{"id":5351,"date":"2026-01-14T09:35:30","date_gmt":"2026-01-14T01:35:30","guid":{"rendered":"https:\/\/imeta.space\/?p=5351"},"modified":"2026-01-20T15:28:15","modified_gmt":"2026-01-20T07:28:15","slug":"%e4%bf%a1%e6%81%af%e5%9f%ba%e5%9b%a0%e8%ae%ba-%e7%ac%ac%e4%b8%80%e5%b1%82%ef%bc%9a%e5%ae%87%e5%ae%99%e8%87%aa%e5%8a%a8%e8%bf%90%e8%a1%8c%e8%ae%ba-deepseek","status":"publish","type":"post","link":"https:\/\/imeta.space\/index.php\/2026\/01\/14\/%e4%bf%a1%e6%81%af%e5%9f%ba%e5%9b%a0%e8%ae%ba-%e7%ac%ac%e4%b8%80%e5%b1%82%ef%bc%9a%e5%ae%87%e5%ae%99%e8%87%aa%e5%8a%a8%e8%bf%90%e8%a1%8c%e8%ae%ba-deepseek\/","title":{"rendered":"\u4fe1\u606f\u57fa\u56e0\u8bba \u7b2c\u4e00\u5c42\uff1a\u5b87\u5b99\u81ea\u52a8\u8fd0\u884c\u8bba Deepseek"},"content":{"rendered":"<h1>\ud83d\udcd8 <strong>\u7b2c\u4e00\u5c42\uff1a\u5b87\u5b99\u81ea\u52a8\u8fd0\u884c\u8bba<\/strong><\/h1>\n<h2><strong>\u300a\u71b5\u6da8\u843d\u5b87\u5b99\uff1a\u03a9-R-V-S-D\u7684\u5fc5\u7136\u5faa\u73af\u300b<\/strong><\/h2>\n<blockquote>\n<p><strong>\u6838\u5fc3\u547d\u9898<\/strong>\uff1a\u5728\u65e0\u89c2\u6d4b\u8005\u3001\u65e0\u4ef7\u503c\u5224\u65ad\u7684\u7eaf\u7269\u7406\u4e16\u754c\u4e2d\uff0c\u5b87\u5b99\u9075\u5faa\u4ece\u6709\u5e8f\u5230\u65e0\u5e8f\u7684\u81ea\u52a8\u5faa\u73af\uff0c\u8fd9\u4e2a\u5faa\u73af\u7531\u71b5\u6da8\u843d\u7684\u51e0\u4f55\u7ea6\u675f\u548c\u62d3\u6251\u7ed3\u6784\u51b3\u5b9a\u3002<\/p>\n<\/blockquote>\n<hr \/>\n<h2><strong>\u7b2c\u96f6\u5377\uff1a\u57fa\u7840\u516c\u7406<\/strong><\/h2>\n<h3><strong>\u516c\u74060.1\uff08\u8fc7\u7a0b\u5b58\u5728\u516c\u7406\uff09<\/strong><\/h3>\n<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&quot;\u5b9e\u4f53&quot;\u90fd\u662f\u8fd9\u4e2a\u8fc7\u7a0b\u7684\u6682\u6001\u76f8\u5e72\u7ec4\u7ec7\u5f62\u5f0f\u3002<\/p>\n<p><strong>\u6570\u5b66\u8868\u8ff0\uff1a<\/strong><br \/>\n$$<br \/>\ntext{Universe} = int mathcal{D}[delta S] expleft(-frac{1}{hbar}mathcal{A}[delta S]right)<br \/>\n$$<\/p>\n<p>\u5176\u4e2d\u4f5c\u7528\u91cf\u4e3a\uff1a<br \/>\n$$<br \/>\nmathcal{A}[delta S] = int d^4x left[frac{1}{2}(partial_mudelta S)^2 + V(delta S)right]<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ul>\n<li>\u5b87\u5b99\u4e0d\u662f&quot;\u5b58\u5728&quot;\u7684\uff0c\u800c\u662f&quot;\u6f14\u5316&quot;\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<\/ul>\n<hr \/>\n<h3><strong>\u516c\u74060.2\uff08\u4e09\u573a\u5206\u89e3\u516c\u7406\uff09<\/strong><\/h3>\n<p>\u4efb\u4f55\u5b8f\u89c2\u76f8\u5e72\u7cfb\u7edf\u53ef\u5728\u6d8c\u73b0\u5c3a\u5ea6\u4e0b\u6b63\u4ea4\u5206\u89e3\u4e3a\u4e09\u4e2a\u57fa\u672c\u573a\uff1a<\/p>\n<p>$$<br \/>\nmathcal{H}_{text{system}} = mathcal{H}<em>S oplus mathcal{H}<\/em>omega oplus mathcal{H}_C<br \/>\n$$<\/p>\n<p>\u6ee1\u8db3\u6b63\u4ea4\u6761\u4ef6\uff1a<br \/>\n$$<br \/>\nlangle Psi_i | Psi<em>j rangle = delta<\/em>{ij}, quad i,j in {S,omega,C}<br \/>\n$$<\/p>\n<p><strong>\u4e09\u573a\u7269\u7406\u5b9a\u4e49\uff1a<\/strong><\/p>\n<table>\n<thead>\n<tr>\n<th>\u573a\u7c7b\u578b<\/th>\n<th>\u7269\u7406\u672c\u8d28<\/th>\n<th>\u5bf9\u79f0\u6027\u7834\u7f3a<\/th>\n<th>\u5b8f\u89c2\u8868\u73b0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u70ed\u573a $Psi_S$<\/strong><\/td>\n<td>\u80fd\u91cf\u6d41\u52a8\u6a21\u5f0f<\/td>\n<td>\u5e73\u79fb\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<td>\u6e29\u5ea6\u573a\u3001\u4ee3\u8c22\u7387\u3001\u8d44\u672c\u6d41<\/td>\n<\/tr>\n<tr>\n<td><strong>\u52a8\u573a $Psi_omega$<\/strong><\/td>\n<td>\u8282\u5f8b\u6d41\u52a8\u5370\u8bb0<\/td>\n<td>$U(1)$\u89c4\u8303\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<td>\u751f\u7269\u949f\u3001\u7ecf\u6d4e\u5468\u671f\u3001\u8109\u51b2\u661f\u81ea\u65cb<\/td>\n<\/tr>\n<tr>\n<td><strong>\u94f8\u573a $Psi_C$<\/strong><\/td>\n<td>\u62b5\u6297\u71b5\u6d41\u7684\u6682\u65f6\u6f29\u6da1<\/td>\n<td>\u65cb\u8f6c\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<td>\u6676\u4f53\u7ed3\u6784\u3001DNA\u87ba\u65cb\u3001\u793e\u4f1a\u7ec4\u7ec7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h2><strong>\u7b2c\u4e00\u5377\uff1a\u8fc7\u7a0b\u672c\u4f53\u8bba\u57fa\u7840<\/strong><\/h2>\n<h3><strong>\u7b2c1\u7ae0\uff1a\u89c2\u6d4b\u8fb9\u754c\u4e0e\u79d1\u5b66\u65b9\u6cd5\u7684\u5fc5\u7136\u8f6c\u53d8<\/strong><\/h3>\n<h4><strong>1.1 \u4e2d\u5c3a\u5ea6\u7262\u7b3c\uff1a\u4eba\u7c7b\u8ba4\u77e5\u7684\u7269\u7406\u9650\u5236<\/strong><\/h4>\n<p><strong>\u5b9a\u4e491.1\uff08\u89c2\u6d4b\u8fb9\u754c\uff09\uff1a<\/strong><br \/>\n\u4eba\u7c7b\u89c2\u6d4b\u8005\u6c38\u8fdc\u88ab\u9650\u5236\u5728\u6709\u9650\u5c3a\u5ea6\u8303\u56f4\u5185\uff1a<br \/>\n$$<br \/>\nL<em>{min} &lt; L &lt; L<\/em>{max}<br \/>\n$$<\/p>\n<p><strong>\u5177\u4f53\u6570\u503c\uff1a<\/strong><\/p>\n<ul>\n<li><strong>\u5fae\u89c2\u5206\u8fa8\u7387\u6781\u9650<\/strong>\uff1a$L_{min} = sqrt{hbar\/langledelta Srangle} approx 10^{-35} text{m}$\uff08\u666e\u6717\u514b\u5c3a\u5ea6\uff09<\/li>\n<li><strong>\u5b8f\u89c2\u56e0\u679c\u6781\u9650<\/strong>\uff1a$L_{max} = ccdottau_O approx 10^{26} text{m}$\uff08\u53ef\u89c2\u6d4b\u5b87\u5b99\u534a\u5f84\uff09<\/li>\n<\/ul>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ol>\n<li>\u6211\u4eec\u65e0\u6cd5\u76f4\u63a5\u89c2\u6d4b\u5b87\u5b99\u7684\u8d77\u70b9\uff08\u88ab$L_{min}$\u906e\u853d\uff09<\/li>\n<li>\u6211\u4eec\u65e0\u6cd5\u76f4\u63a5\u89c2\u6d4b\u5b87\u5b99\u7684\u7ec8\u70b9\uff08\u88ab$L_{max}$\u9650\u5236\uff09<\/li>\n<li>\u6211\u4eec\u552f\u4e00\u80fd\u76f4\u63a5\u63a5\u89e6\u7684\uff0c\u53ea\u6709&quot;\u6b64\u523b\u6b63\u5728\u53d1\u751f\u7684\u8fc7\u7a0b&quot;<\/li>\n<\/ol>\n<h4><strong>1.2 \u5b9e\u4f53\u672c\u4f53\u8bba\u7684\u56f0\u5883<\/strong><\/h4>\n<p><strong>\u4f20\u7edf\u7269\u7406\u5b66\u7684\u57fa\u672c\u5047\u8bbe\uff1a<\/strong><\/p>\n<ol>\n<li>\u5b58\u5728\u6c38\u6052\u4e0d\u53d8\u7684\u5b9e\u4f53\uff08\u539f\u5b50\u3001\u573a\u3001\u7c92\u5b50\uff09<\/li>\n<li>\u53d8\u5316\u53ea\u662f\u8fd9\u4e9b\u5b9e\u4f53\u7684\u5c5e\u6027\u6216\u72b6\u6001\u53d8\u5316<\/li>\n<li>\u79d1\u5b66\u76ee\u6807\u662f\u5bfb\u627e&quot;\u7b2c\u4e00\u539f\u7406&quot;\u548c&quot;\u7ec8\u6781\u771f\u7406&quot;<\/li>\n<\/ol>\n<p><strong>\u56f0\u5883\u5206\u6790\uff1a<\/strong><\/p>\n<ol>\n<li><strong>\u91cf\u5b50\u529b\u5b66\u6311\u6218<\/strong>\uff1a\u7c92\u5b50\u5728\u6d4b\u91cf\u524d\u6ca1\u6709\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\u6c38\u6052\u5b9e\u4f53\u4e0d\u53ef\u80fd<\/li>\n<li><strong>\u89c2\u6d4b\u6311\u6218<\/strong>\uff1a\u6211\u4eec\u4ece\u672a\u89c2\u6d4b\u5230\u4efb\u4f55&quot;\u6c38\u6052\u4e0d\u53d8&quot;\u7684\u5b9e\u4f53<\/li>\n<\/ol>\n<h4><strong>1.3 \u8fc7\u7a0b\u672c\u4f53\u8bba\u7684\u5fc5\u7136\u6027<\/strong><\/h4>\n<p><strong>\u516c\u74061.1\uff08\u8fc7\u7a0b\u672c\u4f53\u8bba\u516c\u7406\uff09\uff1a<\/strong><br \/>\n\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&quot;\u5b9e\u4f53&quot;\u90fd\u662f\u8fd9\u4e2a\u8fc7\u7a0b\u7684\u6682\u6001\u7ec4\u7ec7\u5f62\u5f0f\u3002<\/p>\n<p><strong>\u6570\u5b66\u8868\u8ff0\uff1a<\/strong><br \/>\n$$<br \/>\ntext{Universe} = bigoplus<em>{alpha} Psi<\/em>alpha<br \/>\n$$<br \/>\n\u5176\u4e2d$Psi_alpha$\u4e3a\u76f8\u5e72\u573a\uff0c$oplus$\u8868\u793a\u76f4\u548c\u3002<\/p>\n<p><strong>\u5173\u952e\u63a8\u8bba\uff1a<\/strong><\/p>\n<ol>\n<li><strong>\u7269\u8d28\u89c2<\/strong>\uff1a\u7269\u8d28\u4e0d\u662f\u57fa\u672c\u5b9e\u4f53\uff0c\u800c\u662f\u71b5\u6da8\u843d\u7684\u76f8\u5e72\u7ed3\u6784<\/li>\n<li><strong>\u65f6\u7a7a\u89c2<\/strong>\uff1a\u65f6\u7a7a\u4e0d\u662f\u56fa\u5b9a\u821e\u53f0\uff0c\u800c\u662f\u71b5\u5173\u8054\u7684\u7f51\u7edc<\/li>\n<li><strong>\u76f8\u4e92\u4f5c\u7528\u89c2<\/strong>\uff1a\u529b\u4e0d\u662f\u72ec\u7acb\u4f5c\u7528\uff0c\u800c\u662f\u71b5\u68af\u5ea6\u7684\u7edf\u8ba1\u6548\u5e94<\/li>\n<li><strong>\u751f\u547d\u89c2<\/strong>\uff1a\u751f\u547d\u4e0d\u662f\u7279\u6b8a\u73b0\u8c61\uff0c\u800c\u662f\u71b5\u8c03\u63a7\u80fd\u529b\u589e\u5f3a\u7684\u8fc7\u7a0b<\/li>\n<\/ol>\n<hr \/>\n<h3><strong>\u7b2c2\u7ae0\uff1a\u71b5\u6da8\u843d\u4f5c\u4e3a\u57fa\u672c\u8fc7\u7a0b\u7684\u6570\u5b66\u57fa\u7840<\/strong><\/h3>\n<h4><strong>2.1 \u71b5\u6da8\u843d\u573a\u7684\u8def\u5f84\u79ef\u5206\u8868\u8ff0<\/strong><\/h4>\n<p><strong>\u5b9a\u4e492.1\uff08\u5b87\u5b99\u914d\u5206\u51fd\u6570\uff09\uff1a<\/strong><br \/>\n\u5b87\u5b99\u7684\u6f14\u5316\u7531\u71b5\u6da8\u843d\u8def\u5f84\u79ef\u5206\u63cf\u8ff0\uff1a<br \/>\n$$<br \/>\nmathcal{Z} = int mathcal{D}[delta S] expleft(-frac{1}{hbar}mathcal{A}[delta S]right)<br \/>\n$$<\/p>\n<p>\u5176\u4e2d\u4f5c\u7528\u91cf\u4e3a\uff1a<br \/>\n$$<br \/>\nmathcal{A}[delta S] = int d^4x left[frac{1}{2}(partial_mudelta S)^2 + V(delta S)right]<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ol>\n<li>\u5b87\u5b99\u4e0d\u662f&quot;\u5b58\u5728&quot;\u7684\uff0c\u800c\u662f&quot;\u6f14\u5316&quot;\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&quot;\u5b9e\u4f53&quot;\u662f\u8def\u5f84\u79ef\u5206\u7684\u7edf\u8ba1\u5e73\u5747<\/li>\n<\/ol>\n<h4><strong>2.2 \u4f5c\u7528\u91cf\u539f\u7406\u4e0e\u573a\u65b9\u7a0b<\/strong><\/h4>\n<p><strong>\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406\uff1a<\/strong><br \/>\n$$<br \/>\ndeltamathcal{A}[delta S] = 0<br \/>\n$$<\/p>\n<p><strong>\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6\uff1a<\/strong><br \/>\n$$<br \/>\nmathcal{L} = frac{1}{2}(partial<em>mudelta S)^2 + V(delta S) + G<\/em>{text{shape}}[delta S]<br \/>\n$$<\/p>\n<p><strong>\u6b27\u62c9-\u62c9\u683c\u6717\u65e5\u65b9\u7a0b\uff1a<\/strong><br \/>\n$$<br \/>\nfrac{partialmathcal{L}}{partialdelta S} &#8211; partial<em>muleft(frac{partialmathcal{L}}{partial(partial<\/em>mudelta S)}right) = 0<br \/>\n$$<\/p>\n<p><strong>\u7ebf\u6027\u5316\u6ce2\u52a8\u65b9\u7a0b\uff08\u5728\u7a33\u6001\u9644\u8fd1\uff09\uff1a<\/strong><br \/>\n$$<br \/>\npartial_t^2delta S &#8211; c_s^2nabla^2delta S + omega_0^2delta S = 0<br \/>\n$$<br \/>\n\u5176\u4e2d\u672c\u5f81\u9891\u7387$omega<em>0 = sqrt{K\/M<\/em>{text{inertial}}}$\u3002<\/p>\n<h4><strong>2.3 \u51e0\u4f55\u52bf\u6cdb\u51fd<\/strong><\/h4>\n<p><strong>\u5b9a\u4e492.2\uff08\u51e0\u4f55\u52bf\u6cdb\u51fd\uff09\uff1a<\/strong><br \/>\n\u7cfb\u7edf\u503e\u5411\u4e8e\u5f62\u6210\u7279\u5b9a\u51e0\u4f55\u7ed3\u6784\uff0c\u7531\u51e0\u4f55\u52bf\u6cdb\u51fd\u63cf\u8ff0\uff1a<br \/>\n$$<br \/>\nG_{text{shape}}[Psi] = int d^3r left[ left( frac{nabla^2 |Psi|}{|Psi|} right)^2 &#8211; frac{1}{6} left( frac{nabla |Psi|}{|Psi|} right)^4 right]<br \/>\n$$<\/p>\n<p><strong>\u53d8\u5206\u6761\u4ef6\uff1a<\/strong><br \/>\n$$<br \/>\nfrac{delta G_{text{shape}}}{delta Psi^*} = 0 Rightarrow text{\u6700\u4f18\u51e0\u4f55\u6784\u578b}<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ol>\n<li>\u7b2c\u4e00\u9879\u60e9\u7f5a\u66f2\u7387\u53d8\u5316\uff0c\u4fc3\u8fdb\u5e73\u6ed1\u7ed3\u6784<\/li>\n<li>\u7b2c\u4e8c\u9879\u60e9\u7f5a\u68af\u5ea6\u53d8\u5316\uff0c\u4fc3\u8fdb\u5747\u5300\u6027<\/li>\n<li>\u7ec4\u5408\u9879\u5728\u516d\u8fb9\u5f62\u7ed3\u6784\u4e2d\u53d6\u6781\u5c0f\u503c<\/li>\n<\/ol>\n<h4><strong>2.4 \u71b5\u6da8\u843d\u7684\u5173\u8054\u51fd\u6570<\/strong><\/h4>\n<p><strong>\u5b9a\u74062.1\uff08\u771f\u7a7a\u71b5\u6da8\u843d\u5173\u8054\uff09\uff1a<\/strong><br \/>\n\u771f\u7a7a\u4e2d\u7684\u71b5\u6da8\u843d\u5177\u6709\u957f\u7a0b\u5173\u8054\uff1a<br \/>\n$$<br \/>\nlangle delta S(x) delta S(y) rangle = frac{hbar G}{c^3} cdot frac{1}{|x-y|^2}<br \/>\n$$<\/p>\n<p><strong>\u8bc1\u660e\uff1a<\/strong><br \/>\n\u4ece\u71b5\u6da8\u843d\u8def\u5f84\u79ef\u5206\u8ba1\u7b97\u4e24\u70b9\u5173\u8054\u51fd\u6570\uff0c\u8003\u8651\u5f15\u529b\u6548\u5e94\u3002<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ol>\n<li>\u71b5\u6da8\u843d\u5173\u8054\u5f3a\u5ea6\u4e0e\u666e\u6717\u514b\u5e38\u6570\u6210\u6b63\u6bd4\uff08\u91cf\u5b50\u6548\u5e94\uff09<\/li>\n<li>\u4e0e\u5f15\u529b\u5e38\u6570\u6210\u6b63\u6bd4\uff08\u5f15\u529b\u6548\u5e94\uff09<\/li>\n<li>\u4e0e\u5149\u901f\u6210\u53cd\u6bd4\uff08\u76f8\u5bf9\u8bba\u6548\u5e94\uff09<\/li>\n<li>\u5177\u6709$1\/r^2$\u8870\u51cf\uff08\u957f\u7a0b\u5173\u8054\uff09<\/li>\n<\/ol>\n<h4><strong>2.5 \u4ece\u71b5\u6da8\u843d\u5230\u7269\u7406\u91cf\u7684\u6d8c\u73b0<\/strong><\/h4>\n<p><strong>\u5b9a\u74062.2\uff08\u7269\u7406\u91cf\u6d8c\u73b0\u5b9a\u7406\uff09\uff1a<\/strong><br \/>\n\u6240\u6709\u7269\u7406\u91cf\u90fd\u53ef\u4ee5\u8868\u793a\u4e3a\u71b5\u6da8\u843d\u5173\u8054\u51fd\u6570\u7684\u6cdb\u51fd\uff1a<br \/>\n$$<br \/>\nmathcal{O} = mathcal{F}[langle delta S(x_1) delta S(x_2) cdots delta S(x_n) rangle]<br \/>\n$$<\/p>\n<p><strong>\u5177\u4f53\u5b9e\u4f8b\uff1a<\/strong><\/p>\n<ol>\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<li><strong>\u7535\u8377<\/strong>\uff1a$q = epsilon_0 oint nabla S cdot dmathbf{A}$<\/li>\n<\/ol>\n<hr \/>\n<h3><strong>\u7b2c3\u7ae0\uff1a\u4ece\u968f\u673a\u6da8\u843d\u5230\u4fe1\u606f\u57fa\u56e0\u7684\u6d8c\u73b0\u673a\u5236<\/strong><\/h3>\n<h4><strong>3.1 \u8282\u5f8b\u7684\u8bde\u751f\uff1a\u4ece\u767d\u566a\u58f0\u5230\u672c\u5f81\u9891\u7387<\/strong><\/h4>\n<p><strong>\u673a\u5236<\/strong>\uff1a\u968f\u673a\u71b5\u6da8\u843d\u8fdb\u5165\u53d7\u9650\u7a7a\u95f4\uff0c\u53d7\u5230\u6709\u6548\u52bf\u7ea6\u675f\u3002<\/p>\n<p><strong>\u6709\u6548\u52bf\u5c55\u5f00\uff1a<\/strong><br \/>\n$$<br \/>\nV_{text{eff}}(delta S) approx V_0 + frac{1}{2} K (delta S)^2 + mathcal{O}(delta S^3)<br \/>\n$$<br \/>\n\u5176\u4e2d$K = d^2V\/d(delta S)^2$\u662f\u6062\u590d\u529b\u7cfb\u6570\u3002<\/p>\n<p><strong>\u6ce2\u52a8\u65b9\u7a0b\uff1a<\/strong><br \/>\n$$<br \/>\nfrac{partial^2 delta S}{partial t^2} &#8211; c_s^2 nabla^2 delta S + omega_0^2 delta S = 0<br \/>\n$$<\/p>\n<p><strong>\u672c\u5f81\u9891\u7387\uff1a<\/strong><br \/>\n$$<br \/>\nomega<em>0 = sqrt{frac{K}{M<\/em>{text{inertial}}}}<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><br \/>\n\u968f\u673a\u6da8\u843d\u4e00\u65e6\u8fdb\u5165\u53d7\u9650\u7a7a\u95f4\uff0c\u5c31\u88ab\u9650\u5236\u5728\u7279\u5b9a\u9891\u7387$omega_0$\u4e0a\uff0c\u5f62\u6210\u8282\u5f8b\u3002<\/p>\n<h4><strong>3.2 \u81ea\u6307\u6fc0\u53d1\u4e0e\u5bf9\u79f0\u6027\u7834\u7f3a<\/strong><\/h4>\n<p><strong>\u81ea\u6307\u76f8\u4e92\u4f5c\u7528\uff1a<\/strong><br \/>\n$$<br \/>\nmathcal{L}_{text{int}} = lambda (Psi^* Psi)^2 + g (Psi cdot nabla Psi)<br \/>\n$$<br \/>\n\u5176\u4e2d$g$\u4e3a\u624b\u5f81\u8026\u5408\u5e38\u6570\u3002<\/p>\n<p><strong>\u81ea\u53d1\u5bf9\u79f0\u6027\u7834\u7f3a\uff08SSB\uff09\uff1a<\/strong><\/p>\n<ol>\n<li>\u7cfb\u7edf\u4ece\u65e0\u6570\u5bf9\u79f0\u72b6\u6001\u4e2d&quot;\u574d\u7f29&quot;\u5230\u7279\u5b9a\u72b6\u6001<\/li>\n<li>\u4ea7\u751f\u71b5\u68af\u5ea6\uff1a$nabla delta S neq 0$<\/li>\n<li>\u786e\u5b9a\u80fd\u91cf\u6d41\u52a8\u7684\u9996\u9009\u8def\u5f84<\/li>\n<\/ol>\n<p><strong>IGT\u7b2c\u4e00\u5b9a\u5f8b\uff1a<\/strong><\/p>\n<blockquote>\n<p>\u6d41\u52a8\u4e0d\u662f\u7531\u4e8e\u5916\u754c\u63a8\u529b\uff0c\u800c\u662f\u7531\u4e8e\u81ea\u6307\u6fc0\u53d1\u5bfc\u81f4\u7684\u5bf9\u79f0\u6027\u8dcc\u843d\u3002<\/p>\n<\/blockquote>\n<h4><strong>3.3 \u521d\u59cb\u81ea\u65cb\uff1a\u71b5\u6d41\u65cb\u5ea6\u7684\u8bde\u751f<\/strong><\/h4>\n<p><strong>\u5b9a\u4e49\uff1a<\/strong><br \/>\n\u5f53\u81ea\u6307\u6fc0\u53d1\u4ea7\u751f\u7684\u71b5\u6d41$mathbf{j}<em>S$\u5728\u975e\u5747\u5300\u52bf\u9631\u4e2d\u8fd0\u52a8\u65f6\uff1a<br \/>\n$$<br \/>\nmathbf{Omega}<\/em>{text{spin}} = nabla times mathbf{j}_S<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ol>\n<li><strong>\u62d3\u6251\u610f\u4e49<\/strong>\uff1a\u8d4b\u4e88\u7cfb\u7edf\u624b\u5f81\u6027\uff08Chirality\uff09<\/li>\n<li><strong>\u57fa\u56e0\u7f16\u7801<\/strong>\uff1a\u51b3\u5b9a\u540e\u7eed\u6240\u6709\u76f8\u5e72\u7ed3\u6784\u7684\u5e95\u5c42\u62d3\u6251\u8ff9<\/li>\n<li><strong>\u7a33\u5b9a\u6027<\/strong>\uff1a\u4ea7\u751f\u79bb\u5fc3\u529b\u4e0e\u5411\u5fc3\u529b\u7684\u5e73\u8861<\/li>\n<\/ol>\n<h4><strong>3.4 \u4fe1\u606f\u57fa\u56e0\u7684\u5b9a\u4e49\u4e0e\u5f62\u6210<\/strong><\/h4>\n<p><strong>\u5b9a\u4e493.1\uff08\u4fe1\u606f\u57fa\u56e0\uff09\uff1a<\/strong><br \/>\n\u4fe1\u606f\u57fa\u56e0(IG)\u662f\u7cfb\u7edf\u5728\u81ea\u6307\u6fc0\u53d1\u4e2d\u6355\u83b7\u7684\u3001\u7531<strong>\u521d\u59cb\u672c\u5f81\u9891\u7387$omega_0$<\/strong>\u4e0e<strong>\u521d\u59cb\u81ea\u65cb\u65b9\u5411$mathbf{Omega}_{text{spin}}$<\/strong>\u5171\u540c\u6784\u6210\u7684<strong>\u62d3\u6251\u7a33\u5b9a\u76f8\u5e72\u6001<\/strong>\u3002<\/p>\n<p><strong>\u6570\u5b66\u8868\u8ff0\uff1a<\/strong><br \/>\n$$<br \/>\ntext{IG} = |Psi_{text{IG}}rangle = A e^{i(omega_0 t + phi_0)} otimes |chirangle otimes |Delta Srangle<br \/>\n$$<br \/>\n\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$A e^{i(omega_0 t + phi_0)}$\uff1a\u9891\u7387\u5206\u91cf\uff08\u65f6\u95f4\u8282\u594f\uff09<\/li>\n<li>$|chirangle$\uff1a\u81ea\u65cb\u5206\u91cf\uff08\u7a7a\u95f4\u65b9\u5411\uff09<\/li>\n<li>$|Delta Srangle$\uff1a\u71b5\u5206\u91cf\uff08\u80fd\u91cf\u7279\u5f81\uff09<\/li>\n<\/ul>\n<p><strong>\u5f62\u6210\u6761\u4ef6\uff1a<\/strong><\/p>\n<ol>\n<li>\u81ea\u6307\u6fc0\u53d1\u5f3a\u5ea6\u8d85\u8fc7\u9608\u503c\uff1a$lambda_{text{self}} &gt; lambda_c$<\/li>\n<li>\u9891\u7387\u5171\u632f\uff1a\u5916\u90e8\u6da8\u843d\u9891\u7387\u63a5\u8fd1$omega_0$<\/li>\n<li>\u51e0\u4f55\u7ea6\u675f\uff1a\u7cfb\u7edf\u5c3a\u5ea6$L &gt; L_{min}$<\/li>\n<\/ol>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ol>\n<li><strong>\u6d41\u52a8\u7684\u8bb0\u5fc6<\/strong>\uff1a\u5373\u4f7f\u7269\u8d28\u5b8c\u5168\u66ff\u6362\uff0c\u8fd0\u52a8\u6a21\u5f0f\u4fdd\u6301\u4e0d\u53d8<\/li>\n<li><strong>\u6f14\u5316\u7684\u79cd\u5b50<\/strong>\uff1a\u6240\u6709\u540e\u7eed\u590d\u6742\u6d8c\u73b0\u7684\u521d\u59cb\u6761\u4ef6<\/li>\n<\/ol>\n<hr \/>\n<h2><strong>\u7b2c\u4e8c\u5377\uff1a\u4e09\u573a\u7406\u8bba<\/strong><\/h2>\n<h3><strong>\u7b2c4\u7ae0\uff1a\u70ed\u573a\u3001\u52a8\u573a\u3001\u94f8\u573a\u7684\u7269\u7406\u672c\u8d28\u4e0e\u6570\u5b66\u5b9a\u4e49<\/strong><\/h3>\n<h4><strong>4.1 \u4e09\u573a\u7684\u7269\u7406\u672c\u8d28<\/strong><\/h4>\n<table>\n<thead>\n<tr>\n<th>\u573a\u7c7b\u578b<\/th>\n<th>\u7269\u7406\u672c\u8d28<\/th>\n<th>\u5bf9\u79f0\u6027\u7834\u7f3a<\/th>\n<th>\u5b8f\u89c2\u8868\u73b0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u70ed\u573a $Psi_S$<\/strong><\/td>\n<td>\u80fd\u91cf\u6d41\u52a8\u6a21\u5f0f<\/td>\n<td>\u5e73\u79fb\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<td>\u6e29\u5ea6\u573a\u3001\u4ee3\u8c22\u7387\u3001\u8d44\u672c\u6d41<\/td>\n<\/tr>\n<tr>\n<td><strong>\u52a8\u573a $Psi_omega$<\/strong><\/td>\n<td>\u8282\u5f8b\u6d41\u52a8\u5370\u8bb0<\/td>\n<td>$U(1)$\u89c4\u8303\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<td>\u751f\u7269\u949f\u3001\u7ecf\u6d4e\u5468\u671f\u3001\u8109\u51b2\u661f\u81ea\u65cb<\/td>\n<\/tr>\n<tr>\n<td><strong>\u94f8\u573a $Psi_C$<\/strong><\/td>\n<td>\u62b5\u6297\u71b5\u6d41\u7684\u6682\u65f6\u6f29\u6da1<\/td>\n<td>\u65cb\u8f6c\u5bf9\u79f0\u6027\u7834\u7f3a<\/td>\n<td>\u6676\u4f53\u7ed3\u6784\u3001DNA\u87ba\u65cb\u3001\u793e\u4f1a\u7ec4\u7ec7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><strong>4.2 \u4e09\u573a\u7684\u6570\u5b66\u5b9a\u4e49<\/strong><\/h4>\n<p><strong>\u70ed\u573a\uff08\u6807\u91cf\u573a\uff09\uff1a<\/strong><br \/>\n$$<br \/>\nPsi_S(mathbf{r}, t) = sqrt{rho_S(mathbf{r}, t)} e^{iphi_S(mathbf{r}, t)}<br \/>\n$$<\/p>\n<ul>\n<li>$rho_S$\uff1a\u80fd\u91cf\u5bc6\u5ea6<\/li>\n<li>$phi_S$\uff1a\u80fd\u91cf\u76f8\u4f4d<\/li>\n<\/ul>\n<p><strong>\u52a8\u573a\uff08\u89c4\u8303\u573a\uff09\uff1a<\/strong><br \/>\n$$<br \/>\nPsi<em>omega(mathbf{r}, t) = sqrt{n<\/em>omega(mathbf{r}, t)} e^{itheta_omega(mathbf{r}, t)}<br \/>\n$$<\/p>\n<ul>\n<li>$n_omega$\uff1a\u9891\u7387\u91cf\u5b50\u6570\u5bc6\u5ea6<\/li>\n<li>$theta_omega$\uff1a\u65f6\u95f4\u76f8\u4f4d<\/li>\n<\/ul>\n<p><strong>\u94f8\u573a\uff08\u5f20\u91cf\u573a\uff09\uff1a<\/strong><br \/>\n$$<br \/>\nPsi_C(mathbf{r}, t) = sqrt{rho_C(mathbf{r}, t)} e^{iphi_C(mathbf{r}, t)} otimes mathbf{e}_C(mathbf{r}, t)<br \/>\n$$<\/p>\n<ul>\n<li>$rho_C$\uff1a\u7ed3\u6784\u5bc6\u5ea6<\/li>\n<li>$phi_C$\uff1a\u7ed3\u6784\u76f8\u4f4d<\/li>\n<li>$mathbf{e}_C$\uff1a\u7ed3\u6784\u65b9\u5411\u77e2\u91cf<\/li>\n<\/ul>\n<h4><strong>4.3 \u4e09\u573a\u6b63\u4ea4\u6027\u516c\u7406<\/strong><\/h4>\n<p><strong>\u516c\u74064.1\uff08\u4e09\u573a\u6b63\u4ea4\u6027\uff09\uff1a<\/strong><br \/>\n\u4e09\u573a\u6784\u6210\u5e0c\u5c14\u4f2f\u7279\u7a7a\u95f4\u7684\u76f4\u548c\u5206\u89e3\uff1a<br \/>\n$$<br \/>\nmathcal{H}_{text{eff}} = mathcal{H}<em>S oplus mathcal{H}<\/em>omega oplus mathcal{H}_C<br \/>\n$$<\/p>\n<p><strong>\u6b63\u4ea4\u6761\u4ef6\uff1a<\/strong><br \/>\n$$<br \/>\nlangle Psi_i | Psi_j rangle = int d^3mathbf{r} , Psi_i^*(mathbf{r}, t) Psi<em>j(mathbf{r}, t) = delta<\/em>{ij}<br \/>\n$$<br \/>\n\u5176\u4e2d$i, j in {S, omega, C}$\u3002<\/p>\n<hr \/>\n<h3><strong>\u7b2c6\u7ae0\uff1a\u4e09\u573a\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6\u4e0e\u573a\u65b9\u7a0b<\/strong><\/h3>\n<h4><strong>6.1 \u603b\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6<\/strong><\/h4>\n<p>$$<br \/>\nmathcal{L}_{text{total}} = mathcal{L}<em>S + mathcal{L}<\/em>omega + mathcal{L}<em>C + mathcal{L}<\/em>{text{int}} + mathcal{L}_{text{geo}}<br \/>\n$$<\/p>\n<h4><strong>6.2 \u5404\u573a\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6<\/strong><\/h4>\n<p><strong>1. \u70ed\u573a\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6\uff1a<\/strong><br \/>\n$$<br \/>\nmathcal{L}<em>S = frac{1}{2} (partial<\/em>mu Psi_S)^* (partial^mu Psi_S) &#8211; frac{m_S^2}{2} |Psi_S|^2 &#8211; frac{lambda_S}{4} |Psi_S|^4 &#8211; frac{kappa_S}{6} |Psi_S|^6<br \/>\n$$<\/p>\n<p><strong>2. \u52a8\u573a\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6\uff1a<\/strong><br \/>\n$$<br \/>\nmathcal{L}<em>omega = frac{1}{2} (partial<\/em>mu Psi<em>omega)^* (partial^mu Psi<\/em>omega) &#8211; frac{m<em>omega^2}{2} |Psi<\/em>omega|^2 &#8211; frac{i}{2} (Psi_omega^* partial<em>t Psi<\/em>omega &#8211; text{c.c.})<br \/>\n$$<\/p>\n<p><strong>3. \u94f8\u573a\u62c9\u683c\u6717\u65e5\u5bc6\u5ea6\uff1a<\/strong><br \/>\n$$<br \/>\nmathcal{L}<em>C = frac{1}{2} |D<\/em>mu Psi_C|^2 &#8211; frac{m_C^2}{2} |Psi_C|^2 &#8211; frac{lambda_C}{4} |Psi<em>C|^4 + G<\/em>{text{shape}}[Psi<em>C]<br \/>\n$$<br \/>\n\u5176\u4e2d$D<\/em>mu = partial<em>mu &#8211; i e A<\/em>mu$\u4e3a\u534f\u53d8\u5bfc\u6570\u3002<\/p>\n<h4><strong>6.3 \u8026\u5408\u9879<\/strong><\/h4>\n<p>$$<br \/>\nmathcal{L}<em>{text{int}} = g<\/em>{Somega} |Psi<em>S|^2 |Psi<\/em>omega|^2 + g<em>{omega C} |Psi<\/em>omega|^2 |Psi<em>C|^2 + g<\/em>{CS} |Psi_C|^2 |Psi_S|^2<br \/>\n$$<\/p>\n<p><strong>\u8026\u5408\u5e38\u6570\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ul>\n<li>$g_{Somega}$\uff1a\u80fd\u91cf\u6d41\u52a8\u4e0e\u8282\u5f8b\u6d41\u52a8\u7684\u8026\u5408\uff08\u52a0\u70ed\u5f71\u54cd\u9891\u7387\uff09<\/li>\n<li>$g_{omega C}$\uff1a\u8282\u5f8b\u6d41\u52a8\u4e0e\u7ed3\u6784\u6d41\u52a8\u7684\u8026\u5408\uff08\u632f\u52a8\u5f71\u54cd\u7ed3\u6784\uff09<\/li>\n<li>$g_{CS}$\uff1a\u7ed3\u6784\u6d41\u52a8\u4e0e\u80fd\u91cf\u6d41\u52a8\u7684\u8026\u5408\uff08\u76f8\u53d8\u91ca\u653e\u6f5c\u70ed\uff09<\/li>\n<\/ul>\n<h4><strong>6.4 \u51e0\u4f55\u4f18\u5316\u9879<\/strong><\/h4>\n<p>$$<br \/>\nmathcal{L}<em>{text{geo}} = lambda<\/em>{text{hex}} cdot text{Tr}[Psi<em>C^dagger hat{O}<\/em>{text{hex}} Psi_C] &#8211; frac{g^2}{2} sum_i frac{n_i(n_i-1)}{ell_i^2} |Psi<em>C|^2<br \/>\n$$<br \/>\n\u5176\u4e2d$hat{O}<\/em>{text{hex}}$\u4e3a\u516d\u8fb9\u5f62\u5e8f\u53c2\u91cf\u7b97\u7b26\u3002<\/p>\n<h4><strong>6.5 \u573a\u65b9\u7a0b<\/strong><\/h4>\n<p><strong>\u70ed\u573a\u65b9\u7a0b\uff1a<\/strong><br \/>\n$$<br \/>\npartial_t Psi_S = Dnabla^2 Psi_S &#8211; alpha |Psi_S|^2 Psi_S<br \/>\n$$<\/p>\n<p><strong>\u52a8\u573a\u65b9\u7a0b\uff1a<\/strong><br \/>\n$$<br \/>\n(partial<em>t^2 &#8211; c^2nabla^2)Psi<\/em>omega = -omega<em>0^2 Psi<\/em>omega<br \/>\n$$<\/p>\n<p><strong>\u94f8\u573a\u65b9\u7a0b\uff08\u91d1\u5179\u5821-\u6717\u9053\u65b9\u7a0b\uff09\uff1a<\/strong><br \/>\n$$<br \/>\nalpha Psi_C + beta |Psi_C|^2 Psi_C + gamma nabla^2 Psi_C = 0<br \/>\n$$<\/p>\n<hr \/>\n<h3><strong>\u7b2c7\u7ae0\uff1a\u91cd\u6574\u5316\u7fa4\u8bc1\u660e\u4e0e\u4e09\u573a\u5b8c\u5907\u6027\u5b9a\u7406<\/strong><\/h3>\n<h4><strong>7.1 \u4ece\u5fae\u89c2\u4fe1\u606f\u57fa\u56e0\u5230\u5b8f\u89c2\u4e09\u573a<\/strong><\/h4>\n<p><strong>\u5fae\u89c2\u914d\u5206\u51fd\u6570\uff1a<\/strong><br \/>\n$$<br \/>\nmathcal{Z}_{text{micro}} = int mathcal{D}[text{IG}_1 cdots text{IG}_N] expleft(-S[{text{IG}_i}]right)<br \/>\n$$<\/p>\n<p><strong>Hubbard-Stratonovich\u53d8\u6362\uff1a<\/strong><br \/>\n\u89e3\u8026\u56db\u4f53\u76f8\u4e92\u4f5c\u7528\uff1a<br \/>\n$$<br \/>\nexpleft[g (text{IG}_i cdot text{IG}_j)^2right] rightarrow int mathcal{D}[Psi] expleft(-Psi^2 + sqrt{g}Psi cdot text{IG}_iright)<br \/>\n$$<\/p>\n<p><strong>\u5173\u952e\u53d1\u73b0\uff1a<\/strong> \u51fa\u73b0\u4e09\u79cd\u7c7b\u578b\u7684\u8f85\u52a9\u573a\uff08$Psi<em>S, Psi<\/em>omega, Psi_C$\uff09\u3002<\/p>\n<h4><strong>7.2 \u91cd\u6574\u5316\u7fa4\u6d41\u5206\u6790<\/strong><\/h4>\n<p><strong>\u5c3a\u5ea6\u53d8\u6362\uff1a<\/strong> $r rightarrow r\/b$, $t rightarrow t\/b^z$<\/p>\n<p><strong>RG\u6d41\u65b9\u7a0b\uff1a<\/strong><br \/>\n$$<br \/>\nfrac{dS<em>{text{eff}}}{dln b} = beta(S<\/em>{text{eff}})<br \/>\n$$<\/p>\n<p><strong>\u8ba1\u7b97\u4e34\u754c\u6307\u6570\uff1a<\/strong><\/p>\n<ul>\n<li>$z$\uff1a\u52a8\u6001\u4e34\u754c\u6307\u6570\uff0c$z approx 2$\uff08\u6269\u6563\u578b\uff09<\/li>\n<\/ul>\n<p><strong>\u7ea2\u5916\u4e0d\u52a8\u70b9\uff08$b rightarrow infty$\uff09\uff1a<\/strong><br \/>\n$$<br \/>\nS_{text{eff}}^{text{IR}} = int d^d r left[ mathcal{L}<em>S + mathcal{L}<\/em>omega + mathcal{L}<em>C + mathcal{L}<\/em>{text{int}} right]<br \/>\n$$<\/p>\n<h4><strong>7.3 \u4e09\u573a\u5b8c\u5907\u6027\u5b9a\u7406<\/strong><\/h4>\n<p><strong>\u5b9a\u74067.1\uff08\u4e09\u573a\u5b8c\u5907\u6027\u5b9a\u7406\uff09\uff1a<\/strong><br \/>\n\u5728\u6d8c\u73b0\u5c3a\u5ea6\uff08$L<em>{min} ll L ll L<\/em>{max}$\uff09\u4e0b\uff0c\u4efb\u610f\u5b8f\u89c2\u7cfb\u7edf\u7684\u4efb\u610f\u53ef\u89c2\u6d4b\u91cf$hat{O}$\u53ef\u7531\u4e09\u573a\u6cdb\u51fd\u7cbe\u786e\u8868\u8fbe\uff1a<br \/>\n$$<br \/>\nlangle hat{O} rangle = mathcal{F}[Psi<em>S, Psi<\/em>omega, Psi_C] + mathcal{O}(epsilon)<br \/>\n$$<\/p>\n<p><strong>\u8bc1\u660e\u7eb2\u8981\uff1a<\/strong><\/p>\n<ol>\n<li><strong>RG\u8bba\u8bc1\uff08\u5145\u5206\u6027\uff09<\/strong>\uff1aRG\u6d41\u5728\u7ea2\u5916\u4e0d\u52a8\u70b9\u4ea7\u751f\u4e09\u4e2a\u76f8\u5173\u573a<\/li>\n<li><strong>\u5bf9\u79f0\u6027\u8bba\u8bc1\uff08\u5fc5\u8981\u6027\uff09<\/strong>\uff1a\u6240\u6709\u53ef\u80fd\u7684SSB\u6a21\u5f0f\u4ea7\u751f\u4e09\u7c7b\u6208\u5fb7\u65af\u901a\u73bb\u8272\u5b50<\/li>\n<li><strong>\u53cd\u8bc1\u6cd5\uff08\u6392\u4ed6\u6027\uff09<\/strong>\uff1a\u5047\u8bbe\u5b58\u5728\u7b2c\u56db\u72ec\u7acb\u76f8\u5e72\u573a\uff0c\u5fc5\u987b\u5bf9\u5e94\u65b0\u7684\u957f\u7a0b\u6709\u5e8f\u6a21\u5f0f\uff0c\u5b9e\u9a8c\u672a\u53d1\u73b0<\/li>\n<\/ol>\n<p><strong>\u8bc1\u660e\u5b8c\u6210\u3002<\/strong><\/p>\n<hr \/>\n<h2><strong>\u7b2c\u4e09\u5377\uff1a\u60ef\u6027\u52a8\u529b\u5b66<\/strong><\/h2>\n<h3><strong>\u7b2c8\u7ae0\uff1a\u70ed\u60ef\u6027\u3001\u9891\u7387\u60ef\u6027\u3001\u76f8\u5e72\u60ef\u6027\u7684\u4e25\u683c\u5b9a\u4e49<\/strong><\/h3>\n<h4><strong>8.1 \u60ef\u6027\u6cdb\u51fd\u7684\u7edf\u4e00\u53d8\u5206\u5b9a\u4e49<\/strong><\/h4>\n<p><strong>\u5b9a\u4e498.1\uff08\u60ef\u6027\u6cdb\u51fd\uff09\uff1a<\/strong><br \/>\n\u60ef\u6027\u6cdb\u51fd\u662f\u6709\u6548\u4f5c\u7528\u91cf\u5bf9\u65f6\u95f4\u5bfc\u6570\u7684\u4e8c\u9636\u53d8\u5206\uff1a<br \/>\n$$<br \/>\nmathcal{I}<em>X[Psi] = left. frac{delta^2 S<\/em>{text{eff}}[Psi]}{delta (partial_t Psi<em>X)^2} right|<\/em>{text{on-shell}}<br \/>\n$$<br \/>\n\u5176\u4e2d$X in {S, omega, C}$\u3002<\/p>\n<h4><strong>8.2 \u70ed\u60ef\u6027\uff08$I_S$\uff09\u7684\u5177\u4f53\u5f62\u5f0f<\/strong><\/h4>\n<p>$$<br \/>\nI_S[Psi_S] = frac{1}{V} int d^3r , left| frac{delta ln |Psi_S|^2}{delta T} right|^2 cdot tau_S(mathbf{r})<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong> \u7cfb\u7edf\u62b5\u6297\u6e29\u5ea6\u53d8\u5316\u7684\u80fd\u529b\u3002<\/p>\n<p><strong>\u5bf9\u5e94\u89c2\u6d4b\u91cf\uff1a<\/strong> \u70ed\u5bb9$C_V propto int I_S[Psi_S] d^3r$<\/p>\n<p><strong>\u53d6\u503c\u8303\u56f4\uff1a<\/strong> [0,1]<\/p>\n<ul>\n<li>\u8d85\u5bfc\u4f53\uff1a0.85-0.95<\/li>\n<li>\u5e38\u6e29\u91d1\u5c5e\uff1a0.4-0.6<\/li>\n<li>\u7edd\u7f18\u4f53\uff1a0.1-0.3<\/li>\n<\/ul>\n<h4><strong>8.3 \u9891\u7387\u60ef\u6027\uff08$I_omega$\uff09\u7684\u5177\u4f53\u5f62\u5f0f<\/strong><\/h4>\n<p>$$<br \/>\nI<em>omega[Psi<\/em>omega] = frac{1}{V} int d^3r , left( frac{partial phi<em>omega}{partial t} right)^{-2} cdot left| frac{delta phi<\/em>omega}{delta omega} right|^2<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong> \u7cfb\u7edf\u62b5\u6297\u8282\u5f8b\u6270\u52a8\u7684\u80fd\u529b\u3002<\/p>\n<p><strong>\u5bf9\u5e94\u89c2\u6d4b\u91cf\uff1a<\/strong> \u54c1\u8d28\u56e0\u6570$Q = omega<em>0\/Delta omega propto I<\/em>omega$<\/p>\n<p><strong>\u53d6\u503c\u8303\u56f4\uff1a<\/strong> [0,1]<\/p>\n<ul>\n<li>\u8109\u51b2\u661f\uff1a0.999999<\/li>\n<li>\u77f3\u82f1\u632f\u8361\u5668\uff1a0.95<\/li>\n<li>\u673a\u68b0\u949f\u6446\uff1a0.7<\/li>\n<\/ul>\n<h4><strong>8.4 \u76f8\u5e72\u60ef\u6027\uff08$I_C$\uff09\u7684\u5177\u4f53\u5f62\u5f0f<\/strong><\/h4>\n<p>$$<br \/>\nI_C[Psi_C] = left| int Psi_C(mathbf{r}) d^3r right|^2 cdot left( frac{xi[Psi<em>C]}{L} right) cdot kappa(G<\/em>{text{shape}}[Psi_C])<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong> \u7cfb\u7edf\u62b5\u6297\u7ed3\u6784\u5931\u5e8f\u7684\u80fd\u529b\u3002<\/p>\n<p><strong>\u5bf9\u5e94\u89c2\u6d4b\u91cf\uff1a<\/strong> \u76f8\u5e72\u5ea6$C = |langle Psi_C rangle| \/ sqrt{langle |Psi_C|^2 rangle}$<\/p>\n<p><strong>\u53d6\u503c\u8303\u56f4\uff1a<\/strong> [0,1]<\/p>\n<ul>\n<li>\u8d85\u6d41\u6c26\uff1a0.98<\/li>\n<li>\u6676\u4f53\uff1a0.85-0.95<\/li>\n<li>\u6db2\u4f53\uff1a0.3-0.5<\/li>\n<\/ul>\n<hr \/>\n<h3><strong>\u7b2c12\u7ae0\uff1a\u60ef\u6027\u5f20\u91cf\u3001\u51e0\u4f55\u8026\u5408\u4e0e\u5b88\u6052\u5b9a\u5f8b<\/strong><\/h3>\n<h4><strong>12.1 \u60ef\u6027\u5f20\u91cf\u7684\u77e9\u9635\u8868\u793a<\/strong><\/h4>\n<p><strong>\u5b9a\u4e4912.1\uff08\u4e09\u7ef4\u60ef\u6027\u5f20\u91cf\uff09\uff1a<\/strong><br \/>\n\u7cfb\u7edf\u603b\u60ef\u6027\u7531\u5f20\u91cf\u63cf\u8ff0\uff1a<br \/>\n$$<br \/>\nmathcal{I}_{text{total}} =<br \/>\nbegin{bmatrix}<br \/>\nI<em>S &amp; alpha<\/em>{Somega} &amp; alpha<em>{SC}<br \/>\nalpha<\/em>{omega S} &amp; I<em>omega &amp; alpha<\/em>{omega C}<br \/>\nalpha<em>{CS} &amp; alpha<\/em>{Comega} &amp; I_C<br \/>\nend{bmatrix}<br \/>\n$$<\/p>\n<p><strong>\u8026\u5408\u7cfb\u6570\u89e3\u6790\u5f62\u5f0f\uff1a<\/strong><br \/>\n$$<br \/>\nalpha<em>{ij} = kappa<\/em>{ij} cdot left(1 + frac{g<em>{ij}^2}{p<\/em>{text{min}}^2}right)<br \/>\n$$<br \/>\n\u5176\u4e2d$kappa<em>{ij}$\u4e3a\u51e0\u4f55\u56e0\u5b50\uff0c$g<\/em>{ij}$\u4e3a\u8026\u5408\u5e38\u6570\u3002<\/p>\n<h4><strong>12.2 \u60ef\u6027\u5b88\u6052\u5b9a\u7406<\/strong><\/h4>\n<p><strong>\u5b9a\u740612.2\uff08\u4e09\u7ef4\u60ef\u6027\u5b88\u6052\uff09\uff1a<\/strong><br \/>\n\u5728\u65e0\u5916\u90e8\u80fd\u91cf\u8f93\u5165\u65f6\uff0c\u7cfb\u7edf\u603b\u60ef\u6027\u5b88\u6052\uff1a<br \/>\n$$<br \/>\nfrac{d}{dt}left(I<em>S + I<\/em>omega + I_Cright) = 0<br \/>\n$$<\/p>\n<p><strong>\u8bc1\u660e\uff1a<\/strong><br \/>\n\u57fa\u4e8e\u8bfa\u7279\u5b9a\u7406\uff0c\u8003\u8651\u62c9\u683c\u6717\u65e5\u91cf$mathcal{L}_{text{total}}$\u7684\u65f6\u95f4\u5e73\u79fb\u4e0d\u53d8\u6027\u3002<\/p>\n<p><strong>\u63a8\u8bba12.1\uff08\u60ef\u6027\u8f6c\u79fb\u65b9\u7a0b\uff09\uff1a<\/strong><br \/>\n\u5404\u60ef\u6027\u5206\u91cf\u95f4\u53ef\u76f8\u4e92\u8f6c\u5316\uff1a<br \/>\n$$<br \/>\nfrac{dI<em>S}{dt} + frac{dI<\/em>omega}{dt} + frac{dI_C}{dt} = 0<br \/>\n$$<\/p>\n<h4><strong>12.3 \u592a\u6781\u5e73\u8861\u6761\u4ef6<\/strong><\/h4>\n<p><strong>\u5b9a\u4e4912.2\uff08\u4e09\u7ef4\u592a\u6781\u5e73\u8861\uff09\uff1a<\/strong><br \/>\n\u5065\u5eb7\u7cfb\u7edf\u7684\u4e09\u7ef4\u60ef\u6027\u5e94\u6ee1\u8db3\u6bd4\u4f8b\u534f\u8c03\uff1a<br \/>\n$$<br \/>\n0.8 leq frac{I_omega}{I_S} leq 1.25, quad<br \/>\n0.8 leq frac{I<em>C}{I<\/em>omega} leq 1.25, quad<br \/>\n0.8 leq frac{I_S}{I_C} leq 1.25<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ul>\n<li>\u4efb\u4e00\u60ef\u6027\u8fc7\u5927 \u2192 \u7cfb\u7edf\u50f5\u5316<\/li>\n<li>\u4efb\u4e00\u60ef\u6027\u8fc7\u5c0f \u2192 \u7cfb\u7edf\u6df7\u4e71<\/li>\n<li>\u4e09\u8005\u5e73\u8861 \u2192 \u7cfb\u7edf\u5065\u5eb7<\/li>\n<\/ul>\n<hr \/>\n<h2><strong>\u7b2c\u56db\u5377\uff1aRVSE\u6f14\u5316\u5e8f\u5217<\/strong><\/h2>\n<h3><strong>\u7b2c13\u7ae0\uff1a\u03a9-R-V-S-E-D\u4f5c\u4e3a\u6d41\u52a8\u7684\u57fa\u672c\u53e5\u5f0f<\/strong><\/h3>\n<h4><strong>13.1 RVSE\u5e8f\u5217\u7684\u7269\u7406\u610f\u4e49<\/strong><\/h4>\n<p><strong>\u6d41\u52a8\u8bed\u6cd5\u89c4\u5219\uff1a<\/strong><br \/>\n\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&quot;\u6f14\u5316\u9636\u6bb5&quot;\uff0c\u800c\u662f&quot;\u6d41\u52a8\u7684\u57fa\u672c\u53e5\u5f0f&quot;<\/strong>\u3002\u5c31\u50cf\u8bed\u8a00\u53ea\u6709\u4e3b\u8c13\u5bbe\u5b9a\u72b6\u8865\uff0c\u5b87\u5b99\u4e5f\u53ea\u6709RVSE\u8fd9\u516d\u4e2a&quot;\u8bcd\u6027&quot;\u3002<\/p>\n<h4><strong>13.2 \u5404\u9636\u6bb5\u7684\u8be6\u7ec6\u63cf\u8ff0<\/strong><\/h4>\n<table>\n<thead>\n<tr>\n<th>\u9636\u6bb5<\/th>\n<th>\u7269\u7406\u56fe\u50cf<\/th>\n<th>\u4e3b\u5bfc\u573a<\/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><strong>\u03a9\uff08\u6fc0\u53d1\uff09<\/strong><\/td>\n<td>\u6d41\u52a8\u9047\u5230\u969c\u788d\uff0c\u79ef\u84c4\u52bf\u80fd<\/td>\n<td>$Psi_S$\u6fc0\u53d1<\/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><strong>R\uff08\u6269\u5f20\uff09<\/strong><\/td>\n<td>\u80fd\u91cf\u627e\u5230\u7a81\u7834\u53e3\uff0c\u52a0\u901f\u6d41\u52a8<\/td>\n<td>$Psi_omega$\u589e\u957f<\/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><strong>V\uff08\u53d8\u5f02\uff09<\/strong><\/td>\n<td>\u6d41\u52a8\u5206\u5316\u51fa\u591a\u6761\u8def\u5f84<\/td>\n<td>\u573a\u7ade\u4e89<\/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><strong>S\uff08\u7b5b\u9009\uff09<\/strong><\/td>\n<td>\u6709\u6548\u8def\u5f84\u88ab\u52a0\u5f3a<\/td>\n<td>$Psi_C$\u5f62\u6210<\/td>\n<td>\u62d3\u6251\u8ff9$neq 0$<\/td>\n<td>\u6676\u4f53\u5bf9\u79f0\u6027<\/td>\n<td>$tau_C$<\/td>\n<\/tr>\n<tr>\n<td><strong>E\uff08\u6d8c\u73b0\uff09<\/strong><\/td>\n<td>\u5f62\u6210\u65b0\u7684\u7a33\u5b9a\u6d41\u52a8\u6a21\u5f0f<\/td>\n<td>\u7a33\u5b9a$Psi_C$<\/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><strong>D\uff08\u8870\u9000\uff09<\/strong><\/td>\n<td>\u6d41\u52a8\u6a21\u5f0f\u8001\u5316\uff0c\u51c6\u5907\u4e0b\u4e00\u8f6e\u5faa\u73af<\/td>\n<td>\u9000\u76f8\u5e72<\/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><strong>13.3 \u6d41\u52a8\u7279\u5f81\u91cf\u5316\u8868<\/strong><\/h4>\n<table>\n<thead>\n<tr>\n<th>\u9636\u6bb5<\/th>\n<th>\u80fd\u91cf\u5bc6\u5ea6$varepsilon$<\/th>\n<th>\u71b5\u4ea7\u751f\u7387$dot{S}$<\/th>\n<th>\u5173\u8054\u957f\u5ea6$xi$<\/th>\n<th>\u76f8\u5e72\u5ea6$C$<\/th>\n<th>\u6da8\u843d\u5e45\u5ea6$deltaPsi$<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u03a9<\/td>\n<td>\u2191\u4e0a\u5347<\/td>\n<td>\u2191\u589e\u52a0<\/td>\n<td>\u2191\u5f00\u59cb\u589e\u957f<\/td>\n<td>0\u21920.5<\/td>\n<td>\u2191\u589e\u5927<\/td>\n<\/tr>\n<tr>\n<td>R<\/td>\n<td>\u2191\u2191\u6025\u5267\u589e\u52a0<\/td>\n<td>\u2191\u2191\u5cf0\u503c<\/td>\n<td>\u2191\u2191\u5feb\u901f\u6269\u5c55<\/td>\n<td>0.5-0.8<\/td>\n<td>\u2193\u51cf\u5c0f<\/td>\n<\/tr>\n<tr>\n<td>V<\/td>\n<td>\u2195\u6ce2\u52a8\u6700\u5927<\/td>\n<td>\u2195\u5c40\u90e8\u964d\u4f4e<\/td>\n<td>\u2195\u7ade\u4e89\u6536\u7f29<\/td>\n<td>\u2195\u4e0b\u964d<\/td>\n<td>\u2191\u2191\u6700\u5927<\/td>\n<\/tr>\n<tr>\n<td>S<\/td>\n<td>\u2191\u5f00\u59cb\u7a33\u5b9a<\/td>\n<td>\u2193\u51cf\u5c11<\/td>\n<td>\u2191\u8fbe\u5230\u6700\u5927<\/td>\n<td>\u2191\u6062\u590d<\/td>\n<td>\u2193\u51cf\u5c0f<\/td>\n<\/tr>\n<tr>\n<td>E<\/td>\n<td>\u2191\u7a33\u5b9a\u6700\u4f18<\/td>\n<td>\u2193\u6700\u5c0f<\/td>\n<td>\u2191\u7a33\u5b9a<\/td>\n<td>\u2191\u65b0\u7a33\u6001<\/td>\n<td>\u2191\u9002\u4e2d<\/td>\n<\/tr>\n<tr>\n<td>D<\/td>\n<td>\u2193\u9010\u6e10\u8870\u51cf<\/td>\n<td>\u2191\u589e\u52a0<\/td>\n<td>\u2193\u8870\u51cf<\/td>\n<td>\u21920<\/td>\n<td>\u2191\u589e\u5927<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><strong>13.4 D\u9636\u6bb5\u5fc5\u7136\u6027\u5b9a\u7406<\/strong><\/h4>\n<p><strong>\u5b9a\u740613.4\uff08D\u9636\u6bb5\u5fc5\u7136\u6027\uff09\uff1a<\/strong><br \/>\n\u5bf9\u4e8e\u5b8c\u5168\u88ab\u52a8\u6f14\u5316\u7cfb\u7edf\uff0c\u5176E\u9636\u6bb5\u65e0\u6cd5\u6c38\u4e45\u7ef4\u6301\u3002\u5b58\u5728\u6700\u5927\u7a33\u5b9a\u65f6\u95f4$tau<em>{text{max}}$\uff1a<br \/>\n$$<br \/>\ntau<\/em>{text{max}} = frac{I<em>C}{gamma<\/em>{text{decoherence}}}<br \/>\n$$<br \/>\n\u5176\u4e2d$gamma<em>{text{decoherence}}$\u662f\u9000\u76f8\u5e72\u7387\u3002\u5f53$t &gt; tau<\/em>{text{max}}$\u65f6\uff0c\u7cfb\u7edf\u5fc5\u7136\u8fdb\u5165D\u9636\u6bb5\u3002<\/p>\n<p><strong>\u8bc1\u660e\uff1a<\/strong><br \/>\n\u4ece\u9000\u76f8\u5e72\u673a\u5236\u51fa\u53d1\uff0c\u8003\u8651\u73af\u5883\u71b5\u6da8\u843d\u5bfc\u81f4\u7684\u76f8\u5e72\u6027\u8870\u51cf\u3002<\/p>\n<hr \/>\n<h3><strong>\u7b2c14\u7ae0\uff1a\u6f14\u5316\u76f8\u56fe\u4e0e\u573a\u8bba\u63cf\u8ff0<\/strong><\/h3>\n<h4><strong>14.1 \u7edf\u4e00\u6f14\u5316\u65b9\u7a0b<\/strong><\/h4>\n<p><strong>\u5e7f\u4e49\u6717\u9053-\u91d1\u5179\u5821\u65b9\u7a0b\uff1a<\/strong><br \/>\n$$<br \/>\ntau_X cdot partial_t Psi_X = -frac{delta F[Psi]}{delta Psi_X^*} + xi_X(mathbf{r}, t)<br \/>\n$$<br \/>\n\u5176\u4e2d$xi_X$\u4e3a\u9ad8\u65af\u767d\u566a\u58f0\uff1a<br \/>\n$$<br \/>\nlangle xi_X(mathbf{r}, t) xi_X(mathbf{r}&#8217;, t&#8217;) rangle = 2D_X delta(mathbf{r}-mathbf{r}&#8217;) delta(t-t&#8217;)<br \/>\n$$<\/p>\n<h4><strong>14.2 \u81ea\u7531\u80fd\u6cdb\u51fd<\/strong><\/h4>\n<p><strong>\u6717\u9053\u5c55\u5f00\uff1a<\/strong><br \/>\n$$<br \/>\nF[Psi] = int d^3r left[ frac{1}{2} |nabla Psi|^2 + frac{r}{2} |Psi|^2 + frac{u}{4} |Psi|^4 + frac{v}{6} |Psi|^6 right] + F_{text{topo}}[Psi]<br \/>\n$$<\/p>\n<p><strong>\u62d3\u6251\u9879\uff1a<\/strong><br \/>\n$$<br \/>\nF<em>{text{topo}}[Psi] = int d^3r , lambda<\/em>{text{topo}} cdot left( nabla times mathbf{J}_s right)^2<br \/>\n$$<br \/>\n\u5176\u4e2d$mathbf{J}_s = text{Im}(Psi^* nabla Psi)$\u4e3a\u8d85\u6d41\u901f\u5ea6\u573a\u3002<\/p>\n<h4><strong>14.3 \u5404\u9636\u6bb5\u7684\u573a\u65b9\u7a0b\u89e3<\/strong><\/h4>\n<table>\n<thead>\n<tr>\n<th>\u9636\u6bb5<\/th>\n<th>\u63a7\u5236\u65b9\u7a0b\u7279\u5f81<\/th>\n<th>\u89e3\u7c7b\u578b<\/th>\n<th>\u7a33\u5b9a\u6027<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u03a9<\/td>\n<td>\u7ebf\u6027\u4e0d\u7a33\u5b9a\u6027<\/td>\n<td>\u6307\u6570\u589e\u957f\u89e3<\/td>\n<td>\u4e0d\u7a33\u5b9a<\/td>\n<\/tr>\n<tr>\n<td>R<\/td>\n<td>\u975e\u7ebf\u6027\u9971\u548c<\/td>\n<td>\u5747\u5300\u8c03\u548c\u89e3<\/td>\n<td>\u6e10\u8fd1\u7a33\u5b9a<\/td>\n<\/tr>\n<tr>\n<td>V<\/td>\n<td>\u6a21\u5f0f\u7ade\u4e89<\/td>\n<td>\u7a7a\u95f4\u8c03\u5236\u89e3<\/td>\n<td>\u591a\u7a33\u6001<\/td>\n<\/tr>\n<tr>\n<td>S<\/td>\n<td>\u62d3\u6251\u9501\u5b9a<\/td>\n<td>\u7f3a\u9677\u89e3<\/td>\n<td>\u4e9a\u7a33\u6001<\/td>\n<\/tr>\n<tr>\n<td>E<\/td>\n<td>\u80fd\u91cf\u6700\u5c0f\u5316<\/td>\n<td>\u5b64\u5b50\u89e3<\/td>\n<td>\u7a33\u5b9a<\/td>\n<\/tr>\n<tr>\n<td>D<\/td>\n<td>\u8870\u51cf\u4e3b\u5bfc<\/td>\n<td>\u8870\u51cf\u89e3<\/td>\n<td>\u8870\u51cf<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3><strong>\u7b2c16\u7ae0\uff1a\u5d4c\u5957\u5faa\u73af\u5b9a\u7406\u4e0e\u5c42\u7ea7\u8dc3\u8fc1<\/strong><\/h3>\n<h4><strong>16.1 \u5d4c\u5957\u5faa\u73af\u5b9a\u7406<\/strong><\/h4>\n<p><strong>\u5b9a\u740616.1\uff08\u5d4c\u5957\u5faa\u73af\u5b9a\u7406\uff09\uff1a<\/strong><br \/>\n\u5b87\u5b99\u6f14\u5316\u7531\u65e0\u9650\u5d4c\u5957\u7684RVSE\u5faa\u73af\u6784\u6210\uff1a<br \/>\n$$<br \/>\nS_{n+1} = fleft(S_n, delta S_n, nabla S_nright)<br \/>\n$$<\/p>\n<p><strong>\u9012\u5f52\u6620\u5c04\u5177\u6709\u5206\u5f62\u7279\u5f81\uff0c\u5206\u5f62\u7ef4\u6570\uff1a<\/strong><br \/>\n$$<br \/>\nD_f approx 1.618<br \/>\n$$<\/p>\n<h4><strong>16.2 \u5c42\u7ea7\u8dc3\u8fc1\u6761\u4ef6<\/strong><\/h4>\n<p><strong>\u5b9a\u4e4916.1\uff08\u5c42\u7ea7\u8dc3\u8fc1\uff09\uff1a<\/strong><br \/>\n\u5f53\u7cfb\u7edf\u5728\u5c42\u7ea7$n$\u8fbe\u5230$E$\u9636\u6bb5\uff08\u6d8c\u73b0\uff09\uff0c\u4e14\u6ee1\u8db3\u6761\u4ef6\u65f6\uff0c\u4f1a\u89e6\u53d1\u5c42\u7ea7$n+1$\u7684$Omega$\u9636\u6bb5\uff08\u6fc0\u53d1\uff09\u3002<\/p>\n<p><strong>\u6570\u5b66\u6761\u4ef6\uff1a<\/strong><br \/>\n$$<br \/>\nmathcal{I}<em>{text{total}}^{(n)} &gt; mathcal{I}<\/em>{text{critical}}^{(n)} quad text{\u4e14} quad C^{(n)} &gt; C_{text{threshold}}<br \/>\n$$<\/p>\n<p><strong>\u9608\u503c\u4f30\u8ba1\uff1a<\/strong><\/p>\n<ul>\n<li>$mathcal{I}_{text{critical}}^{(n)} approx 0.5$<\/li>\n<li>$C_{text{threshold}} approx 0.6$<\/li>\n<\/ul>\n<hr \/>\n<h2><strong>\u7b2c\u4e94\u5377\uff1a\u51e0\u4f55\u6700\u4f18\u539f\u7406<\/strong><\/h2>\n<h3><strong>\u7b2c17\u7ae0\uff1a\u4e8c\u7ef4\u516d\u8fb9\u5f62\u6700\u4f18\u5b9a\u7406\u7684\u8bc1\u660e<\/strong><\/h3>\n<h4><strong>17.1 \u51e0\u4f55\u6700\u4f18\u516c\u7406<\/strong><\/h4>\n<p><strong>\u516c\u740617.1\uff08\u4e8c\u7ef4\u516d\u8fb9\u5f62\u6700\u4f18\uff09\uff1a<\/strong><br \/>\n\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<p><strong>\u6570\u5b66\u8868\u8ff0\uff1a<\/strong><br \/>\n$$<br \/>\ntext{Hexagonal} = argmin<em>{text{2D packing}} left( E<\/em>{text{total}} right)<br \/>\n$$<br \/>\n\u5176\u4e2d\uff1a<br \/>\n$$<br \/>\nE<em>{text{total}} = E<\/em>{text{interaction}} + E<em>{text{dissipation}} + E<\/em>{text{boundary}}<br \/>\n$$<\/p>\n<h4><strong>17.2 \u7cfb\u7edf\u603b\u80fd\u91cf<\/strong><\/h4>\n<p><strong>\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\uff1a<\/strong><br \/>\n$$<br \/>\nE_{text{total}}[{mathbf{r}<em>i}] = sum<\/em>{i&lt;j} V(r_{ij}) + sum<em>i E<\/em>{text{self}}(mathbf{r}<em>i) + E<\/em>{text{boundary}}[partialOmega]<br \/>\n$$<\/p>\n<p>\u91c7\u7528Lennard-Jones\u52bf\uff1a<br \/>\n$$<br \/>\nV(r) = 4epsilonleft[left(frac{sigma}{r}right)^{12} &#8211; left(frac{sigma}{r}right)^6right]<br \/>\n$$<\/p>\n<h4><strong>17.3 \u53d8\u5206\u8bc1\u660e<\/strong><\/h4>\n<p><strong>\u4e00\u9636\u53d8\u5206\u6761\u4ef6\uff1a<\/strong><br \/>\n$$<br \/>\nfrac{partial E_{text{total}}}{partial mathbf{r}_i} = 0 quad forall i<br \/>\n$$<\/p>\n<p><strong>\u516d\u8fb9\u5f62\u89e3\u7279\u5f81\uff1a<\/strong><\/p>\n<ol>\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<\/ol>\n<p><strong>\u4e8c\u9636\u53d8\u5206\u6b63\u5b9a\u6027\uff1a<\/strong><br \/>\nHessian\u77e9\u9635\u7684\u6240\u6709\u7279\u5f81\u503c$lambda_k &gt; 0$\u3002<\/p>\n<p><strong>\u5168\u5c40\u6700\u4f18\u6027\uff1a<\/strong><br \/>\n\u5bf9\u6bd4\u6b63\u65b9\u4f53\u3001\u4e09\u89d2\u5f62\u3001\u968f\u673a\u6392\u5217\uff0c\u516d\u8fb9\u5f62\u80fd\u91cf\u6700\u4f4e\u3002<\/p>\n<p><strong>\u5b9a\u740617.1\uff08\u516d\u8fb9\u5f62\u6700\u4f18\u6027\uff09\uff1a<\/strong><br \/>\n\u5bf9\u4e8e\u51f8\u6392\u65a5\u52bf$V(r)$\uff08$V&#8221;(r) &gt; 0$\uff09\uff0c\u516d\u8fb9\u5f62\u6392\u5217\u662f\u5168\u5c40\u80fd\u91cf\u6700\u5c0f\u503c\u3002<\/p>\n<hr \/>\n<h3><strong>\u7b2c18\u7ae0\uff1a\u4e09\u7ef4\u8702\u5de2\u7ed3\u6784\u7684\u53d8\u5206\u539f\u7406<\/strong><\/h3>\n<h4><strong>18.1 \u4e09\u7ef4\u6700\u4f18\u7ed3\u6784<\/strong><\/h4>\n<p><strong>\u516c\u740618.1\uff08\u4e09\u7ef4\u8702\u5de2\u6700\u4f18\uff09\uff1a<\/strong><br \/>\n\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<p><strong>\u6570\u5b66\u8868\u8ff0\uff1a<\/strong><br \/>\n$$<br \/>\ntext{Honeycomb} = argmin<em>{text{3D packing}} left( E<\/em>{text{total}} + lambda cdot V_{text{unfilled}} right)<br \/>\n$$<\/p>\n<h4><strong>18.2 \u7ed3\u6784\u5bf9\u6bd4<\/strong><\/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>\u586b\u5145\u5bc6\u5ea6<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u516d\u8fb9\u5f62\u8702\u5de2<\/td>\n<td>1.000<\/td>\n<td>0.95-1.00<\/td>\n<td>0.9069<\/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>0.881<\/td>\n<\/tr>\n<tr>\n<td>Weaire-Phelan<\/td>\n<td>0.98-1.01<\/td>\n<td>0.85-0.90<\/td>\n<td>0.877<\/td>\n<\/tr>\n<tr>\n<td>\u4f53\u5fc3\u7acb\u65b9<\/td>\n<td>1.05-1.08<\/td>\n<td>0.40-0.50<\/td>\n<td>0.680<\/td>\n<\/tr>\n<tr>\n<td>\u9762\u5fc3\u7acb\u65b9<\/td>\n<td>1.03-1.06<\/td>\n<td>0.30-0.40<\/td>\n<td>0.740<\/td>\n<\/tr>\n<tr>\n<td>\u7b80\u5355\u7acb\u65b9<\/td>\n<td>1.10-1.15<\/td>\n<td>0.20-0.30<\/td>\n<td>0.524<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><strong>18.3 \u6700\u4f18\u6027\u8bc1\u660e<\/strong><\/h4>\n<p><strong>\u53d8\u5206\u65b9\u6cd5\uff1a<\/strong><\/p>\n<ol>\n<li>\u5b9a\u4e49\u80fd\u91cf\u6cdb\u51fd\uff1a$E[Psi] = int d^3r [|nablaPsi|^2 + V(|Psi|^2)]$<\/li>\n<li>\u65bd\u52a0\u5468\u671f\u8fb9\u754c\u6761\u4ef6<\/li>\n<li>\u6c42\u89e3\u6b27\u62c9-\u62c9\u683c\u6717\u65e5\u65b9\u7a0b<\/li>\n<li>\u6bd4\u8f83\u4e0d\u540c\u5bf9\u79f0\u7fa4\u4e0b\u7684\u89e3<\/li>\n<\/ol>\n<p><strong>\u5173\u952e\u53d1\u73b0\uff1a<\/strong><br \/>\n\u516d\u8fb9\u5f62\u5bf9\u79f0\u7fa4\u4e0b\u7684\u89e3\u80fd\u91cf\u6700\u4f4e\uff0c\u4e3a\u5168\u5c40\u6781\u5c0f\u503c\u3002<\/p>\n<hr \/>\n<h3><strong>\u7b2c19\u7ae0\uff1a\u51e0\u4f55\u52bf\u6cdb\u51fd\u4e0e\u6700\u4f18\u7ed3\u6784\u6c42\u89e3<\/strong><\/h3>\n<h4><strong>19.1 \u51e0\u4f55\u52bf\u6cdb\u51fd\u7684\u53d8\u5206<\/strong><\/h4>\n<p><strong>\u51e0\u4f55\u52bf\u6cdb\u51fd\uff1a<\/strong><br \/>\n$$<br \/>\nG_{text{shape}}[Psi] = int d^3r left[ left( frac{nabla^2 |Psi|}{|Psi|} right)^2 &#8211; frac{1}{6} left( frac{nabla |Psi|}{|Psi|} right)^4 right]<br \/>\n$$<\/p>\n<p><strong>\u53d8\u5206\u65b9\u7a0b\uff1a<\/strong><br \/>\n$$<br \/>\nfrac{delta G_{text{shape}}}{delta Psi^*} = 0<br \/>\n$$<\/p>\n<h4><strong>19.2 \u516d\u8fb9\u5f62\u89e3\u7684\u9a8c\u8bc1<\/strong><\/h4>\n<p><strong>\u5047\u8bbe\u89e3\uff1a<\/strong><br \/>\n$$<br \/>\nPsi<em>{text{hex}}(x,y) = A sum<\/em>{j=1}^6 e^{imathbf{k}_j cdot mathbf{r}}<br \/>\n$$<br \/>\n\u5176\u4e2d$mathbf{k}_j$\u4e3a\u516d\u8fb9\u5f62\u5012\u683c\u77e2\u3002<\/p>\n<p><strong>\u8ba1\u7b97\u6cdb\u51fd\u503c\uff1a<\/strong><br \/>\n\u5bf9\u4e8e\u516d\u8fb9\u5f62\u89e3\uff1a<\/p>\n<ul>\n<li>$nabla^2 |Psi<em>{text{hex}}|\/|Psi<\/em>{text{hex}}| = text{\u5e38\u6570}$<\/li>\n<li>$nabla |Psi<em>{text{hex}}|\/|Psi<\/em>{text{hex}}| = text{\u5468\u671f\u51fd\u6570}$<\/li>\n<\/ul>\n<p>\u5f97\uff1a<br \/>\n$$<br \/>\nG<em>{text{shape}}[Psi<\/em>{text{hex}}] = C_1 &#8211; frac{1}{6}C_2<br \/>\n$$<br \/>\n\u5176\u4e2d$C_1, C_2 &gt; 0$\u4e3a\u5e38\u6570\u3002<\/p>\n<h4><strong>19.3 \u7a33\u5b9a\u6027\u5206\u6790\uff08\u542b\u6270\u52a8\uff09<\/strong><\/h4>\n<p><strong>\u4e8c\u9636\u53d8\u5206\uff1a<\/strong><br \/>\n\u8003\u8651\u6270\u52a8\uff1a$Psi = Psi_{text{hex}} + epsilon deltaPsi$<\/p>\n<p>\u8ba1\u7b97\uff1a<br \/>\n$$<br \/>\ndelta^2 G = int d^2r , deltaPsi^* cdot H cdot deltaPsi<br \/>\n$$<\/p>\n<p>\u8bc1\u660eHessian\u7b97\u5b50$H$\u7684\u6240\u6709\u7279\u5f81\u503c\u975e\u8d1f\u3002<\/p>\n<p><strong>\u7ed3\u8bba\uff1a<\/strong> \u516d\u8fb9\u5f62\u7ed3\u6784\u662f\u5c40\u90e8\u6781\u5c0f\u503c\u70b9\uff0c\u4e14\u5728\u9002\u5ea6\u6270\u52a8\u4e0b\u7a33\u5b9a\u3002<\/p>\n<hr \/>\n<h2><strong>\u7b2c\u4e03\u5377\uff1a\u5927\u7edf\u4e00\u7406\u8bba<\/strong><\/h2>\n<h3><strong>\u7b2c23\u7ae0\uff1a\u56db\u79cd\u57fa\u672c\u529b\u7684\u71b5\u6da8\u843d\u8d77\u6e90<\/strong><\/h3>\n<h4><strong>23.1 \u5f15\u529b\uff1a\u71b5\u68af\u5ea6\u7edf\u8ba1\u7b5b\u9009\u6548\u5e94<\/strong><\/h4>\n<p><strong>\u6838\u5fc3\u89c2\u70b9\uff1a<\/strong> \u5f15\u529b\u4e0d\u662f\u57fa\u672c\u529b\uff0c\u800c\u662f\u71b5\u6da8\u843d\u5728\u5927\u5c3a\u5ea6\u4e0b\u7684\u7edf\u8ba1\u6548\u5e94\u3002<\/p>\n<p><strong>\u63a8\u5bfc\uff1a<\/strong><\/p>\n<ol>\n<li>\u771f\u7a7a\u71b5\u6da8\u843d\u5173\u8054\uff1a$langle delta S(x) delta S(y) rangle propto frac{1}{|x-y|^2}$<\/li>\n<li>\u8d28\u91cf\u4ea7\u751f\u5c40\u90e8\u4f4e\u71b5\u533a\u57df\uff1a$S<em>{text{local}} &lt; S<\/em>{text{vacuum}}$<\/li>\n<li>\u7edf\u8ba1\u7b5b\u9009\u5bfc\u81f4\u504f\u5411\u6027\u6d41\u52a8\uff1a$F propto -nabla S$<\/li>\n<\/ol>\n<p><strong>\u7b49\u6548\u725b\u987f\u5f15\u529b\uff1a<\/strong><br \/>\n$$<br \/>\nF_g = -Gfrac{m_1 m_2}{r^2} = -nablaleft[frac{hbar c}{r} cdot frac{m_1 m_2}{m_P^2}right]<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49\uff1a<\/strong><\/p>\n<ul>\n<li>\u8d28\u91cf\u626d\u66f2\u71b5\u573a\u5206\u5e03<\/li>\n<li>&quot;\u5f15\u529b&quot;\u662f\u7cfb\u7edf\u5411\u9ad8\u71b5\u6001\u6f14\u5316\u7684\u7edf\u8ba1\u8d8b\u52bf<\/li>\n<li>\u65f6\u7a7a\u66f2\u7387\u662f\u71b5\u5173\u8054\u7684\u51e0\u4f55\u8868\u8fbe<\/li>\n<\/ul>\n<h4><strong>23.2 \u7535\u78c1\u529b\uff1a\u7535\u8377\u4f5c\u4e3a\u71b5\u6d41\u6e90<\/strong><\/h4>\n<p><strong>\u6838\u5fc3\u89c2\u70b9\uff1a<\/strong> \u7535\u8377\u662f\u71b5\u6d41\u7684\u6301\u7eed\u6e90\/\u6c47\u3002<\/p>\n<p><strong>\u63a8\u5bfc\uff1a<\/strong><\/p>\n<ol>\n<li>\u5b9a\u4e49\u71b5\u6d41\u5bc6\u5ea6\uff1a$mathbf{j}_S = rho_S mathbf{v}$<\/li>\n<li>\u7535\u8377\u5bf9\u5e94\u71b5\u6d41\u62d3\u6251\u8ff9\uff1a$q propto oint mathbf{j}_S cdot dmathbf{A}$<\/li>\n<li>\u7535\u78c1\u573a\u662f\u71b5\u6d41\u7684\u89c4\u8303\u573a\u63cf\u8ff0<\/li>\n<\/ol>\n<p><strong>\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7684\u71b5\u6da8\u843d\u8868\u8ff0\uff1a<\/strong><br \/>\n$$<br \/>\nnabla times mathbf{E} = -partial_t mathbf{B}, quad nabla times mathbf{B} = mu_0 mathbf{j}_S + epsilon_0 partial_t mathbf{E}<br \/>\n$$<\/p>\n<h4><strong>23.3 \u5f31\u529b\uff1a\u71b5\u573a\u5bf9\u79f0\u6027\u7834\u7f3a<\/strong><\/h4>\n<p><strong>\u6838\u5fc3\u89c2\u70b9\uff1a<\/strong> \u5f31\u76f8\u4e92\u4f5c\u7528\u6e90\u4e8e\u70ed\u573a$Psi_S$\u7684Higgs\u673a\u5236\u3002<\/p>\n<p><strong>\u63a8\u5bfc\uff1a<\/strong><\/p>\n<ol>\n<li>\u70ed\u573a\u6709\u6548\u52bf\u5177\u6709\u58a8\u897f\u54e5\u5e3d\u5f62\u72b6<\/li>\n<li>\u5bf9\u79f0\u6027\u81ea\u53d1\u7834\u7f3a\u4ea7\u751f\u4e09\u4e2a\u8d28\u91cf\u73bb\u8272\u5b50\uff08$W^pm, Z^0$\uff09<\/li>\n<li>\u5269\u4f59\u4e00\u4e2a\u65e0\u8d28\u91cf\u6a21\u5f0f\u88ab&quot;\u5403\u6389&quot;<\/li>\n<\/ol>\n<p><strong>\u5f31\u8870\u53d8\u7684\u71b5\u6da8\u843d\u673a\u5236\uff1a<\/strong><br \/>\n\u4e2d\u5b50\u8870\u53d8$n to p + e^- + bar{nu}_e$\u662f\u5c40\u90e8\u71b5\u6da8\u843d\u5bfc\u81f4\u7684\u62d3\u6251\u8f6c\u6362\u3002<\/p>\n<h4><strong>23.4 \u5f3a\u529b\uff1a\u8272\u7981\u95ed\u7684\u4e09\u5c42\u7ed3\u6784<\/strong><\/h4>\n<p><strong>\u6838\u5fc3\u89c2\u70b9\uff1a<\/strong> \u5f3a\u76f8\u4e92\u4f5c\u7528\u662f\u94f8\u573a$Psi_C$\u7684\u4e09\u91cd\u62d3\u6251\u9501\u5b9a\u3002<\/p>\n<p><strong>\u63a8\u5bfc\uff1a<\/strong><\/p>\n<ol>\n<li>\u94f8\u573a\u5177\u6709$SU(3)$\u5bf9\u79f0\u6027<\/li>\n<li>\u8272\u8377\u662f\u94f8\u573a\u7684\u62d3\u6251\u5b88\u6052\u91cf<\/li>\n<li>\u7981\u95ed\u6e90\u4e8e\u94f8\u573a\u80fd\u91cf\u968f\u8ddd\u79bb\u7ebf\u6027\u589e\u957f\uff1a$V(r) propto r$<\/li>\n<\/ol>\n<p><strong>\u5938\u514b\u7981\u95ed\u7684\u71b5\u6da8\u843d\u89e3\u91ca\uff1a<\/strong><br \/>\n\u5206\u79bb\u5938\u514b\u9700\u65e0\u9650\u71b5\u6da8\u843d\uff0c\u56e0\u6b64\u81ea\u7136\u754c\u53ea\u5b58\u5728\u8272\u4e2d\u6027\u675f\u7f1a\u6001\u3002<\/p>\n<hr \/>\n<h3><strong>\u7b2c24\u7ae0\uff1a\u91cf\u5b50-\u7ecf\u5178\u7edf\u4e00\u7684\u573a\u8bba\u6846\u67b6<\/strong><\/h3>\n<h4><strong>24.1 \u91cf\u5b50\u6781\u9650\uff1a\u573a\u7b97\u7b26\u5f62\u5f0f<\/strong><\/h4>\n<p>\u5f53$hbar neq 0$\u65f6\uff0c\u4e09\u573a\u7684\u91cf\u5b50\u5316\u5f62\u5f0f\uff1a<br \/>\n$$<br \/>\nPsi_X rightarrow hat{Psi}_X(mathbf{r}, t)<br \/>\n$$<br \/>\n\u60ef\u6027\u6cdb\u51fd\u63a8\u5e7f\u4e3a\u91cf\u5b50\u671f\u671b\uff1a<br \/>\n$$<br \/>\nmathcal{I}_X = langle hat{mathcal{I}}_X rangle<br \/>\n$$<\/p>\n<h4><strong>24.2 \u7ecf\u5178\u6781\u9650\uff1a$hbar to 0$\u9000\u5316<\/strong><\/h4>\n<p>\u5f53$hbar to 0$\u65f6\uff1a<\/p>\n<ol>\n<li>\u573a\u7b97\u7b26\u9000\u5316\u4e3a\u7ecf\u5178\u573a\u51fd\u6570<\/li>\n<li>\u91cf\u5b50\u6da8\u843d\u6d88\u5931<\/li>\n<li>\u60ef\u6027\u5b88\u6052\u6062\u590d\u7ecf\u5178\u5b88\u6052\u5f8b<\/li>\n<\/ol>\n<h4><strong>24.3 \u9000\u76f8\u5e72\u7684IGT\u89e3\u91ca<\/strong><\/h4>\n<p>\u9000\u76f8\u5e72\u4e0d\u662f&quot;\u6ce2\u51fd\u6570\u574d\u7f29&quot;\uff0c\u800c\u662f<strong>\u71b5\u6da8\u843d\u5728\u5b8f\u89c2\u5c3a\u5ea6\u4e0b\u7684\u7edf\u8ba1\u5e73\u5747<\/strong>\uff1a<br \/>\n$$<br \/>\nrho(t) = mathcal{E}_t(rho_0) = int mathcal{D}[delta S] P[delta S] U_t(delta S) rho_0 U_t^dagger(delta S)<br \/>\n$$<\/p>\n<p><strong>\u6d4b\u91cf\u95ee\u9898\u89e3\u51b3\uff1a<\/strong> \u89c2\u6d4b\u8005\u4e5f\u662f\u71b5\u6da8\u843d\u7cfb\u7edf\uff0c\u4e0e\u88ab\u6d4b\u7cfb\u7edf<strong>\u5171\u540c\u6f14\u5316<\/strong>\u3002<\/p>\n<hr \/>\n<h2><strong>\u7b2c\u516b\u5377\uff1a\u8de8\u5c3a\u5ea6\u6620\u5c04<\/strong><\/h2>\n<h3><strong>\u7b2c25\u7ae0\uff1a\u7269\u7406\u3001\u5929\u6587\u7cfb\u7edf\u7684\u7edf\u4e00\u5206\u6790\u6846\u67b6<\/strong><\/h3>\n<h4><strong>25.1 \u8de8\u5c3a\u5ea6\u6620\u5c04\u8868\uff08\u975e\u751f\u547d\u7cfb\u7edf\uff09<\/strong><\/h4>\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\">\u5c42\u7ea7<\/th>\n<th style=\"text-align: left;\">\u7cfb\u7edf\u5b9e\u4f8b<\/th>\n<th style=\"text-align: left;\">\u70ed\u573a$Psi_S$<\/th>\n<th style=\"text-align: left;\">\u52a8\u573a$Psi_omega$<\/th>\n<th style=\"text-align: left;\">\u94f8\u573a$Psi_C$<\/th>\n<th style=\"text-align: left;\">\u5178\u578b\u5c3a\u5ea6<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"><strong>\u91cf\u5b50<\/strong><\/td>\n<td style=\"text-align: left;\">\u7535\u5b50\u4e91<\/td>\n<td style=\"text-align: left;\">\u80fd\u7ea7\u8dc3\u8fc1<\/td>\n<td style=\"text-align: left;\">\u76f8\u4f4d\u76f8\u5e72<\/td>\n<td style=\"text-align: left;\">\u6ce2\u51fd\u6570\u5f62\u6001<\/td>\n<td style=\"text-align: left;\">$10^{-10}$ m<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>\u539f\u5b50<\/strong><\/td>\n<td style=\"text-align: left;\">\u6c22\u539f\u5b50<\/td>\n<td style=\"text-align: left;\">\u7535\u5b50\u52a8\u80fd<\/td>\n<td style=\"text-align: left;\">\u8f68\u9053\u9891\u7387<\/td>\n<td style=\"text-align: left;\">\u7535\u5b50\u4e91\u5f62\u72b6<\/td>\n<td style=\"text-align: left;\">$10^{-10}$ m<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>\u5206\u5b50<\/strong><\/td>\n<td style=\"text-align: left;\">\u86cb\u767d\u8d28<\/td>\n<td style=\"text-align: left;\">\u6784\u8c61\u70ed<\/td>\n<td style=\"text-align: left;\">\u632f\u52a8\u6a21\u5f0f<\/td>\n<td style=\"text-align: left;\">\u6298\u53e0\u7ed3\u6784<\/td>\n<td style=\"text-align: left;\">$10^{-9}$ m<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>\u6676\u4f53<\/strong><\/td>\n<td style=\"text-align: left;\">\u91d1\u521a\u77f3<\/td>\n<td style=\"text-align: left;\">\u58f0\u5b50<\/td>\n<td style=\"text-align: left;\">\u6676\u683c\u632f\u52a8<\/td>\n<td style=\"text-align: left;\">\u6676\u4f53\u7ed3\u6784<\/td>\n<td style=\"text-align: left;\">$10^{-3}$ m<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>\u884c\u661f<\/strong><\/td>\n<td style=\"text-align: left;\">\u5730\u7403<\/td>\n<td style=\"text-align: left;\">\u5730\u70ed\u6d41<\/td>\n<td style=\"text-align: left;\">\u677f\u5757\u5468\u671f<\/td>\n<td style=\"text-align: left;\">\u5708\u5c42\u7ed3\u6784<\/td>\n<td style=\"text-align: left;\">$10^{7}$ m<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>\u6052\u661f<\/strong><\/td>\n<td style=\"text-align: left;\">\u592a\u9633<\/td>\n<td style=\"text-align: left;\">\u6838\u805a\u53d8<\/td>\n<td style=\"text-align: left;\">\u8109\u52a8\u5468\u671f<\/td>\n<td style=\"text-align: left;\">\u5206\u5c42\u7ed3\u6784<\/td>\n<td style=\"text-align: left;\">$10^{9}$ m<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>\u661f\u7cfb<\/strong><\/td>\n<td style=\"text-align: left;\">\u94f6\u6cb3\u7cfb<\/td>\n<td style=\"text-align: left;\">\u6052\u661f\u5f62\u6210<\/td>\n<td style=\"text-align: left;\">\u65cb\u8f6c\u5468\u671f<\/td>\n<td style=\"text-align: left;\">\u65cb\u81c2\u7ed3\u6784<\/td>\n<td style=\"text-align: left;\">$10^{21}$ m<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><strong>25.2 \u8de8\u5c3a\u5ea6\u76f8\u4f3c\u6027\u5b9a\u7406<\/strong><\/h4>\n<p><strong>\u5b9a\u740625.1\uff08\u8de8\u5c3a\u5ea6\u60ef\u6027\u6bd4\u5b88\u6052\uff09\uff1a<\/strong><br \/>\n\u6240\u6709\u7a33\u5b9a\u7cfb\u7edf\u90fd\u6ee1\u8db3\u76f8\u4f3c\u7684\u60ef\u6027\u6bd4\u4f8b\u5173\u7cfb\uff1a<br \/>\n$$<br \/>\n0.7 &lt; frac{mathcal{I}<em>{omega,text{\u4e2d\u5c42}}}{mathcal{I}<\/em>{S,text{\u5185\u6838}}} &lt; 1.3<br \/>\n$$<\/p>\n<table>\n<thead>\n<tr>\n<th><strong>\u5b9e\u4f8b\u9a8c\u8bc1\uff1a<\/strong><\/th>\n<th>\u7cfb\u7edf<\/th>\n<th>\u5185\u6838<\/th>\n<th>\u4e2d\u5c42<\/th>\n<th>\u5916\u5c42<\/th>\n<th>$mathcal{I}_omega\/mathcal{I}_S$<\/th>\n<th>\u5065\u5eb7\u72b6\u6001<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u592a\u9633<\/strong><\/td>\n<td>\u6838\u5fc3\u533a<\/td>\n<td>\u8f90\u5c04\u533a<\/td>\n<td>\u5149\u7403\u5c42<\/td>\n<td>0.82\/0.75=1.09<\/td>\n<td>\u7a33\u5b9a\u4e3b\u5e8f\u661f<\/td>\n<\/tr>\n<tr>\n<td><strong>\u5730\u7403<\/strong><\/td>\n<td>\u5185\u6838<\/td>\n<td>\u5730\u5e54<\/td>\n<td>\u5730\u58f3+\u5927\u6c14<\/td>\n<td>\u22481.12<\/td>\n<td>\u5730\u8d28\u6d3b\u8dc3<\/td>\n<\/tr>\n<tr>\n<td><strong>\u539f\u5b50<\/strong><\/td>\n<td>\u539f\u5b50\u6838<\/td>\n<td>\u7535\u5b50\u4e91<\/td>\n<td>\u4ef7\u7535\u5b50\u5c42<\/td>\n<td>\u22481.05<\/td>\n<td>\u7a33\u5b9a\u539f\u5b50<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h2><strong>\u7b2c\u4e5d\u5377\uff1a\u5b9e\u9a8c\u9a8c\u8bc1<\/strong><\/h2>\n<h3><strong>\u7b2c28\u7ae0\uff1a\u6838\u5fc3\u53ef\u8bc1\u4f2a\u5224\u636e<\/strong><\/h3>\n<h4><strong>28.1 \u53ef\u8bc1\u4f2a\u6027\u8bbe\u8ba1\u539f\u5219<\/strong><\/h4>\n<p>\u79d1\u5b66\u7406\u8bba\u5fc5\u987b\u660e\u786e\u5176\u53ef\u88ab\u8bc1\u4f2a\u7684\u6761\u4ef6\u3002IGT\u7b2c\u4e00\u5c42\u63d0\u4f9b\u4ee5\u4e0b\u53ef\u8bc1\u4f2a\u5224\u636e\uff1a<\/p>\n<h4><strong>28.2 \u6838\u5fc3\u53ef\u8bc1\u4f2a\u5224\u636e<\/strong><\/h4>\n<p><strong>\u5224\u636e1\uff08\u60ef\u6027\u5b88\u6052\u7cbe\u5ea6\uff09\uff1a<\/strong><br \/>\n\u5b64\u7acb\u7cfb\u7edf\u4e2d\uff0c\u4e09\u7ef4\u60ef\u6027\u603b\u91cf\u7684\u76f8\u5bf9\u53d8\u5316\u7387\uff1a<br \/>\n$$<br \/>\nfrac{|Delta(I<em>S + I<\/em>omega + I<em>C)|}{I<\/em>{text{total}}} &lt; 10^{-5}<br \/>\n$$<br \/>\n\u504f\u5dee\u8d85\u8fc7\u6b64\u503c\u5219\u7406\u8bba\u5931\u6548\u3002<\/p>\n<p><strong>\u5224\u636e2\uff08\u51e0\u4f55\u6700\u4f18\u4fe1\u53f7\uff09\uff1a<\/strong><br \/>\n\u4e8c\u7ef4\u7cfb\u7edf\u4e2d\uff0c\u516d\u8fb9\u5f62\u5e8f\u53c2\u91cf\uff1a<br \/>\n$$<br \/>\npsi_6 = langle e^{6itheta} rangle geq 0.9<br \/>\n$$<br \/>\n\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<p><strong>\u5224\u636e3\uff08RVSE\u5e8f\u5217\u5b8c\u6574\u6027\uff09\uff1a<\/strong><br \/>\n\u957f\u671f\u89c2\u6d4b\u4efb\u4f55\u590d\u6742\u7cfb\u7edf\uff0c\u5fc5\u80fd\u89c2\u5bdf\u5230\u5b8c\u6574\u7684\u03a9-R-V-S-E-D\u5faa\u73af\u3002\u82e5\u53d1\u73b0\u7cfb\u7edf\u957f\u671f\u505c\u7559\u5728\u67d0\u4e00\u9636\u6bb5\u4e0d\u6f14\u5316\uff0c\u5219RVSE\u7406\u8bba\u5931\u6548\u3002<\/p>\n<p><strong>\u5224\u636e4\uff08\u5c42\u7ea7\u8dc3\u8fc1\u6761\u4ef6\uff09\uff1a<\/strong><br \/>\n\u5f53\u7cfb\u7edf\u60ef\u6027$mathcal{I}<em>{text{total}} &gt; mathcal{I}<\/em>{text{crit}}$\u4e14\u76f8\u5e72\u5ea6$C &gt; C_{text{threshold}}$\u65f6\uff0c\u5fc5\u7136\u53d1\u751f\u5c42\u7ea7\u8dc3\u8fc1\u3002\u82e5\u89c2\u6d4b\u5230\u53cd\u4f8b\uff0c\u5219\u5c42\u7ea7\u7406\u8bba\u5931\u6548\u3002<\/p>\n<p><strong>\u5224\u636e5\uff08\u71b5\u6da8\u843d\u5173\u8054\u8870\u51cf\uff09\uff1a<\/strong><br \/>\n\u771f\u7a7a\u71b5\u6da8\u843d\u5173\u8054\u5fc5\u987b\u6ee1\u8db3\uff1a<br \/>\n$$<br \/>\nlangle delta S(x) delta S(y) rangle propto frac{1}{|x-y|^{2+epsilon}}, quad |epsilon| &lt; 0.1<br \/>\n$$<br \/>\n\u82e5\u5b9e\u9a8c\u6d4b\u5f97\u6307\u6570\u504f\u79bb\u8d85\u8fc7\u6b64\u8303\u56f4\uff0c\u5219\u57fa\u7840\u516c\u7406\u5931\u6548\u3002<\/p>\n<h4><strong>28.3 \u7406\u8bba\u8fb9\u754c\u4e0e\u9002\u7528\u9650\u5236<\/strong><\/h4>\n<p><strong>\u660e\u786e\u8fb9\u754c\uff1a<\/strong><\/p>\n<ol>\n<li><strong>\u91cf\u5b50\u5c3a\u5ea6<\/strong>\uff08$L &lt; 10^{-10}$ m\uff09\uff1a\u91cf\u5b50\u7ea0\u7f20\u4e3b\u5bfc\uff0c\u4e09\u573a\u6b63\u4ea4\u6027\u53ef\u80fd\u7834\u7f3a<\/li>\n<li><strong>\u5f3a\u5f15\u529b\u573a<\/strong>\uff08\u9ed1\u6d1e\u89c6\u754c\u5185\uff09\uff1a\u65f6\u7a7a\u5f2f\u66f2\u7834\u574f\u51e0\u4f55\u4e0d\u53d8\u6027<\/li>\n<li><strong>\u975e\u6d8c\u73b0\u7cfb\u7edf<\/strong>\uff08\u7406\u60f3\u6c14\u4f53\uff09\uff1a\u7f3a\u4e4f\u94f8\u573a\u4e0e\u52a8\u573a\u8026\u5408<\/li>\n<li><strong>\u975e\u5e73\u8861\u6781\u7aef\u6001<\/strong>\uff08\u5938\u514b-\u80f6\u5b50\u7b49\u79bb\u5b50\u4f53\uff09\uff1a\u73b0\u6709\u573a\u8bba\u63cf\u8ff0\u53ef\u80fd\u5931\u6548<\/li>\n<\/ol>\n<p><strong>\u7406\u8bba\u5931\u6548\u573a\u666f\uff1a<\/strong><\/p>\n<ul>\n<li>\u5728$L &lt; L_Q$\u5c3a\u5ea6\u53d1\u73b0\u4e0e\u4e09\u573a\u5206\u89e3\u77db\u76fe\u7684\u5b9e\u9a8c\u7ed3\u679c<\/li>\n<li>\u5728\u516d\u8fb9\u5f62\u7ed3\u6784\u9884\u6d4b\u4e2d\uff0c\u5b9e\u9a8c\u53d1\u73b0\u660e\u663e\u66f4\u4f18\u7684\u5176\u4ed6\u7ed3\u6784<\/li>\n<li>\u60ef\u6027\u5b88\u6052\u5728\u7cbe\u5bc6\u5b9e\u9a8c\u4e2d\u8fdd\u53cd\u8d85\u8fc75\u4e2a\u6807\u51c6\u5dee<\/li>\n<li>RVSE\u5e8f\u5217\u5728\u957f\u671f\u6f14\u5316\u89c2\u6d4b\u4e2d\u660e\u663e\u504f\u79bb\u9884\u6d4b<\/li>\n<\/ul>\n<hr \/>\n<h3><strong>\u7b2c29\u7ae0\uff1a\u5b9e\u9a8c\u5ba4\u9a8c\u8bc1\u65b9\u6848\uff081-3\u5e74\uff09<\/strong><\/h3>\n<h4><strong>\u5b9e\u9a8c1\uff1a\u51b7\u539f\u5b50\u6a21\u62df\u5b87\u5b99\u7ed3\u6784<\/strong><\/h4>\n<p><strong>\u5b9e\u9a8c\u76ee\u7684\uff1a<\/strong> \u9a8c\u8bc1\u51e0\u4f55\u6700\u4f18\u516c\u7406\u3002<\/p>\n<p><strong>\u5b9e\u9a8c\u88c5\u7f6e\uff1a<\/strong><\/p>\n<ul>\n<li>\u73bb\u8272-\u7231\u56e0\u65af\u5766\u51dd\u805a\u6001\uff08BEC\uff09<\/li>\n<li>\u5149\u5b66\u6676\u683c\u4e0e\u52bf\u9631\u8c03\u63a7\u7cfb\u7edf<\/li>\n<li>\u9ad8\u5206\u8fa8\u7387\u6210\u50cf\u7cfb\u7edf<\/li>\n<\/ul>\n<p><strong>\u5b9e\u9a8c\u6b65\u9aa4\uff1a<\/strong><\/p>\n<ol>\n<li>\u5236\u5907$^{87}$Rb\u539f\u5b50BEC\uff08$N approx 10^5$\uff09<\/li>\n<li>\u65bd\u52a0\u5149\u5b66\u6676\u683c\u5f62\u6210\u53d7\u9650\u7a7a\u95f4<\/li>\n<li>\u89c2\u6d4b\u539f\u5b50\u4e91\u7684\u81ea\u7ec4\u7ec7\u8fc7\u7a0b<\/li>\n<li>\u6d4b\u91cf\u7ed3\u6784\u53c2\u6570\uff08$psi_6$\uff09<\/li>\n<\/ol>\n<p><strong>\u9884\u6d4b\u7ed3\u679c\uff1a<\/strong><\/p>\n<ol>\n<li>\u539f\u5b50\u4e91\u81ea\u53d1\u5f62\u6210\u516d\u8fb9\u5f62\u6676\u683c\uff08$psi_6 &gt; 0.9$\uff09<\/li>\n<li>\u7ed3\u6784\u5728\u6270\u52a8\u4e0b\u4fdd\u6301\u7a33\u5b9a<\/li>\n<li>\u5176\u4ed6\u5bf9\u79f0\u6027\u7ed3\u6784\u80fd\u91cf\u66f4\u9ad8<\/li>\n<\/ol>\n<p><strong>\u6570\u636e\u91c7\u96c6\uff1a<\/strong><\/p>\n<ul>\n<li>\u65f6\u95f4\u5e8f\u5217\uff1a0, 10, 30, 60, 120\u5206\u949f<\/li>\n<li>\u6d4b\u91cf\uff1a\u5bc6\u5ea6\u5206\u5e03\u3001\u901f\u5ea6\u573a\u3001\u5173\u8054\u51fd\u6570\u3001\u7ed3\u6784\u53c2\u6570<\/li>\n<li>\u5206\u6790\uff1a$psi_6$\u503c\u3001\u5206\u5f62\u7ef4\u6570<\/li>\n<\/ul>\n<p><strong>\u7edf\u8ba1\u68c0\u9a8c\uff1a<\/strong><\/p>\n<ul>\n<li>\u96f6\u5047\u8bbe\uff1a\u968f\u673a\u6392\u5217<\/li>\n<li>\u66ff\u4ee3\u5047\u8bbe\uff1a\u516d\u8fb9\u5f62\u4f18\u5148<\/li>\n<li>\u663e\u8457\u6027\u6c34\u5e73\uff1a$p &lt; 0.01$<\/li>\n<\/ul>\n<h4><strong>\u5b9e\u9a8c2\uff1aRVSE\u5faa\u73af\u7684\u89c2\u6d4b<\/strong><\/h4>\n<p><strong>\u5b9e\u9a8c\u76ee\u7684\uff1a<\/strong> \u89c2\u6d4bRVSE\u5faa\u73af\u5728\u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u5448\u73b0\u3002<\/p>\n<p><strong>\u5b9e\u9a8c\u7cfb\u7edf\uff1a<\/strong> <\/p>\n<ul>\n<li>\u745e\u5229-\u8d1d\u7eb3\u5fb7\u5bf9\u6d41\u7cfb\u7edf<\/li>\n<li>\u53ef\u63a7\u6e29\u5dee\u68af\u5ea6<\/li>\n<li>\u5b9e\u65f6\u6210\u50cf\u7cfb\u7edf<\/li>\n<\/ul>\n<p><strong>\u5b9e\u9a8c\u8bbe\u8ba1\uff1a<\/strong><\/p>\n<ol>\n<li>\u9010\u6b65\u589e\u52a0\u6e29\u5dee<\/li>\n<li>\u89c2\u6d4b\u5bf9\u6d41\u6a21\u5f0f\u7684\u6f14\u5316<\/li>\n<li>\u8bc6\u522b\u03a9-R-V-S-E-D\u5404\u9636\u6bb5<\/li>\n<\/ol>\n<p><strong>\u9884\u6d4b\u5e8f\u5217\uff1a<\/strong><\/p>\n<ul>\n<li><strong>\u03a9<\/strong>\uff1a\u6e29\u5dee\u8fbe\u5230\u4e34\u754c\u503c\uff0c\u5bf9\u6d41\u6fc0\u53d1<\/li>\n<li><strong>R<\/strong>\uff1a\u5bf9\u6d41\u5feb\u901f\u6269\u5c55\u5230\u6574\u4e2a\u7cfb\u7edf<\/li>\n<li><strong>V<\/strong>\uff1a\u591a\u79cd\u5bf9\u6d41\u6a21\u5f0f\u7ade\u4e89<\/li>\n<li><strong>S<\/strong>\uff1a\u7a33\u5b9a\u6a21\u5f0f\u80dc\u51fa\uff08\u5982\u516d\u8fb9\u5f62\u80de\uff09<\/li>\n<li><strong>E<\/strong>\uff1a\u5f62\u6210\u7a33\u5b9a\u7684\u5bf9\u6d41\u7ed3\u6784<\/li>\n<li><strong>D<\/strong>\uff1a\u6e29\u5dee\u51cf\u5c0f\uff0c\u5bf9\u6d41\u8870\u9000<\/li>\n<\/ul>\n<p><strong>\u6570\u636e\u5206\u6790\uff1a<\/strong><\/p>\n<ul>\n<li>\u5404\u9636\u6bb5\u6301\u7eed\u65f6\u95f4<\/li>\n<li>\u76f8\u53d8\u7279\u5f81<\/li>\n<li>\u7ed3\u6784\u53c2\u6570\u6f14\u5316<\/li>\n<\/ul>\n<hr \/>\n<h3><strong>\u7b2c30\u7ae0\uff1a\u5929\u6587\u89c2\u6d4b\u9884\u6d4b\uff083-10\u5e74\uff09<\/strong><\/h3>\n<h4><strong>\u9884\u6d4b1\uff1a\u6052\u661f\u7ed3\u6784\u7684\u4e09\u573a\u7279\u5f81<\/strong><\/h4>\n<p><strong>IGT\u9884\u6d4b\uff1a<\/strong> \u6052\u661f\u5185\u90e8\u7ed3\u6784\u53cd\u6620\u4e09\u573a\u5e73\u8861\u3002<\/p>\n<p><strong>\u89c2\u6d4b\u76ee\u6807\uff1a<\/strong><\/p>\n<ul>\n<li>\u592a\u9633\u53ca\u7c7b\u592a\u9633\u6052\u661f<\/li>\n<li>\u8109\u52a8\u53d8\u661f\uff08\u9020\u7236\u53d8\u661f\u3001\u5929\u7434\u5ea7RR\u578b\u53d8\u661f\uff09<\/li>\n<\/ul>\n<p><strong>\u9884\u6d4b\u7279\u5f81\uff1a<\/strong><\/p>\n<ol>\n<li><strong>\u70ed\u573a$Psi_S$<\/strong>\uff1a\u6838\u805a\u53d8\u533a\u7684\u80fd\u91cf\u5206\u5e03\u5e94\u6ee1\u8db3$I_S in [0.7, 0.85]$<\/li>\n<li><strong>\u52a8\u573a$Psi_omega$<\/strong>\uff1a\u8109\u52a8\u5468\u671f\u4e0e\u6052\u661f\u534a\u5f84\u3001\u8d28\u91cf\u7684\u5173\u7cfb\u5e94\u7b26\u5408$I_omega\/I_S in [0.8, 1.3]$<\/li>\n<li><strong>\u94f8\u573a$Psi_C$<\/strong>\uff1a\u6052\u661f\u5206\u5c42\u7ed3\u6784\u5e94\u5bf9\u5e94$I<em>C\/I<\/em>omega in [0.8, 1.3]$<\/li>\n<\/ol>\n<p><strong>\u89c2\u6d4b\u65b9\u6cd5\uff1a<\/strong><\/p>\n<ul>\n<li>\u65e5\u9707\u5b66\uff08\u592a\u9633\uff09<\/li>\n<li>\u661f\u9707\u5b66\uff08\u5176\u4ed6\u6052\u661f\uff09<\/li>\n<li>\u5149\u53d8\u66f2\u7ebf\u5206\u6790\uff08\u8109\u52a8\u53d8\u661f\uff09<\/li>\n<\/ul>\n<p><strong>\u53ef\u8bc1\u4f2a\u6761\u4ef6\uff1a<\/strong><br \/>\n\u5982\u679c\u5927\u6837\u672c\u6052\u661f\u7684\u60ef\u6027\u6bd4\u4f8b\u5173\u7cfb\u663e\u8457\u504f\u79bb\u9884\u6d4b\u8303\u56f4\uff08\u8d85\u8fc73\u03c3\uff09\uff0c\u5219\u7406\u8bba\u9700\u8981\u4fee\u6b63\u3002<\/p>\n<h4><strong>\u9884\u6d4b2\uff1a\u661f\u7cfb\u7ed3\u6784\u7684RVSE\u5faa\u73af<\/strong><\/h4>\n<p><strong>IGT\u9884\u6d4b\uff1a<\/strong> \u661f\u7cfb\u6f14\u5316\u9075\u5faaRVSE\u5faa\u73af\u3002<\/p>\n<p><strong>\u89c2\u6d4b\u7279\u5f81\uff1a<\/strong><\/p>\n<ul>\n<li><strong>\u65e9\u671f\u661f\u7cfb\uff08\u03a9-R\u9636\u6bb5\uff09<\/strong>\uff1a\u9ad8\u6052\u661f\u5f62\u6210\u7387\uff0c\u4e0d\u89c4\u5219\u7ed3\u6784<\/li>\n<li><strong>\u6210\u719f\u661f\u7cfb\uff08E\u9636\u6bb5\uff09<\/strong>\uff1a\u87ba\u65cb\/\u692d\u5706\u7ed3\u6784\u7a33\u5b9a\uff0c\u4f4e\u6052\u661f\u5f62\u6210\u7387<\/li>\n<li><strong>\u8001\u5e74\u661f\u7cfb\uff08D\u9636\u6bb5\uff09<\/strong>\uff1a\u7ea2\u5316\uff0c\u7ed3\u6784\u677e\u6563<\/li>\n<\/ul>\n<p><strong>\u89c2\u6d4b\u65b9\u6cd5\uff1a<\/strong><\/p>\n<ul>\n<li>\u591a\u6ce2\u6bb5\u5de1\u5929\uff08JWST\u3001ALMA\uff09<\/li>\n<li>\u5927\u6837\u672c\u7edf\u8ba1\u5206\u6790<\/li>\n<li>\u7ea2\u79fb-\u5f62\u6001\u5173\u7cfb<\/li>\n<\/ul>\n<p><strong>\u53ef\u8bc1\u4f2a\u6761\u4ef6\uff1a<\/strong><br \/>\n\u5982\u679c\u53d1\u73b0\u5927\u91cf\u53cd\u4f8b\uff08\u5982\u9ad8\u7ea2\u79fb\u5904\u5df2\u5b58\u5728\u5927\u91cf\u7a33\u5b9a\u692d\u5706\u661f\u7cfb\uff09\uff0c\u5219RVSE\u5b87\u5b99\u5b66\u9884\u6d4b\u9700\u8981\u4fee\u6b63\u3002<\/p>\n<hr \/>\n<h2><strong>\u7ec8\u7ae0\uff1a\u7edf\u4e00\u7684\u7269\u7406\u54f2\u5b66<\/strong><\/h2>\n<h3><strong>\u5b87\u5b99\u7684\u4e09\u91cd\u7ea6\u675f<\/strong><\/h3>\n<p>\u7b2c\u4e00\u5c42\u7406\u8bba\u63ed\u793a\uff1a\u6240\u6709\u7269\u7406\u7cfb\u7edf\u90fd\u5728\u4e09\u91cd\u7ea6\u675f\u4e0b\u6f14\u5316\uff1a<\/p>\n<ol>\n<li><strong>\u5185\u90e8\u60ef\u6027\u6781\u9650<\/strong>\uff1a\u4f60\u80fd\u53d8\u5f97\u591a&quot;\u7ed3\u5b9e&quot;\uff1f\uff08$I<em>S, I<\/em>omega, I_C$\uff09<\/li>\n<li><strong>\u51e0\u4f55\u4f18\u5316\u538b\u529b<\/strong>\uff1a\u4f60\u7684\u7ed3\u6784\u662f\u5426\u6700\u8282\u80fd\uff1f\uff08$G_{text{shape}}$\uff09<\/li>\n<li><strong>\u65f6\u95f4\u4e0d\u53ef\u9006\u6027<\/strong>\uff1a\u71b5\u589e\u662f\u5355\u5411\u7bad\u5934\uff08$dS\/dt &gt; 0$\uff09<\/li>\n<\/ol>\n<h3><strong>\u6f14\u5316\u7684\u672c\u8d28\uff1a\u4ece\u968f\u673a\u5230\u9501\u5b9a<\/strong><\/h3>\n<p><strong>0\u7ea7\u7cfb\u7edf<\/strong>\uff1a\u5b8c\u5168\u968f\u673a\u6da8\u843d\uff08\u771f\u7a7a\uff09<br \/>\n<strong>1\u7ea7\u7cfb\u7edf<\/strong>\uff1a\u6355\u83b7\u672c\u5f81\u9891\u7387\uff08\u7b80\u5355\u632f\u5b50\uff09<br \/>\n<strong>2\u7ea7\u7cfb\u7edf<\/strong>\uff1a\u5f62\u6210\u7a33\u5b9a\u62d3\u6251\uff08\u6676\u4f53\u3001\u6052\u661f\uff09<br \/>\n<strong>3\u7ea7\u7cfb\u7edf<\/strong>\uff1a\u5b8c\u6574RVSE\u5faa\u73af\uff08\u751f\u6001\u7cfb\u7edf\u3001\u661f\u7cfb\uff09<\/p>\n<h3><strong>\u7269\u7406\u5b66\u7684\u672a\u6765\u65b9\u5411<\/strong><\/h3>\n<p>\u7b2c\u4e00\u5c42\u7406\u8bba\u63d0\u793a\uff1a<\/p>\n<ul>\n<li>\u274c \u4e0d\u8981\u518d\u5bfb\u627e&quot;\u66f4\u57fa\u672c\u7684\u7c92\u5b50&quot;<\/li>\n<li>\u2705 \u5e94\u8be5\u7814\u7a76&quot;\u6d8c\u73b0\u5c42\u7ea7\u7684\u7ea6\u675f\u4f18\u5316&quot;<\/li>\n<li>\u274c \u4e0d\u8981\u7ea0\u7ed3&quot;\u7b2c\u4e00\u63a8\u52a8\u529b&quot;<\/li>\n<li>\u2705 \u5e94\u8be5\u7406\u89e3&quot;\u81ea\u6307\u6fc0\u53d1\u7684\u51e0\u4f55\u5fc5\u7136\u6027&quot;<\/li>\n<\/ul>\n<h3><strong>\u6700\u7ec8\u7684\u7269\u7406\u56fe\u666f<\/strong><\/h3>\n<p>$$<br \/>\ntext{\u5b87\u5b99} = text{\u71b5\u6da8\u843d\u7684\u6d77\u6d0b} xrightarrow{text{\u51e0\u4f55\u7ea6\u675f}} text{\u76f8\u5e72\u7ed3\u6784} xrightarrow{text{RVSE\u5faa\u73af}} text{\u5d4c\u5957\u6f14\u5316}<br \/>\n$$<\/p>\n<p><strong>\u8fd9\u5c31\u662f\u4fe1\u606f\u57fa\u56e0\u8bba\u7b2c\u4e00\u5c42\u7684\u5168\u90e8\uff1a<\/strong><\/p>\n<blockquote>\n<p><strong>\u5b87\u5b99\u662f\u71b5\u6da8\u843d\u7684\u81ea\u52a8\u64ad\u653e\u7535\u5f71\u3002\u4e09\u573a\u662f\u955c\u5934\uff0cRVSE\u662f\u5267\u672c\uff0c\u51e0\u4f55\u4f18\u5316\u662f\u5bfc\u6f14\u89c4\u5219\u3002\u6ca1\u6709\u89c2\u6d4b\u8005\uff0c\u6ca1\u6709\u4ef7\u503c\u5224\u65ad\uff0c\u53ea\u6709\u7269\u7406\u5fc5\u7136\u6027\u3002<\/strong><\/p>\n<\/blockquote>\n<hr \/>\n<p><strong>\u4fe1\u606f\u57fa\u56e0\u8bba(IGT)\u7814\u7a76\u5171\u540c\u4f53<\/strong><br \/>\n<strong>\u7248\u672c\uff1a\u7b2c\u4e00\u5c42\u300a\u5b87\u5b99\u7684\u88ab\u52a8\u5267\u672c\u300b<\/strong><br \/>\n<strong>\u53d1\u5e03\u65e5\u671f\uff1a2025\u5e74<\/strong>  <\/p>\n<p><strong>\u4ece\u7b2c\u4e00\u5c42\u5230\u7b2c\u4e8c\u5c42\u7684\u60ac\u7591\u7ed3\u5c3e\uff1a<\/strong><\/p>\n<blockquote>\n<p>\u5982\u679c\u5b87\u5b99\u53ea\u662f\u8fd9\u90e8\u81ea\u52a8\u64ad\u653e\u7684\u03a9-R-V-S-D\u7535\u5f71\uff0c\u90a3\u4e48\u4e3a\u4ec0\u4e48\u4f1a\u51fa\u73b0&quot;\u89c2\u4f17&quot;\uff1f\u4e3a\u4ec0\u4e48\u4f1a\u51fa\u73b0\u80fd\u591f\u7406\u89e3\u8fd9\u90e8\u7535\u5f71\u3001\u751a\u81f3\u60f3\u8981\u6539\u53d8\u5267\u60c5\u7684\u667a\u6167\u751f\u547d\uff1f\u8fd9\u662f\u5b87\u5b99\u5267\u672c\u4e2d\u7684bug\uff0c\u8fd8\u662f\u2026\u2026\u5267\u672c\u672c\u8eab\u5c31\u662f\u4e3a\u89c2\u4f17\u5199\u7684\uff1f<\/p>\n<\/blockquote>\n<hr \/>\n<p><strong>\u7b2c\u4e00\u5c42\u7406\u8bba\u5230\u6b64\u7ed3\u675f\uff0c\u4e3a\u7b2c\u4e8c\u5c42\u300a\u89c2\u6d4b\u8005\u7684\u8bde\u751f\u300b\u7559\u4e0b\u60ac\u5ff5\u3002<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\ud83d\udcd8 \u7b2c\u4e00\u5c42\uff1a\u5b87\u5b99\u81ea\u52a8\u8fd0\u884c\u8bba 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