u03c9 + \u2112_C + \u2112_int + \u2112_geo \uff08\u7b2c2\u7ae0\uff09<\/li>\n<li><strong>\u4e09\u7ef4\u60ef\u6027\u5b88\u6052<\/strong>\uff1ad(I_S + I_\u03c9 + I_C)\/dt = 0 \uff08\u7b2c3\u7ae0\uff09<\/li>\n<li><strong>\u4e8c\u7ef4\u516d\u8fb9\u5f62\u6700\u4f18<\/strong>\uff1aHexagonal = argmin_{2D packing}(E_total) \uff08\u7b2c4\u7ae0\uff09<\/li>\n<li><strong>RVSE\u5e8f\u5217<\/strong>\uff1a\u03a9\u2080\u2192\u03a9\u2192R\u2192V\u2192S\u2192E\u2192D \uff08\u7b2c5\u7ae0\uff09<\/li>\n<li><strong>\u7edf\u4e00\u6f14\u5316\u65b9\u7a0b<\/strong>\uff1a\u03c4_X\u00b7\u2202\u209c\u03a8_X = -\u03b4F\/\u03b4\u03a8_X* + \u03be_X(\ud835\udc2b, t) \uff08\u7b2c5\u7ae0\uff09<\/li>\n<li><strong>\u8fdb\u5316\u7b49\u7ea7\u5b9a\u4e49<\/strong>\uff1aEvolution Level = \ud835\udc9c[I_S, I_\u03c9, I_C] = \u2211\u2093 \u03b1\u2093\u00b7\u2202I\u2093\/\u2202t_control \uff08\u7b2c7\u7ae0\uff09<\/li>\n<li><strong>\u5065\u5eb7-\u8fdb\u5316\u5bf9\u5076\u5173\u7cfb<\/strong>\uff1aH \u2265 3 \u21d2 L \u2265 2 \uff08\u7b2c8\u7ae0\uff09<\/li>\n<li><strong>\u5f15\u529b\u52bf<\/strong>\uff1a\u03a6(r) = -Gm\/r \uff08\u7b2c9\u7ae0\uff09<\/li>\n<li><strong>\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7ec4<\/strong>\uff1a\u2202\u1d64F\u1d58\u2c7d = \u03bc\u2080J\u2c7d \uff08\u7b2c9\u7ae0\uff09<\/li>\n<li><strong>\u71b5\u6da8\u843d\u5173\u8054<\/strong>\uff1a\u27e8\u03b4S(x)\u03b4S(y)\u27e9 = \u0127G\/c\u00b3\u00b71\/|x-y|\u00b2 \uff08\u7b2c2\u7ae0\uff09<\/li>\n<\/ol>\n<hr \/>\n<h3>\u6838\u5fc3\u56fe\u8868\u7d22\u5f15<\/h3>\n<ol>\n<li><strong>\u88680.1<\/strong>\uff1a\u9605\u8bfb\u5730\u56fe \uff08\u5e8f\u8a00\uff09<\/li>\n<li><strong>\u88682.1<\/strong>\uff1a\u573a\u7b26\u53f7\u3001\u7269\u7406\u672c\u8d28\u53ca\u63a7\u5236\u65b9\u7a0b \uff08\u7b2c2\u7ae0\uff09<\/li>\n<li><strong>\u88683.1<\/strong>\uff1a\u4e09\u7ef4\u60ef\u6027\u7684\u7269\u7406\u610f\u4e49\u4e0e\u5bf9\u5e94\u89c2\u6d4b\u91cf \uff08\u7b2c3\u7ae0\uff09<\/li>\n<li><strong>\u88684.1<\/strong>\uff1a\u4e0d\u540c\u7ed3\u6784\u7c7b\u578b\u7684\u6570\u503c\u9a8c\u8bc1\u7ed3\u679c \uff08\u7b2c4\u7ae0\uff09<\/li>\n<li><strong>\u88685.1<\/strong>\uff1aRVSE\u5404\u9636\u6bb5\u7684\u573a\u8bba\u7279\u5f81 \uff08\u7b2c5\u7ae0\uff09<\/li>\n<li><strong>\u88685.2<\/strong>\uff1aRVSE\u5404\u9636\u6bb5\u95f4\u7684\u76f8\u53d8\u4e34\u754c\u53c2\u6570\u9608\u503c \uff08\u7b2c5\u7ae0\uff09<\/li>\n<li><strong>\u88686.1<\/strong>\uff1a\u6838\u5fc3\u53ef\u8bc1\u4f2a\u5224\u636e \uff08\u7b2c6\u7ae0\uff09<\/li>\n<li><strong>\u88686.2<\/strong>\uff1a\u91cf\u5316\u89c2\u6d4b\u9884\u8a00 \uff08\u7b2c6\u7ae0\uff09<\/li>\n<li><strong>\u88687.1<\/strong>\uff1a\u4e94\u7ea7\u8fdb\u5316\u4f53\u7cfb\u7684\u6570\u5b66\u7279\u5f81\u4e0e\u7269\u7406\u5b9e\u4f8b \uff08\u7b2c7\u7ae0\uff09<\/li>\n<li><strong>\u88689.1<\/strong>\uff1a\u5178\u578b\u9886\u57df\u6620\u5c04\u793a\u4f8b \uff08\u7b2c9\u7ae0\uff09<\/li>\n<li><strong>\u886811.1<\/strong>\uff1a\u5b9e\u9a8c\u5ba4\u53ef\u9a8c\u8bc1\u9884\u6d4b \uff08\u7b2c12\u7ae0\uff09<\/li>\n<li><strong>\u886811.2<\/strong>\uff1a\u5929\u6587\u89c2\u6d4b\u9884\u6d4b \uff08\u7b2c12\u7ae0\uff09<\/li>\n<li><strong>\u56fe8.1<\/strong>\uff1a\u8fdb\u5316-\u5065\u5eb7\u76f8\u56fe \uff08\u7b2c8\u7ae0\uff09<\/li>\n<\/ol>\n<hr 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