{"id":5362,"date":"2026-01-20T15:29:13","date_gmt":"2026-01-20T07:29:13","guid":{"rendered":"https:\/\/imeta.space\/?p=5362"},"modified":"2026-01-20T15:29:14","modified_gmt":"2026-01-20T07:29:14","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%e7%86%b5%e6%b6%a8%e8%90%bd%e5%ae%87%e5%ae%99%ef%bc%9a%e6%89%8b%e6%80%a7-%e5%8e%8b%e5%8a%9b%e5%88%86%e5%8c%96%e4%b8%8e","status":"publish","type":"post","link":"https:\/\/imeta.space\/index.php\/2026\/01\/20\/%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%e7%86%b5%e6%b6%a8%e8%90%bd%e5%ae%87%e5%ae%99%ef%bc%9a%e6%89%8b%e6%80%a7-%e5%8e%8b%e5%8a%9b%e5%88%86%e5%8c%96%e4%b8%8e\/","title":{"rendered":"\u4fe1\u606f\u57fa\u56e0\u8bba \u7b2c\u4e00\u5c42\uff1a\u71b5\u6da8\u843d\u5b87\u5b99\uff1a\u624b\u6027-\u538b\u529b\u5206\u5316\u4e0e\u03a9-R-V-S-E-D\u5fc5\u7136\u5faa\u73af deepseek \u71b5\u503a\u6574\u5408"},"content":{"rendered":"<h1>\ud83d\udcd8 <strong>\u4fe1\u606f\u57fa\u56e0\u8bba\u7b2c\u4e00\u5c42\uff1a\u71b5\u503a\u6574\u5408\u5b8c\u6574\u7248\uff08\u4f18\u5316\u4fee\u8ba2\u7248\uff09<\/strong><\/h1>\n<h2><strong>\u300a\u71b5\u6da8\u843d\u5b87\u5b99\uff1a\u624b\u6027-\u538b\u529b\u5206\u5316\u4e0e\u03a9-R-V-S-E-D\u5fc5\u7136\u5faa\u73af\u300b<\/strong><\/h2>\n<blockquote><p><strong>\u5c42\u7ea7\u5b9a\u4f4d\u58f0\u660e<\/strong>\uff1a<br \/>\n\u672c\u7406\u8bba\u5c5e\u4e8e<strong>\u8fc7\u7a0b\u2014\u6d8c\u73b0\u2014\u7edf\u8ba1\u7ed3\u6784\u5c42<\/strong>\uff0c\u662f\u4e00\u5957\u63cf\u8ff0\u5b8f\u89c2\u76f8\u5e72\u7cfb\u7edf\u6f14\u5316\u89c4\u5f8b\u7684\u6709\u6548\u7406\u8bba\u3002\u5b83\u4e0d\u66ff\u4ee3\u91cf\u5b50\u573a\u8bba\u3001\u5e7f\u4e49\u76f8\u5bf9\u8bba\u7b49\u5e95\u5c42\u52a8\u529b\u5b66\u7406\u8bba\uff0c\u800c\u662f\u65e8\u5728\u63ed\u793a\u4ece\u5fae\u89c2\u6da8\u843d\u5230\u5b8f\u89c2\u7ed3\u6784\u4e4b\u95f4\u7684<strong>\u8de8\u5c3a\u5ea6\u7edf\u8ba1\u7ea6\u675f\u4e0e\u51e0\u4f55\u5fc5\u7136\u6027<\/strong>\u3002<br \/>\n\u6838\u5fc3\u65b9\u6cd5\u662f\uff1a\u5c06\u7cfb\u7edf\u89c6\u4e3a\u71b5\u573a\u6da8\u843d\u8fc7\u7a0b\u4e2d\u6682\u6001\u5f62\u6210\u7684\u76f8\u5e72\u7ed3\u6784\uff0c\u7814\u7a76\u5176\u5728\u51e0\u4f55\u6700\u4f18\u3001\u71b5\u503a\u79ef\u7d2f\u7b49\u7ea6\u675f\u4e0b\u7684\u6f14\u5316\u8bed\u6cd5\u3002<\/p><\/blockquote>\n<hr \/>\n<h2><strong>\u7b2c\u96f6\u5377\uff1a\u57fa\u7840\u516c\u7406<\/strong><\/h2>\n<h3><strong>\u516c\u74060.0\uff08\u5c42\u7ea7\u5b9a\u4f4d\u516c\u7406\uff09<\/strong><\/h3>\n<p>\u4fe1\u606f\u57fa\u56e0\u8bba\uff08IGT\uff09\u662f\u4e00\u5957<strong>\u5b8f\u89c2\u6d8c\u73b0\u6709\u6548\u7406\u8bba<\/strong>\uff0c\u5176\u7814\u7a76\u5bf9\u8c61\u4e3a\uff1a<\/p>\n<ol>\n<li><strong>\u5df2\u5f62\u6210\u76f8\u5e72\u7ed3\u6784\u7684\u7cfb\u7edf<\/strong>\uff08\u5982\u6676\u4f53\u3001\u7ec6\u80de\u3001\u6052\u661f\u3001\u6587\u660e\uff09<\/li>\n<li><strong>\u5728\u6d8c\u73b0\u5c3a\u5ea6\uff08mesoscale\uff09\u4e0a\u8868\u73b0\u51fa\u7edf\u8ba1\u89c4\u5f8b\u6027<\/strong><\/li>\n<li><strong>\u5176\u884c\u4e3a\u53ef\u7531\u201c\u8fc7\u7a0b\u2014\u51e0\u4f55\u2014\u503a\u52a1\u201d\u4e09\u91cd\u7ea6\u675f\u8fd1\u4f3c\u63cf\u8ff0<\/strong><\/li>\n<\/ol>\n<p>\u672c\u7406\u8bba\u4e0d\u6d89\u53ca\uff1a<\/p>\n<ul>\n<li>\u57fa\u672c\u7c92\u5b50\u5185\u90e8\u7ed3\u6784\uff08\u6807\u51c6\u6a21\u578b\u9886\u57df\uff09<\/li>\n<li>\u91cf\u5b50\u5f15\u529b\u5c3a\u5ea6\uff08\u666e\u6717\u514b\u5c3a\u5ea6\u4ee5\u4e0b\uff09<\/li>\n<li>\u4e25\u683c\u53ef\u91cd\u6574\u5316\u7684\u7edf\u4e00\u573a\u8bba\u6784\u9020<\/li>\n<\/ul>\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\u201c\u5b9e\u4f53\u201d\u90fd\u662f\u8fd9\u4e2a\u8fc7\u7a0b\u7684\u6682\u6001\u76f8\u5e72\u7ec4\u7ec7\u5f62\u5f0f\u3002<\/p>\n<p><strong>\u5f62\u5f0f\u5316\u8868\u8ff0<\/strong>\uff08\u4f5c\u4e3a\u7c7b\u6bd4\u6846\u67b6\uff09\uff1a<br \/>\n$$<br \/>\ntext{Universe} sim int mathcal{D}[delta S] expleft(-frac{1}{hbar}mathcal{A}[delta S]right)<br \/>\n$$<br \/>\n\u5176\u4e2d\u4f5c\u7528\u91cf\uff1a<br \/>\n$$<br \/>\nmathcal{A}[delta S] sim int d^4x left[frac{1}{2}(partial_mudelta S)^2 + V(delta S)right]<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a\u5b87\u5b99\u4e0d\u662f\u201c\u5b58\u5728\u201d\u7684\uff0c\u800c\u662f\u201c\u6f14\u5316\u201d\u7684\u3002\u6f14\u5316\u7684\u8def\u5f84\u53ef\u7531\u7c7b\u4f5c\u7528\u91cf\u6781\u503c\u539f\u7406\u63cf\u8ff0\uff0c\u91cf\u5b50\u6da8\u843d\u4f7f\u6f14\u5316\u8def\u5f84\u5177\u6709\u6982\u7387\u6027\u3002<\/p>\n<h3><strong>\u516c\u74060.2\uff08\u4e09\u573a\u8fd1\u4f3c\u5206\u89e3\u516c\u7406\uff09<\/strong><\/h3>\n<p>\u4efb\u4f55\u5b8f\u89c2\u76f8\u5e72\u7cfb\u7edf\u5728<strong>\u51c6\u7a33\u6001\u3001\u5f31\u8026\u5408\u6761\u4ef6\u4e0b<\/strong>\uff0c\u53ef\u5728\u6d8c\u73b0\u5c3a\u5ea6\u4e0b\u8fd1\u4f3c\u6b63\u4ea4\u5206\u89e3\u4e3a\u4e09\u4e2a\u57fa\u672c\u573a\uff1a<\/p>\n<p>$$<br \/>\nmathcal{H}_{text{system}} approx mathcal{H}<em>S oplus mathcal{H}<\/em>omega oplus mathcal{H}_C<br \/>\n$$<br \/>\n\u6ee1\u8db3\u8fd1\u4f3c\u6b63\u4ea4\u6761\u4ef6\uff1a$langle Psi_i | Psi<em>j rangle approx delta<\/em>{ij}, quad i,j in {S,omega,C}$<\/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<h3><strong>\u516c\u74060.3\uff08\u51e0\u4f55\u6700\u4f18\u516c\u7406\uff09<\/strong><\/h3>\n<p>\u5728\u7ea6\u675f\u6761\u4ef6\u4e0b\uff0c\u7cfb\u7edf\u7ed3\u6784\u8d8b\u5411\u4e8e<strong>\u80fd\u91cf\u8017\u6563\u6700\u5c0f\u3001\u7a33\u5b9a\u6027\u6700\u9ad8\u7684\u51e0\u4f55\u5f62\u6001<\/strong>\u3002\u5728\u4e8c\u7ef4\u6b27\u51e0\u91cc\u5f97\u7a7a\u95f4\u4e2d\uff0c\u516d\u8fb9\u5f62\u6392\u5217\u662f\u5168\u5c40\u6700\u4f18\u89e3\uff1b\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u8702\u5de2\u6216\u5f00\u5c14\u6587\u4f53\u7ed3\u6784\u4e3a\u6700\u4f18\u3002<\/p>\n<p>$$<br \/>\ntext{Hexagonal}<em>{2D} sim argmin<\/em>{text{packing}} left( E<em>{text{interaction}} + E<\/em>{text{dissipation}} + E_{text{boundary}} right)<br \/>\n$$<\/p>\n<h3><strong>\u516c\u74060.4\uff08\u71b5\u6d41\u5e73\u8861\u516c\u7406\uff09<\/strong><\/h3>\n<p>\u4efb\u4f55\u6709\u9650\u7cfb\u7edf\u4e2d\u7684\u71b5\u4ea7\u751f\u7387$dot{S}<em>{text{gen}}$\u5fc5\u987b\u4e0e\u73af\u5883\u71b5\u5438\u6536\u7387$dot{S}<\/em>{text{absorb}}$\u4fdd\u6301\u52a8\u6001\u5e73\u8861\uff0c\u5426\u5219\u7cfb\u7edf\u5c06\u79ef\u7d2f<strong>\u71b5\u503a\u52a1<\/strong>\uff1a<\/p>\n<p>$$<br \/>\nlim_{Ttoinfty} frac{1}{T} int<em>0^T [dot{S}<\/em>{text{gen}}(t) &#8211; dot{S}_{text{absorb}}(t)] dt = 0<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a\u8fd9\u662f\u03a9-R-V-S-E-D\u5faa\u73af\u7684<strong>\u9690\u85cf\u6210\u672c<\/strong>\u2014\u2014\u5faa\u73af\u53ef\u4ee5\u7ee7\u7eed\uff0c\u4f46\u6bcf\u4e2a\u5faa\u73af\u7684\u201c\u6e05\u6d01\u6210\u672c\u201d\u5982\u679c\u672a\u652f\u4ed8\uff0c\u5c31\u4f1a\u7d2f\u79ef\u4e3a\u503a\u52a1\u3002\u503a\u52a1\u7684\u79ef\u7d2f\u4f1a\u5bfc\u81f4\u7cfb\u7edf\u6709\u6548\u60ef\u6027\u7684\u8870\u51cf\u3002<\/p>\n<h3><strong>\u516c\u74060.5\uff08\u60ef\u6027\u7a0e\u5fc5\u7136\u6027\uff09<\/strong><\/h3>\n<p>\u4efb\u4f55\u504f\u79bb\u5e73\u8861\u6001\u7684\u76f8\u5e72\u7ed3\u6784\uff0c\u5176\u60ef\u6027\u4f1a\u56e0\u71b5\u503a\u79ef\u7d2f\u800c\u88ab\u6301\u7eed\u4fb5\u8680\u3002\u4fb5\u8680\u901f\u7387\u4e0e\u8be5\u7ed3\u6784\u7684\u51e0\u4f55\u6700\u4f18\u504f\u79bb\u5ea6\u6210\u6b63\u6bd4\u3002<\/p>\n<p><strong>\u6570\u5b66\u8868\u8ff0<\/strong>\uff1a<br \/>\n$$<br \/>\nfrac{dI_X^{text{eff}}}{dt} = -lambda<em>X cdot Delta G<\/em>{text{shape}} cdot I<em>X<br \/>\n$$<br \/>\n\u5176\u4e2d$Delta G<\/em>{text{shape}} = G<em>{text{actual}} &#8211; G<\/em>{text{optimal}}$<\/p>\n<h3><strong>\u71b5\u503a\u52a1\uff08ED\uff09\u7684\u51e0\u4f55\u5316\u5b9a\u4e49<\/strong><\/h3>\n<p><strong>\u5b9a\u4e49<\/strong>\uff1a\u71b5\u503a\u52a1$ED$\u662f\u7cfb\u7edf\u72b6\u6001\u8f68\u8ff9$Psi(t)$<strong>\u504f\u79bb\u5176\u6700\u4f18\u6f14\u5316\u6d41\u5f62<\/strong>\u7684\u5386\u53f2\u7d2f\u79ef\u5ea6\u91cf\uff1a<\/p>\n<p>$$<br \/>\nED(t) = int<em>0^t left| dot{Psi}<\/em>{text{actual}}(tau) &#8211; dot{Psi}_{text{optimal}}(tau) right| , dtau<br \/>\n$$<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ul>\n<li>$dot{Psi}_{text{optimal}}$\u7531\u51e0\u4f55\u6700\u4f18\u516c\u7406\u4e0e\u71b5\u6d41\u5e73\u8861\u516c\u7406\u5171\u540c\u51b3\u5b9a<\/li>\n<li>$|cdot|$\u4e3a\u9002\u5f53\u5b9a\u4e49\u7684\u8303\u6570\uff08\u53cd\u6620\u7cfb\u7edf\u5c3a\u5ea6\u548c\u6027\u8d28\uff09<\/li>\n<li><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1aED\u8861\u91cf\u7cfb\u7edf\u201c\u8d70\u4e86\u591a\u5c11\u5f2f\u8def\u201d\uff0c\u8fd9\u4e9b\u5f2f\u8def\u6700\u7ec8\u9700\u8981\u652f\u4ed8\u80fd\u91cf\u4e0e\u7ed3\u6784\u4ee3\u4ef7<\/li>\n<\/ul>\n<hr \/>\n<h2><strong>\u7b2c\u4e00\u5377\uff1a\u8fc7\u7a0b\u672c\u4f53\u8bba\u4e0e\u4fe1\u606f\u57fa\u56e0\u6d8c\u73b0<\/strong><\/h2>\n<h3><strong>\u7b2c1\u7ae0\uff1a\u89c2\u6d4b\u8fb9\u754c\u4e0e\u79d1\u5b66\u65b9\u6cd5\u7684\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>\u4eba\u7c7b\u89c2\u6d4b\u8005\u88ab\u9650\u5236\u5728\u6709\u9650\u5c3a\u5ea6\u5185\uff1a<\/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>\u6211\u4eec\u65e0\u6cd5\u76f4\u63a5\u89c2\u6d4b\u5b87\u5b99\u7684\u8d77\u70b9\u548c\u7ec8\u70b9\uff0c\u552f\u4e00\u80fd\u76f4\u63a5\u63a5\u89e6\u7684\u53ea\u6709<strong>\u201c\u6b64\u523b\u6b63\u5728\u53d1\u751f\u7684\u8fc7\u7a0b\u201d<\/strong>\u3002<\/p>\n<h4><strong>1.2 \u4ece\u5b9e\u4f53\u5230\u8fc7\u7a0b\u7684\u672c\u4f53\u8bba\u9769\u547d<\/strong><\/h4>\n<p><strong>\u4f20\u7edf\u7269\u7406\u5b66\u7684\u56f0\u5883<\/strong>\uff1a<\/p>\n<ol>\n<li>\u91cf\u5b50\u529b\u5b66\uff1a\u7c92\u5b50\u5728\u6d4b\u91cf\u524d\u6ca1\u6709\u786e\u5b9a\u72b6\u6001<\/li>\n<li>\u76f8\u5bf9\u8bba\uff1a\u65f6\u7a7a\u672c\u8eab\u662f\u52a8\u6001\u7684<\/li>\n<li>\u70ed\u529b\u5b66\uff1a\u71b5\u589e\u5b9a\u5f8b\u8868\u660e\u6c38\u6052\u5b9e\u4f53\u4e0d\u53ef\u80fd<\/li>\n<\/ol>\n<p><strong>\u8fc7\u7a0b\u672c\u4f53\u8bba\u516c\u7406<\/strong>\uff1a<br \/>\n\u6240\u6709\u7269\u7406\u5b9e\u5728\u90fd\u6e90\u81ea\u71b5\u573a\u7684\u91cf\u5b50\u6da8\u843d\u8fc7\u7a0b\u3002\u7269\u8d28\u4e0d\u662f\u57fa\u672c\u5b9e\u4f53\uff0c\u800c\u662f\u71b5\u6da8\u843d\u7684\u76f8\u5e72\u7ed3\u6784\uff1b\u65f6\u7a7a\u4e0d\u662f\u56fa\u5b9a\u821e\u53f0\uff0c\u800c\u662f\u71b5\u5173\u8054\u7684\u7f51\u7edc\u3002<\/p>\n<h3><strong>\u7b2c2\u7ae0\uff1a\u71b5\u6da8\u843d\u4f5c\u4e3a\u57fa\u672c\u8fc7\u7a0b\u7684\u6570\u5b66\u8868\u8ff0<\/strong><\/h3>\n<h4><strong>2.1 \u71b5\u6da8\u843d\u573a\u7684\u8def\u5f84\u79ef\u5206\u8868\u8ff0<\/strong><\/h4>\n<p>\u5b87\u5b99\u7684\u6f14\u5316\u7531\u71b5\u6da8\u843d\u8def\u5f84\u79ef\u5206\u63cf\u8ff0\uff08\u4f5c\u4e3a\u5f62\u5f0f\u7c7b\u6bd4\uff09\uff1a<\/p>\n<p>$$<br \/>\nmathcal{Z} sim int mathcal{D}[delta S] expleft(-frac{1}{hbar}mathcal{A}[delta S]right)<br \/>\n$$<\/p>\n<p><strong>\u6700\u5c0f\u4f5c\u7528\u91cf\u539f\u7406<\/strong>\uff1a$deltamathcal{A}[delta S] = 0$<\/p>\n<p><strong>\u7ebf\u6027\u5316\u6ce2\u52a8\u65b9\u7a0b<\/strong>\uff1a<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>2.2 \u51e0\u4f55\u52bf\u6cdb\u51fd\u4e0e\u6700\u4f18\u7ed3\u6784<\/strong><\/h4>\n<p>$$<br \/>\nG_{text{shape}}[Psi] = int d^3r left[ left( frac{nabla^2 |Psi|}{|Psi|} right)^2 &#8211; frac{1}{6} left( frac{nabla |Psi|}{|Psi|} right)^4 right]<br \/>\n$$<\/p>\n<p>\u53d8\u5206\u6761\u4ef6\uff1a$frac{delta G_{text{shape}}}{delta Psi^*} = 0 Rightarrow text{\u6700\u4f18\u51e0\u4f55\u6784\u578b}$<\/p>\n<p><strong>\u5b9a\u74062.1\uff08\u516d\u8fb9\u5f62\u6700\u4f18\u6027\uff09<\/strong>\uff1a<br \/>\n\u5bf9\u4e8e\u51f8\u6392\u65a5\u52bf$V(r)$\uff08$V&#8221;(r) &gt; 0$\uff09\uff0c\u516d\u8fb9\u5f62\u6392\u5217\u662f\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u7684\u5168\u5c40\u80fd\u91cf\u6700\u5c0f\u503c\u70b9\u3002<\/p>\n<h3><strong>\u7b2c3\u7ae0\uff1a\u4fe1\u606f\u57fa\u56e0\u7684\u5b8c\u6574\u5b9a\u4e49\u4e0e\u6d8c\u73b0\u673a\u5236<\/strong><\/h3>\n<h4><strong>3.1 \u4fe1\u606f\u57fa\u56e0\u7684\u6570\u5b66\u5b9a\u4e49<\/strong><\/h4>\n<p><strong>\u5b9a\u4e493.1\uff08\u4fe1\u606f\u57fa\u56e0IG\uff09<\/strong>\uff1a<br \/>\n\u4fe1\u606f\u57fa\u56e0\u662f\u7cfb\u7edf\u5728\u81ea\u6307\u6fc0\u53d1\u4e2d\u6355\u83b7\u7684\u3001\u7531\u4ee5\u4e0b\u4e03\u4e2a\u5206\u91cf\u6784\u6210\u7684\u62d3\u6251\u7a33\u5b9a\u76f8\u5e72\u6001\uff1a<\/p>\n<p>$$<br \/>\ntext{IG} = {omega_0, mathbf{Omega}_0, chi, pi_0, I<em>S, I<\/em>omega, I_C}<br \/>\n$$<\/p>\n<p>\u5404\u5206\u91cf\u7269\u7406\u610f\u4e49\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th>\u5206\u91cf<\/th>\n<th>\u7269\u7406\u542b\u4e49<\/th>\n<th>\u6765\u6e90\u573a<\/th>\n<th>\u6570\u5b66\u5b9a\u4e49<\/th>\n<th>\u53d6\u503c\u8303\u56f4<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>$omega_0$<\/td>\n<td>\u672c\u5f81\u9891\u7387<\/td>\n<td>$Psi_omega$<\/td>\n<td>$omega<em>0 = sqrt{K\/M<\/em>{text{inertial}}}$<\/td>\n<td>$(0, infty)$<\/td>\n<\/tr>\n<tr>\n<td>$mathbf{Omega}_0$<\/td>\n<td>\u521d\u59cb\u81ea\u65cb<\/td>\n<td>$Psi_S$<\/td>\n<td>$mathbf{Omega}_{text{spin}} = nabla times mathbf{j}_S$<\/td>\n<td>$mathbb{R}^3$<\/td>\n<\/tr>\n<tr>\n<td>$chi$<\/td>\n<td>\u624b\u6027<\/td>\n<td>$Psi_C$<\/td>\n<td>$chi = frac{1}{2pi}oint_C nabla phi_C cdot dmathbf{l}$<\/td>\n<td>${-1, +1}$<\/td>\n<\/tr>\n<tr>\n<td>$pi_0$<\/td>\n<td>\u521d\u59cb\u538b\u529b<\/td>\n<td>\u71b5\u6d41<\/td>\n<td>$pi = nabla cdot mathbf{J}_S = nabla cdot (rho_S mathbf{v})$<\/td>\n<td>$(-infty, +infty)$<\/td>\n<\/tr>\n<tr>\n<td>$I<em>S, I<\/em>omega, I_C$<\/td>\n<td>\u4e09\u573a\u60ef\u6027<\/td>\n<td>\u5168\u573a<\/td>\n<td>\u60ef\u6027\u6cdb\u51fd<\/td>\n<td>$[0, 1]$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>\u6ce8\u610f<\/strong>\uff1a\u8fd9\u4e9b\u662f<strong>\u540d\u4e49\u60ef\u6027<\/strong>\uff0c\u5b9e\u9645\u7684\u6709\u6548\u60ef\u6027\u53d7\u71b5\u503a\u4fb5\u8680\u3002<\/p>\n<h4><strong>3.2 \u624b\u6027\u4e0e\u538b\u529b\u7684\u7269\u7406\u610f\u4e49<\/strong><\/h4>\n<p><strong>\u624b\u6027\u03c7<\/strong>\uff1a\u7cfb\u7edf\u7684\u5185\u7980\u62d3\u6251\u6027\u8d28\uff0c\u51b3\u5b9a\u4fe1\u606f\u5904\u7406\u6a21\u5f0f<\/p>\n<ul>\n<li>$chi = +1$\uff08\u53f3\u65cb\u7cfb\u7edf\uff09\uff1a\u4fe1\u606f\u5904\u7406\u504f\u5411\u987a\u5e8f\u3001\u5206\u6790\u3001\u5206\u89e3<\/li>\n<li>$chi = -1$\uff08\u5de6\u65cb\u7cfb\u7edf\uff09\uff1a\u4fe1\u606f\u5904\u7406\u504f\u5411\u5e76\u884c\u3001\u7efc\u5408\u3001\u6574\u4f53<\/li>\n<\/ul>\n<p><strong>\u538b\u529b\u03c0<\/strong>\uff1a\u71b5\u6d41\u6563\u5ea6\uff0c\u51b3\u5b9a\u80fd\u91cf\u6d41\u52a8\u65b9\u5411<\/p>\n<ul>\n<li>$pi &gt; 0$\uff1a\u71b5\u6d41\u8f90\u5c04\uff08\u6269\u5f20\u578b\u7cfb\u7edf\uff09\uff0c\u80fd\u91cf\u5411\u5916\u6d41\u52a8<\/li>\n<li>$pi &lt; 0$\uff1a\u71b5\u6d41\u5438\u6536\uff08\u51dd\u805a\u578b\u7cfb\u7edf\uff09\uff0c\u80fd\u91cf\u5411\u5185\u805a\u96c6<\/li>\n<li>$|pi| to 0$\uff1a\u5e73\u8861\u6001\uff0c\u80fd\u91cf\u6d41\u52a8\u8fbe\u5230\u7a33\u6001<\/li>\n<\/ul>\n<h4><strong>3.3 \u56db\u578b\u57fa\u672c\u7cfb\u7edf\u5206\u7c7b<\/strong><\/h4>\n<table>\n<thead>\n<tr>\n<th>\u7c7b\u578b<\/th>\n<th>\u624b\u6027\u03c7<\/th>\n<th>\u538b\u529b\u03c0<\/th>\n<th>\u71b5\u6d41\u7279\u5f81<\/th>\n<th>\u7269\u7406\u5b9e\u4f8b<\/th>\n<th>\u6f14\u5316\u503e\u5411<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u6269\u5f20\u53f3\u65cb<\/strong><\/td>\n<td>+1<\/td>\n<td>&gt;0<\/td>\n<td>\u8f90\u5c04\uff0c\u6709\u5e8f\u6269\u5f20<\/td>\n<td>\u6052\u661f\u3001\u79d1\u6280\u6587\u660e<\/td>\n<td>\u5feb\u901f\u751f\u957f\uff0c\u6613\u79ef\u7d2f\u7269\u7406\u71b5\u503a<\/td>\n<\/tr>\n<tr>\n<td><strong>\u51dd\u805a\u53f3\u65cb<\/strong><\/td>\n<td>+1<\/td>\n<td>&lt;0<\/td>\n<td>\u5438\u6536\uff0c\u6709\u5e8f\u51dd\u805a<\/td>\n<td>\u6676\u4f53\u3001\u4f20\u7edf\u793e\u4f1a<\/td>\n<td>\u7a33\u5b9a\u7ed3\u6784\uff0c\u6613\u79ef\u7d2f\u4fe1\u606f\u71b5\u503a<\/td>\n<\/tr>\n<tr>\n<td><strong>\u6269\u5f20\u5de6\u65cb<\/strong><\/td>\n<td>-1<\/td>\n<td>&gt;0<\/td>\n<td>\u8f90\u5c04\uff0c\u7f51\u7edc\u5316<\/td>\n<td>\u751f\u6001\u7cfb\u7edf\u3001\u6587\u5316\u8fd0\u52a8<\/td>\n<td>\u591a\u6837\u6f14\u5316\uff0c\u53cc\u91cd\u503a\u52a1\u98ce\u9669<\/td>\n<\/tr>\n<tr>\n<td><strong>\u51dd\u805a\u5de6\u65cb<\/strong><\/td>\n<td>-1<\/td>\n<td>&lt;0<\/td>\n<td>\u5438\u6536\uff0c\u81ea\u9002\u5e94<\/td>\n<td>\u9ed1\u6d1e\u3001\u7ec6\u80de<\/td>\n<td>\u9ad8\u6548\u6574\u5408\uff0c\u503a\u52a1\u53ef\u63a7\u6027\u8f83\u597d<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h2><strong>\u7b2c\u4e8c\u5377\uff1a\u60ef\u6027\u52a8\u529b\u5b66\u4e0e\u5b88\u6052\u5b9a\u5f8b<\/strong><\/h2>\n<h3><strong>\u7b2c4\u7ae0\uff1a\u70ed\u60ef\u6027\u3001\u9891\u7387\u60ef\u6027\u3001\u76f8\u5e72\u60ef\u6027<\/strong><\/h3>\n<h4><strong>4.1 \u60ef\u6027\u6cdb\u51fd\u7684\u7edf\u4e00\u53d8\u5206\u5b9a\u4e49<\/strong><\/h4>\n<p>$$<br \/>\nmathcal{I}<em>X[Psi] = left. frac{delta^2 S<\/em>{text{eff}}[Psi]}{delta (partial_t Psi<em>X)^2} right|<\/em>{text{on-shell}}<br \/>\n$$<br \/>\n\u5176\u4e2d$X in {S, omega, C}$\u3002<\/p>\n<h4><strong>4.2 \u4e09\u573a\u60ef\u6027\u7684\u5177\u4f53\u5f62\u5f0f<\/strong><\/h4>\n<p><strong>\u70ed\u60ef\u6027\uff08$I_S$\uff09<\/strong>\uff1a<br \/>\n$$<br \/>\nI_S[Psi_S] = frac{1}{V} int d^3r , left| frac{delta ln |Psi_S|^2}{delta T} right|^2 cdot tau_S(mathbf{r})<br \/>\n$$<br \/>\n\u53d6\u503c\u8303\u56f4\uff1a[0,1]\uff0c\u8d85\u5bfc\u4f53\uff1a0.85-0.95\uff0c\u7edd\u7f18\u4f53\uff1a0.1-0.3<\/p>\n<p><strong>\u9891\u7387\u60ef\u6027\uff08$I_omega$\uff09<\/strong>\uff1a<br \/>\n$$<br \/>\nI<em>omega[Psi<\/em>omega] = frac{1}{V} int d^3r , left( frac{partial phi<em>omega}{partial t} right)^{-2} cdot left| frac{delta phi<\/em>omega}{delta omega} right|^2<br \/>\n$$<br \/>\n\u53d6\u503c\u8303\u56f4\uff1a[0,1]\uff0c\u8109\u51b2\u661f\uff1a0.999999\uff0c\u673a\u68b0\u949f\u6446\uff1a0.7<\/p>\n<p><strong>\u76f8\u5e72\u60ef\u6027\uff08$I_C$\uff09<\/strong>\uff1a<br \/>\n$$<br \/>\nI_C[Psi_C] = left| int Psi_C(mathbf{r}) d^3r right|^2 cdot left( frac{xi[Psi<em>C]}{L} right) cdot kappa(G<\/em>{text{shape}}[Psi_C])<br \/>\n$$<br \/>\n\u53d6\u503c\u8303\u56f4\uff1a[0,1]\uff0c\u8d85\u6d41\u6c26\uff1a0.98\uff0c\u6db2\u4f53\uff1a0.3-0.5<\/p>\n<h3><strong>\u7b2c5\u7ae0\uff1a\u71b5\u503a\u5bf9\u4e09\u573a\u60ef\u6027\u7684\u672c\u8d28\u4fb5\u8680<\/strong><\/h3>\n<h4><strong>5.1 \u6709\u6548\u60ef\u6027\uff1a\u4ece\u540d\u4e49\u503c\u5230\u5b9e\u9645\u503c<\/strong><\/h4>\n<p><strong>\u6838\u5fc3\u53d1\u73b0<\/strong>\uff1a\u7cfb\u7edf\u4e2d\u6d4b\u91cf\u7684\u60ef\u6027\u503c\u4e0d\u662f\u540d\u4e49\u503c$I_X$\uff0c\u800c\u662f<strong>\u88ab\u71b5\u503a\u4fb5\u8680\u540e\u7684\u6709\u6548\u503c<\/strong>\uff1a<br \/>\n$$<br \/>\nI_X^{text{eff}} = I_X cdot exp(-lambda_X cdot ED_X), quad X in {S, omega, C}<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u540d\u4e49\u60ef\u6027$I_X$\uff1a\u7cfb\u7edf\u5728\u7406\u60f3\u65e0\u503a\u72b6\u6001\u4e0b\u7684\u7406\u8bba\u60ef\u6027<\/li>\n<li>\u6709\u6548\u60ef\u6027$I_X^{text{eff}}$\uff1a\u8003\u8651\u5b9e\u9645\u71b5\u503a\u8d1f\u62c5\u540e\u7684\u53ef\u7528\u60ef\u6027<\/li>\n<li>\u4fb5\u8680\u7cfb\u6570$lambda_X$\uff1a\u8be5\u60ef\u6027\u5bf9\u71b5\u503a\u7684\u654f\u611f\u5ea6<\/li>\n<\/ul>\n<h4><strong>5.2 \u4e09\u573a\u60ef\u6027\u7684\u503a\u52a1\u4fb5\u8680\u673a\u5236<\/strong><\/h4>\n<h5><strong>\u70ed\u60ef\u6027$I_S$\u7684\u503a\u52a1\u4fb5\u8680<\/strong><\/h5>\n<p>\u7269\u7406\u71b5\u503a\u4f7f\u70ed\u573a$Psi_S$\u201c\u5145\u6ee1\u6742\u8d28\u201d\uff0c\u80fd\u91cf\u4f20\u9012\u6548\u7387\u4e0b\u964d\uff1a<br \/>\n$$<br \/>\nI_S^{text{eff}} = I<em>S cdot expleft[-lambda<\/em>{S1} P_ED &#8211; lambda_{S2} int frac{(nabla T)^2}{T^2} dtright]<br \/>\n$$<\/p>\n<p><strong>\u53cc\u4fb5\u8680\u673a\u5236<\/strong>\uff1a<\/p>\n<ol>\n<li><strong>\u76f4\u63a5\u503a\u52a1\u4fb5\u8680<\/strong>\uff08$lambda_{S1}$\u9879\uff09\uff1a\u71b5\u503a\u672c\u8eab\u6d88\u8017\u80fd\u91cf\u7ba1\u7406\u80fd\u529b<\/li>\n<li><strong>\u6e29\u5ea6\u68af\u5ea6\u5f3a\u5316\u4fb5\u8680<\/strong>\uff08$lambda_{S2}$\u9879\uff09\uff1a\u6e29\u5ea6\u5206\u5e03\u4e0d\u5747\u589e\u52a0\u70ed\u529b\u5b66\u52bf\uff0c\u52a0\u901f\u60ef\u6027\u8870\u51cf<\/li>\n<\/ol>\n<h5><strong>\u9891\u7387\u60ef\u6027$I_omega$\u7684\u503a\u52a1\u4fb5\u8680<\/strong><\/h5>\n<p>\u4fe1\u606f\u71b5\u503a\u4f7f\u52a8\u573a$Psi<em>omega$\u7684\u8282\u5f8b\u5931\u7a33\uff0c\u5185\u90e8\u632f\u8361\u5668\u5931\u8c10\uff1a<br \/>\n$$<br \/>\nI<\/em>omega^{text{eff}} = I<em>omega cdot expleft[-lambda<\/em>{omega1} I_ED &#8211; lambda<em>{omega2} frac{sigma<\/em>omega^2}{langleomegarangle^2}right]<br \/>\n$$<\/p>\n<p><strong>\u53cc\u4fb5\u8680\u673a\u5236<\/strong>\uff1a<\/p>\n<ol>\n<li><strong>\u8ba4\u77e5\u503a\u52a1\u4fb5\u8680<\/strong>\uff08$lambda_{omega1}$\u9879\uff09\uff1a\u4fe1\u606f\u6c61\u67d3\u76f4\u63a5\u5e72\u6270\u65f6\u5e8f\u5224\u65ad<\/li>\n<li><strong>\u9891\u7387\u5f25\u6563\u4fb5\u8680<\/strong>\uff08$lambda_{omega2}$\u9879\uff09\uff1a\u8282\u594f\u4e0d\u4e00\u81f4\u6027\u81ea\u8eab\u9020\u6210\u60ef\u6027\u635f\u5931<\/li>\n<\/ol>\n<h5><strong>\u76f8\u5e72\u60ef\u6027$I_C$\u7684\u503a\u52a1\u4fb5\u8680<\/strong><\/h5>\n<p>\u53cc\u91cd\u71b5\u503a\u534f\u540c\u4fb5\u8680\u94f8\u573a$Psi_C$\u7684\u7ed3\u6784\u5b8c\u6574\u6027\uff0c\u4ea7\u751f\u201c\u62d3\u6251\u7f3a\u9677\u201d\uff1a<br \/>\n$$<br \/>\nI_C^{text{eff}} = I<em>C cdot expleft[-lambda<\/em>{C1} P_ED &#8211; lambda<em>{C2} I_ED &#8211; lambda<\/em>{C3} int G_{text{defect}} dtright]<br \/>\n$$<\/p>\n<p><strong>\u4e09\u91cd\u4fb5\u8680\u673a\u5236<\/strong>\uff1a<\/p>\n<ol>\n<li><strong>\u7269\u7406\u503a\u52a1\u4fb5\u8680<\/strong>\uff08$lambda_{C1}$\u9879\uff09\uff1a\u7269\u7406\u7834\u574f\u76f4\u63a5\u524a\u5f31\u7ed3\u6784<\/li>\n<li><strong>\u4fe1\u606f\u503a\u52a1\u4fb5\u8680<\/strong>\uff08$lambda_{C2}$\u9879\uff09\uff1a\u9519\u8bef\u8bbe\u8ba1\u6216\u7ef4\u62a4\u51b3\u7b56\u635f\u5bb3\u7ed3\u6784<\/li>\n<li><strong>\u7f3a\u9677\u79ef\u7d2f\u4fb5\u8680<\/strong>\uff08$lambda_{C3}$\u9879\uff09\uff1a\u5fae\u89c2\u7f3a\u9677\u7684\u534f\u540c\u6548\u5e94<\/li>\n<\/ol>\n<p><strong>\u62d3\u6251\u7f3a\u9677\u7684\u6570\u5b66\u5b9a\u4e49<\/strong>\uff1a<br \/>\n$$<br \/>\nG<em>{text{defect}} = oint<\/em>{partial D} nabla phi_C cdot dmathbf{l} neq 2pi n<br \/>\n$$<\/p>\n<h4><strong>5.3 \u4fb5\u8680\u7cfb\u6570\u7684\u4f30\u8ba1\u4e0e\u6807\u5b9a<\/strong><\/h4>\n<table>\n<thead>\n<tr>\n<th>\u4fb5\u8680\u7cfb\u6570<\/th>\n<th>\u7269\u7406\u610f\u4e49<\/th>\n<th>\u4f30\u8ba1\u65b9\u6cd5<\/th>\n<th>\u5178\u578b\u503c\u8303\u56f4<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>$lambda_{S1}$<\/td>\n<td>\u70ed\u60ef\u6027\u5bf9\u7269\u7406\u503a\u654f\u611f\u5ea6<\/td>\n<td>\u78b3\u6392\u653e\u4e0e\u80fd\u6e90\u6548\u7387\u76f8\u5173\u6027<\/td>\n<td>0.01-0.05 (\u0398\u00b7yr)\u207b\u00b9<\/td>\n<\/tr>\n<tr>\n<td>$lambda_{S2}$<\/td>\n<td>\u6e29\u5ea6\u68af\u5ea6\u5bf9\u70ed\u60ef\u6027\u5f71\u54cd<\/td>\n<td>\u70ed\u6d41\u5206\u5e03\u4e0e\u6e29\u5dee\u5173\u7cfb<\/td>\n<td>0.001-0.005 (K\u207b\u00b2\u00b7yr\u207b\u00b9)<\/td>\n<\/tr>\n<tr>\n<td>$lambda_{omega1}$<\/td>\n<td>\u9891\u7387\u60ef\u6027\u5bf9\u4fe1\u606f\u503a\u654f\u611f\u5ea6<\/td>\n<td>\u5a92\u4f53\u73af\u5883\u4e0e\u793e\u4f1a\u8282\u594f\u540c\u6b65\u6027<\/td>\n<td>0.02-0.08 (\u03a8\u00b7yr)\u207b\u00b9<\/td>\n<\/tr>\n<tr>\n<td>$lambda_{omega2}$<\/td>\n<td>\u9891\u7387\u5f25\u6563\u4fb5\u8680\u5f3a\u5ea6<\/td>\n<td>\u591a\u632f\u8361\u5668\u7cfb\u7edf\u540c\u6b65\u5ea6\u6d4b\u91cf<\/td>\n<td>0.1-0.5 (\u65e0\u91cf\u7eb2)<\/td>\n<\/tr>\n<tr>\n<td>$lambda_{C1}$<\/td>\n<td>\u94f8\u573a\u5bf9\u7269\u7406\u503a\u654f\u611f\u5ea6<\/td>\n<td>\u751f\u6001\u9000\u5316\u4e0e\u7ed3\u6784\u5b8c\u6574\u6027\u5173\u7cfb<\/td>\n<td>0.005-0.02 (\u0398\u00b7yr)\u207b\u00b9<\/td>\n<\/tr>\n<tr>\n<td>$lambda_{C2}$<\/td>\n<td>\u94f8\u573a\u5bf9\u4fe1\u606f\u503a\u654f\u611f\u5ea6<\/td>\n<td>\u51b3\u7b56\u8d28\u91cf\u4e0e\u57fa\u7840\u8bbe\u65bd\u53ef\u9760\u6027<\/td>\n<td>0.01-0.04 (\u03a8\u00b7yr)\u207b\u00b9<\/td>\n<\/tr>\n<tr>\n<td>$lambda_{C3}$<\/td>\n<td>\u7f3a\u9677\u7d2f\u79ef\u7cfb\u6570<\/td>\n<td>\u6750\u6599\u75b2\u52b3\u3001\u793e\u4f1a\u77db\u76fe\u79ef\u7d2f\u901f\u7387<\/td>\n<td>0.001-0.01 (defect\u00b7yr\u207b\u00b9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><strong>5.4 \u6709\u6548\u60ef\u6027\u7684\u592a\u6781\u5e73\u8861\u6761\u4ef6<\/strong><\/h4>\n<p><strong>\u5b9a\u4e495.1\uff08\u57fa\u4e8e\u6709\u6548\u60ef\u6027\u7684\u4e09\u7ef4\u592a\u6781\u5e73\u8861\uff09<\/strong>\uff1a<br \/>\n\u5065\u5eb7\u7cfb\u7edf\u7684\u4e09\u7ef4\u6709\u6548\u60ef\u6027\u5e94\u6ee1\u8db3\u6bd4\u4f8b\u534f\u8c03\uff1a<br \/>\n$$<br \/>\n0.8 leq frac{I_omega^{text{eff}}}{I_S^{text{eff}}} leq 1.25, quad<br \/>\n0.8 leq frac{I<em>C^{text{eff}}}{I<\/em>omega^{text{eff}}} leq 1.25, quad<br \/>\n0.8 leq frac{I_S^{text{eff}}}{I_C^{text{eff}}} leq 1.25<br \/>\n$$<\/p>\n<p><strong>\u5931\u8861\u6761\u4ef6<\/strong>\uff1a<br \/>\n\u5f53$(lambda_j ED_j &#8211; lambda_i ED<em>i) &gt; ln(1.25\/0.8) approx 0.47$\u65f6\uff0c\u5373\u4f7f\u540d\u4e49\u60ef\u6027\u6bd4$r<\/em>{ij}^{text{nom}}=1$\uff0c\u6709\u6548\u60ef\u6027\u6bd4\u4e5f\u4f1a\u8d85\u51fa\u5065\u5eb7\u8303\u56f4\u3002<\/p>\n<h3><strong>\u7b2c6\u7ae0\uff1a\u60ef\u6027\u5f20\u91cf\u4e0e\u7ed3\u6784\u4e0d\u53d8\u91cf<\/strong><\/h3>\n<h4><strong>6.1 \u4e09\u7ef4\u60ef\u6027\u5f20\u91cf<\/strong><\/h4>\n<p>$$<br \/>\nmathcal{I}_{text{total}} =<br \/>\nbegin{bmatrix}<br \/>\nI<em>S &amp; alpha<\/em>{Somega} &amp; alpha<em>{SC}<br \/>\nalpha<\/em>{omega S} &amp; I<em>omega &amp; alpha<\/em>{omega C}<br \/>\nalpha<em>{CS} &amp; alpha<\/em>{Comega} &amp; I_C<br \/>\nend{bmatrix}<br \/>\n$$<\/p>\n<p>\u8026\u5408\u7cfb\u6570\uff1a<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>6.2 \u60ef\u6027\u7ed3\u6784\u4e0d\u53d8\u91cf\u5b9a\u7406<\/strong><\/h4>\n<p><strong>\u5b9a\u74066.1\uff08\u4e09\u7ef4\u6709\u6548\u60ef\u6027\u7ed3\u6784\u4e0d\u53d8\u91cf\uff09<\/strong>\uff1a<br \/>\n\u5728\u7edf\u8ba1\u5e73\u5747\u610f\u4e49\u4e0a\uff0c\u7cfb\u7edf\u603b\u6709\u6548\u60ef\u6027\u4fdd\u6301\u76f8\u5bf9\u7a33\u5b9a\uff1a<br \/>\n$$<br \/>\nfrac{d}{dt}leftlangle I<em>S^{text{eff}} + I<\/em>omega^{text{eff}} + I_C^{text{eff}} rightrangle approx 0<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u89e3\u91ca<\/strong>\uff1a\u8fd9\u4e0d\u662f\u5fae\u89c2\u5b88\u6052\u5f8b\uff0c\u800c\u662f<strong>\u5b8f\u89c2\u76f8\u5e72\u7cfb\u7edf\u4e3a\u7ef4\u6301\u81ea\u8eab\u7ed3\u6784\u5b8c\u6574\u6027\u800c\u8868\u73b0\u51fa\u7684\u7edf\u8ba1\u89c4\u5f8b<\/strong>\u3002\u7cfb\u7edf\u901a\u8fc7\u03a9-R-V-S-E-D\u5faa\u73af\u5728\u4e09\u7ef4\u60ef\u6027\u95f4\u52a8\u6001\u8c03\u914d\u8d44\u6e90\u3002<\/p>\n<p><strong>\u63a8\u8bba6.1\uff08\u6709\u6548\u60ef\u6027\u8f6c\u79fb\u65b9\u7a0b\uff09<\/strong>\uff1a<br \/>\n\u5404\u6709\u6548\u60ef\u6027\u5206\u91cf\u95f4\u53ef\u76f8\u4e92\u8f6c\u5316\uff0c\u4f46\u603b\u53d7\u503a\u52a1\u4fb5\u8680\uff1a<br \/>\n$$<br \/>\nfrac{dI<em>S^{text{eff}}}{dt} + frac{dI<\/em>omega^{text{eff}}}{dt} + frac{dI_C^{text{eff}}}{dt} = -sum_X lambda_X I_X cdot ED_X<br \/>\n$$<\/p>\n<hr \/>\n<h2><strong>\u7b2c\u4e09\u5377\uff1a\u03a9-R-V-S-E-D\u6f14\u5316\u5e8f\u5217<\/strong><\/h2>\n<h3><strong>\u7b2c7\u7ae0\uff1a\u5b87\u5b99\u7684\u57fa\u672c\u8bed\u6cd5<\/strong><\/h3>\n<h4><strong>7.1 RVSE\u5e8f\u5217\u7684\u7269\u7406\u610f\u4e49<\/strong><\/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\u7684\u03a9-R-V-S-E-D<\/code><\/pre>\n<p>\u8fd9\u4e0d\u662f\u201c\u6f14\u5316\u9636\u6bb5\u201d\uff0c\u800c\u662f<strong>\u6d41\u52a8\u7684\u57fa\u672c\u53e5\u5f0f<\/strong>\u3002\u5c31\u50cf\u8bed\u8a00\u53ea\u6709\u4e3b\u8c13\u5bbe\u5b9a\u72b6\u8865\uff0c\u5b87\u5b99\u4e5f\u53ea\u6709\u03a9-R-V-S-E-D\u8fd9\u516d\u4e2a\u201c\u8bcd\u6027\u201d\u3002<\/p>\n<h4><strong>7.2 \u5404\u9636\u6bb5\u7684\u5b8c\u6574\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>\u624b\u6027\u03c7\u72b6\u6001<\/th>\n<th>\u538b\u529b\u03c0\u72b6\u6001<\/th>\n<th>\u60ef\u6027\u7a0e\u79ef\u7d2f\u7387<\/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>\u672a\u9501\u5b9a\uff0c\u63a2\u7d22\u4e2d<\/td>\n<td>\u5f00\u59cb\u504f\u79bb0<\/td>\n<td>\u4f4e\uff08\u63a2\u7d22\u4e2d\uff0c\u7a0e\u57fa\u5c0f\uff09<\/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>\u9501\u5b9a\uff08\u5076\u7136\u51b3\u5b9a\uff09<\/td>\n<td>\u5feb\u901f\u53d8\u5316<\/td>\n<td>\u4e2d\uff08\u5feb\u901f\u6269\u5f20\uff0c\u5ffd\u7565\u7a0e\u8d1f\uff09<\/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>\u5c1d\u8bd5\u7ffb\u8f6c<\/td>\n<td>\u5267\u70c8\u6ce2\u52a8<\/td>\n<td>\u9ad8\uff08\u8def\u5f84\u5206\u5316\uff0c\u7a0e\u5236\u6df7\u4e71\uff09<\/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>\u7b5b\u9009\u6700\u4f18\u503c<\/td>\n<td>\u8d8b\u5411\u6700\u4f18\u8303\u56f4<\/td>\n<td>\u964d\u81f3\u6700\u4f18\uff08\u7b5b\u9009\u51fa\u4f4e\u7a0e\u7ed3\u6784\uff09<\/td>\n<\/tr>\n<tr>\n<td><strong>[E\uff08\u7a33\u6001\u7ef4\u6301\uff09]<\/strong><\/td>\n<td>\u5f62\u6210\u7a33\u5b9a\u6d41\u52a8\u6a21\u5f0f<\/td>\n<td>\u7a33\u5b9a$Psi_C$<\/td>\n<td>\u7ef4\u6301<\/td>\n<td>\u7ef4\u6301<\/td>\n<td>\u7ef4\u6301\u6700\u4f4e\uff08\u6700\u4f18\u7ed3\u6784\uff09<\/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>\u5931\u6548<\/td>\n<td>\u5931\u8861<\/td>\n<td>\u7206\u53d1\u6027\u589e\u957f\uff08\u7a0e\u8d1f\u8d85\u8fc7\u627f\u53d7\u529b\uff09<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><strong>7.3 \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>\u76f8\u5e72\u5ea6$C$<\/th>\n<th>\u624b\u6027\u4e00\u81f4\u6027<\/th>\n<th>\u538b\u529b\u7a33\u5b9a\u6027<\/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>0\u21920.5<\/td>\n<td>\u4f4e<\/td>\n<td>\u4f4e<\/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>0.5-0.8<\/td>\n<td>\u9ad8\uff08\u5df2\u9501\u5b9a\uff09<\/td>\n<td>\u5b9a\u5411\u53d8\u5316<\/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>\u4e0b\u964d<\/td>\n<td>\u6ce2\u52a8<\/td>\n<td>\u5267\u70c8\u6ce2\u52a8<\/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>\u6062\u590d\u63d0\u5347<\/td>\n<td>\u4f18\u5316<\/td>\n<td>\u8d8b\u4e8e\u6700\u4f18<\/td>\n<\/tr>\n<tr>\n<td>[E]<\/td>\n<td>\u2191\u7a33\u5b9a\u6700\u4f18<\/td>\n<td>\u6700\u5c0f<\/td>\n<td>\u7a33\u6001\u7ef4\u6301<\/td>\n<td>\u7ef4\u6301<\/td>\n<td>\u7ef4\u6301<\/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>\u21920<\/td>\n<td>\u4e27\u5931<\/td>\n<td>\u5931\u8861<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><strong>7.4 D\u9636\u6bb5\u5fc5\u7136\u6027\u5b9a\u7406<\/strong><\/h4>\n<p><strong>\u5b9a\u74067.1\uff08D\u9636\u6bb5\u5fc5\u7136\u6027\uff09<\/strong>\uff1a<br \/>\n\u5bf9\u4e8e\u5b8c\u5168\u88ab\u52a8\u6f14\u5316\u7cfb\u7edf\uff0c\u5176\u7a33\u5b9a\u9636\u6bb5\u65e0\u6cd5\u6c38\u4e45\u7ef4\u6301\u3002\u5b58\u5728\u6700\u5927\u7a33\u5b9a\u65f6\u95f4$tau<em>{text{max}}$\uff1a<br \/>\n$$<br \/>\ntau<\/em>{text{max}} = minleft(frac{I<em>C}{gamma<\/em>{text{decoherence}}}, frac{E<em>{text{reserve}}}{dot{S}<\/em>{text{unbalanced}}}right)<br \/>\n$$<br \/>\n\u5176\u4e2d$dot{S}<em>{text{unbalanced}}$\u662f\u4e0d\u5e73\u8861\u71b5\u4ea7\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<\/strong>\uff1a\u4ece\u9000\u76f8\u5e72\u673a\u5236\u51fa\u53d1\uff0c\u8003\u8651\u73af\u5883\u71b5\u6da8\u843d\u5bfc\u81f4\u7684\u76f8\u5e72\u6027\u8870\u51cf\uff0c\u4ee5\u53ca\u71b5\u503a\u79ef\u7d2f\u5bf9\u80fd\u91cf\u50a8\u5907\u7684\u8017\u5c3d\u3002<\/p>\n<h4><strong>7.5 \u71b5\u503a\u52a0\u901f\u8870\u9000\u5b9a\u7406<\/strong><\/h4>\n<p><strong>\u5b9a\u74067.2\uff08\u71b5\u503a\u52a0\u901f\u8870\u9000\uff09<\/strong>\uff1a<br \/>\n\u7cfb\u7edf\u7684D\u9636\u6bb5\u6301\u7eed\u65f6\u95f4$tau_D$\u7531\u6709\u6548\u76f8\u5e72\u60ef\u6027$I_C^{text{eff}}$\u51b3\u5b9a\uff1a<br \/>\n$$<br \/>\ntau_D = frac{I<em>C^{text{eff}}}{gamma<\/em>{text{decoherence}}} = frac{I<em>C cdot expleft[-lambda<\/em>{C1} P_ED &#8211; lambda_{C2} I_EDright]}{gamma}<br \/>\n$$<\/p>\n<p><strong>\u8bc1\u660e<\/strong>\uff1a<\/p>\n<ol>\n<li>\u4ece\u94f8\u573a\u65b9\u7a0b\u51fa\u53d1\uff1a$alpha Psi_C + beta |Psi_C|^2 Psi_C + gamma nabla^2 Psi_C = 0$<\/li>\n<li>\u8003\u8651\u71b5\u503a\u5bfc\u81f4\u7684\u201c\u6709\u6548\u521a\u5ea6\u4e0b\u964d\u201d\uff1a$alpha rightarrow alpha cdot (1 + epsilon cdot ED)$<\/li>\n<li>\u7ebf\u6027\u7a33\u5b9a\u6027\u5206\u6790\u7ed9\u51fa\u7279\u5f81\u8870\u51cf\u65f6\u95f4$tau propto 1\/sqrt{alpha}$<\/li>\n<li>\u4ee3\u5165\u6709\u6548\u53c2\u6570\u5f97$tau_D propto exp(-lambda ED)$<\/li>\n<\/ol>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a<\/p>\n<ul>\n<li>\u65e0\u503a\u7cfb\u7edf\uff1a$tau_D approx I_C\/gamma$\uff08\u56fa\u6709\u5bff\u547d\uff09<\/li>\n<li>\u6709\u503a\u7cfb\u7edf\uff1a$tau_D$\u6307\u6570\u7f29\u77ed\uff0c$ED$\u6bcf\u589e\u52a01\u5355\u4f4d\uff0c\u5bff\u547d\u7f29\u77ed$e^{-lambda}$\u500d<\/li>\n<\/ul>\n<p><strong>\u5b9a\u74067.3\uff08\u7a33\u6001\u7ef4\u6301\u7684\u503a\u52a1\u4e0a\u9650\uff09<\/strong>\uff1a<br \/>\n\u7cfb\u7edf\u80fd\u5728E\u9636\u6bb5\uff08\u7a33\u6001\uff09\u7ef4\u6301\u7684\u65f6\u95f4$tau_E$\u53d7\u9650\u4e8e\uff1a<br \/>\n$$<br \/>\ntau<em>E leq minleft(tau<\/em>{text{decoherence}}, frac{ln(I<em>C\/I<\/em>{text{crit}})}{lambda<em>{C1} dot{P}_ED + lambda<\/em>{C2} dot{I}_ED}right)<br \/>\n$$<\/p>\n<h3><strong>\u7b2c8\u7ae0\uff1a\u76f8\u4e92\u4f5c\u7528\u4e0e\u5c42\u7ea7\u8dc3\u8fc1<\/strong><\/h3>\n<h4><strong>8.1 \u4e24\u4e2a\u7cfb\u7edf\u7684\u76f8\u4e92\u4f5c\u7528\u52bf<\/strong><\/h4>\n<p><strong>\u603b\u76f8\u4e92\u4f5c\u7528\u52bf<\/strong>\uff1a<br \/>\n$$<br \/>\nV<em>{text{total}} = V<\/em>{text{\u4e09\u573a}} + V<em>{chipi} + V<\/em>{text{debt}}<br \/>\n$$<\/p>\n<p>\u5176\u4e2d\uff1a<\/p>\n<ol>\n<li><strong>\u4e09\u573a\u76f8\u4e92\u4f5c\u7528<\/strong>\uff1a<br \/>\n$$<br \/>\nV<em>{text{\u4e09\u573a}} = g<\/em>{Somega} |Psi<em>S|^2 |Psi<\/em>omega|^2 + g<em>{omega C} |Psi<\/em>omega|^2 |Psi<em>C|^2 + g<\/em>{CS} |Psi_C|^2 |Psi_S|^2<br \/>\n$$<\/li>\n<li><strong>\u624b\u6027\u538b\u529b\u76f8\u4e92\u4f5c\u7528<\/strong>\uff1a<br \/>\n$$<br \/>\nV<em>{chipi} = -J<\/em>{chi} chi_A chi<em>B &#8211; J<\/em>{pi} (pi_A &#8211; pi_B)^2<br \/>\n$$<\/li>\n<li><strong>\u503a\u52a1\u76f8\u4e92\u4f5c\u7528\uff08\u65b0\u589e\uff09<\/strong>\uff1a<br \/>\n$$<br \/>\nV<em>{text{debt}} = -eta<\/em>{text{debt}} (ED_A &#8211; ED<em>B)^2 + kappa<\/em>{text{debt}} ED_A ED_B<br \/>\n$$<\/p>\n<ul>\n<li>\u7b2c\u4e00\u9879\uff1a\u503a\u52a1\u5dee\u5f02\u5bfc\u81f4\u6392\u65a5\uff08\u9ad8\u503a\u7cfb\u7edf\u4e0d\u613f\u4e0e\u4f4e\u503a\u7cfb\u7edf\u8026\u5408\uff09<\/li>\n<li>\u7b2c\u4e8c\u9879\uff1a\u503a\u52a1\u5171\u540c\u6027\u5bfc\u81f4\u5438\u5f15\uff08\u76f8\u4f3c\u503a\u52a1\u6c34\u5e73\u7cfb\u7edf\u6613\u5f62\u6210\u8054\u76df\uff09<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h4><strong>8.2 \u76f8\u4e92\u4f5c\u7528\u5206\u7c7b<\/strong><\/h4>\n<table>\n<thead>\n<tr>\n<th>\u7c7b\u578b<\/th>\n<th>\u624b\u6027\u6761\u4ef6<\/th>\n<th>\u538b\u529b\u6761\u4ef6<\/th>\n<th>\u503a\u52a1\u6761\u4ef6<\/th>\n<th>\u7ed3\u679c<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td><strong>\u5171\u632f\u878d\u5408<\/strong><\/td>\n<td>$chi_A = chi_B$<\/td>\n<td>$pi_A approx pi_B$<\/td>\n<td>$ED_A approx ED_B$<\/td>\n<td>\u5408\u5e76<\/td>\n<\/tr>\n<tr>\n<td><strong>\u7ade\u4e89\u6291\u5236<\/strong><\/td>\n<td>$chi_A = -chi_B$<\/td>\n<td>$pi_A cdot pi_B &gt; 0$<\/td>\n<td>\u4efb\u4f55<\/td>\n<td>\u5bf9\u6297<\/td>\n<\/tr>\n<tr>\n<td><strong>\u50ac\u5316\u8f85\u52a9<\/strong><\/td>\n<td>$chi_A = chi_B$<\/td>\n<td>$pi_A cdot pi_B &lt; 0$<\/td>\n<td>$ED_A ll ED_B$<\/td>\n<td>\u4e92\u8865\uff08\u4f4e\u503a\u50ac\u5316\u9ad8\u503a\u507f\u8fd8\uff09<\/td>\n<\/tr>\n<tr>\n<td><strong>\u503a\u52a1\u6b96\u6c11<\/strong><\/td>\n<td>\u4efb\u4f55<\/td>\n<td>$pi_A &gt; 0, pi_B &lt; 0$<\/td>\n<td>$ED_A &gt; ED_B$<\/td>\n<td>\u9ad8\u503a\u7cfb\u7edf\u5411\u4f4e\u503a\u7cfb\u7edf\u8f6c\u79fb\u503a\u52a1<\/td>\n<\/tr>\n<tr>\n<td><strong>\u5171\u751f\u51c0\u5316<\/strong><\/td>\n<td>$chi_A = -chi_B$<\/td>\n<td>$pi_A cdot pi_B &lt; 0$<\/td>\n<td>$ED_A approx ED_B$<\/td>\n<td>\u534f\u540c\u503a\u52a1\u507f\u8fd8<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h4><strong>8.3 \u5d4c\u5957\u5faa\u73af\u4e0e\u5c42\u7ea7\u8dc3\u8fc1<\/strong><\/h4>\n<p><strong>\u5b9a\u74068.1\uff08\u5d4c\u5957\u5faa\u73af\u5b9a\u7406\uff09<\/strong>\uff1a<br \/>\n\u5b87\u5b99\u6f14\u5316\u7531\u65e0\u9650\u5d4c\u5957\u7684\u03a9-R-V-S-E-D\u5faa\u73af\u6784\u6210\uff1a<br \/>\n$$<br \/>\nS_{n+1} = fleft(S_n, delta S_n, nabla S_n, chi_n, pi_n, ED_nright)<br \/>\n$$<\/p>\n<p><strong>\u5c42\u7ea7\u8dc3\u8fc1\u6761\u4ef6<\/strong>\uff1a<br \/>\n\u5f53\u7cfb\u7edf\u5728\u5c42\u7ea7$n$\u8fbe\u5230\u7a33\u5b9a\u72b6\u6001\uff0c\u4e14\u6ee1\u8db3\uff1a<\/p>\n<ol>\n<li>$mathcal{I}<em>{text{total}}^{(n)} &gt; mathcal{I}<\/em>{text{critical}}^{(n)} approx 0.5$<\/li>\n<li>$C^{(n)} &gt; C_{text{threshold}} approx 0.6$<\/li>\n<li>\u624b\u6027\u538b\u529b\u7ec4\u5408\u8fbe\u5230\u5c40\u90e8\u6700\u4f18<\/li>\n<li><strong>$ED^{(n)} &lt; ED_{text{max}}^{(n)}$\uff08\u503a\u52a1\u53ef\u63a7\uff09<\/strong><\/li>\n<\/ol>\n<p>\u65f6\uff0c\u4f1a\u89e6\u53d1\u5c42\u7ea7$n+1$\u7684\u03a9\u9636\u6bb5\uff08\u6fc0\u53d1\uff09\u3002<\/p>\n<hr \/>\n<h2><strong>\u7b2c\u56db\u5377\uff1a\u6d8c\u73b0\u7269\u7406\u56fe\u666f<\/strong><\/h2>\n<h3><strong>\u7b2c9\u7ae0\uff1a\u56db\u79cd\u57fa\u672c\u529b\u7684\u6d8c\u73b0\u89e3\u91ca\u6846\u67b6<\/strong><\/h3>\n<p><strong>\u5b9a\u4f4d\u58f0\u660e<\/strong>\uff1a\u672c\u8282\u4e0d\u63d0\u4f9b\u53ef\u91cd\u6574\u5316\u7684\u7edf\u4e00\u573a\u8bba\uff0c\u800c\u662f\u4e3a\u5df2\u77e5\u57fa\u672c\u529b\u63d0\u4f9b\u4e00\u5957<strong>\u5b8f\u89c2\u6d8c\u73b0\u89e3\u91ca\u6846\u67b6<\/strong>\uff0c\u65e8\u5728\u63ed\u793a\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u201c\u51e0\u4f55\u7ea6\u675f\u201d\u7684\u4e00\u81f4\u6027\u3002<\/p>\n<h4><strong>9.1 \u5f15\u529b\uff1a\u71b5\u68af\u5ea6\u7edf\u8ba1\u7b5b\u9009<\/strong><\/h4>\n<p>\u5f15\u529b\u4e0d\u662f\u57fa\u672c\u529b\uff0c\u800c\u662f\u71b5\u6da8\u843d\u5728\u5927\u5c3a\u5ea6\u4e0b\u7684\u7edf\u8ba1\u6548\u5e94\uff08\u5f62\u5f0f\u7c7b\u6bd4\uff09\uff1a<br \/>\n$$<br \/>\nF_g sim -Gfrac{m_1 m_2}{r^2} = -nablaleft[frac{hbar c}{r} cdot frac{m_1 m_2}{m_P^2}right]<br \/>\n$$<\/p>\n<p><strong>\u7269\u7406\u610f\u4e49<\/strong>\uff1a\u8d28\u91cf\u626d\u66f2\u71b5\u573a\u5206\u5e03\uff0c\u201c\u5f15\u529b\u201d\u662f\u7cfb\u7edf\u5411\u9ad8\u71b5\u6001\u6f14\u5316\u7684\u7edf\u8ba1\u8d8b\u52bf\u3002<\/p>\n<h4><strong>9.2 \u7535\u78c1\u529b\uff1a\u7535\u8377\u4f5c\u4e3a\u71b5\u6d41\u6e90<\/strong><\/h4>\n<p>\u7535\u8377\u662f\u71b5\u6d41\u7684\u6301\u7eed\u6e90\/\u6c47\u3002\u9ea6\u514b\u65af\u97e6\u65b9\u7a0b\u7684\u71b5\u6da8\u843d\u7c7b\u6bd4\u8868\u8ff0\uff1a<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>9.3 \u5f31\u529b\uff1a\u70ed\u573a\u7684Higgs\u673a\u5236<\/strong><\/h4>\n<p>\u5f31\u76f8\u4e92\u4f5c\u7528\u53ef\u7c7b\u6bd4\u4e3a\u70ed\u573a$Psi_S$\u7684\u5bf9\u79f0\u6027\u81ea\u53d1\u7834\u7f3a\uff0c\u4ea7\u751f$W^pm, Z^0$\u73bb\u8272\u5b50\u3002<\/p>\n<h4><strong>9.4 \u5f3a\u529b\uff1a\u94f8\u573a\u7684\u4e09\u91cd\u62d3\u6251\u9501\u5b9a<\/strong><\/h4>\n<p>\u5f3a\u76f8\u4e92\u4f5c\u7528\u53ef\u7c7b\u6bd4\u4e3a\u94f8\u573a$Psi_C$\u7684$SU(3)$\u5bf9\u79f0\u6027\u8868\u73b0\uff0c\u8272\u7981\u95ed\u6e90\u4e8e$V(r) propto r$\u7684\u7ebf\u6027\u589e\u957f\u52bf\u3002<\/p>\n<h3><strong>\u7b2c10\u7ae0\uff1a\u91cf\u5b50-\u7ecf\u5178\u7684\u573a\u8bba\u5f62\u5f0f\u7edf\u4e00<\/strong><\/h3>\n<h4><strong>10.1 \u91cf\u5b50\u6781\u9650\uff1a\u573a\u7b97\u7b26\u5f62\u5f0f\uff08\u5f62\u5f0f\u6620\u5c04\uff09<\/strong><\/h4>\n<p>\u5f53$hbar neq 0$\u65f6\uff0c\u4e09\u573a\u7684\u91cf\u5b50\u5316\u5f62\u5f0f\uff08\u4f5c\u4e3a\u5f62\u5f0f\u7c7b\u6bd4\uff09\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$mathcal{I}_X = langle hat{mathcal{I}}_X rangle$<\/p>\n<h4><strong>10.2 \u7ecf\u5178\u6781\u9650\uff1a$hbar to 0$\u9000\u5316<\/strong><\/h4>\n<p>\u5f53$hbar to 0$\u65f6\uff0c\u573a\u7b97\u7b26\u9000\u5316\u4e3a\u7ecf\u5178\u573a\u51fd\u6570\uff0c\u91cf\u5b50\u6da8\u843d\u6d88\u5931\uff0c\u60ef\u6027\u7ed3\u6784\u4e0d\u53d8\u91cf\u6062\u590d\u7ecf\u5178\u5f62\u5f0f\u3002<\/p>\n<h4><strong>10.3 \u9000\u76f8\u5e72\u7684IGT\u89e3\u91ca<\/strong><\/h4>\n<p>\u9000\u76f8\u5e72\u4e0d\u662f\u201c\u6ce2\u51fd\u6570\u574d\u7f29\u201d\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<\/strong>\uff1a\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<h3><strong>\u7b2c11\u7ae0\uff1a\u8de8\u5c3a\u5ea6\u6620\u5c04\u8868<\/strong><\/h3>\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;\">\u624b\u6027\u03c7<\/th>\n<th style=\"text-align: left;\">\u538b\u529b\u03c0<\/th>\n<th style=\"text-align: left;\"><strong>\u60ef\u6027\u4fb5\u8680\u7279\u5f81<\/strong><\/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;\">\u968f\u673a<\/td>\n<td style=\"text-align: left;\">\u5fae\u6270<\/td>\n<td style=\"text-align: left;\">\u9000\u76f8\u5e72\u5386\u53f2\u6c61\u67d3\u6d4b\u91cf\u57fa<\/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;\">\u56fa\u5b9a<\/td>\n<td style=\"text-align: left;\">\u5e73\u8861<\/td>\n<td style=\"text-align: left;\">\u78b0\u649e\u5bfc\u81f4\u76f8\u4f4d\u8bb0\u5fc6\u4e22\u5931<\/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;\">\u7279\u5b9a<\/td>\n<td style=\"text-align: left;\">\u53ef\u8c03<\/td>\n<td style=\"text-align: left;\">\u9519\u8bef\u6298\u53e0\u7d2f\u79ef\u4e3a\u6784\u8c61\u71b5\u503a<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>\u7ec6\u80de<\/strong><\/td>\n<td style=\"text-align: left;\">\u771f\u6838\u7ec6\u80de<\/td>\n<td style=\"text-align: left;\">\u4ee3\u8c22\u6d41<\/td>\n<td style=\"text-align: left;\">\u751f\u7269\u949f<\/td>\n<td style=\"text-align: left;\">\u819c\u4e0e\u9aa8\u67b6<\/td>\n<td style=\"text-align: left;\">-1\uff08\u5de6\u65cb\u4e3b\uff09<\/td>\n<td style=\"text-align: left;\">\u52a8\u6001<\/td>\n<td style=\"text-align: left;\">\u6d3b\u6027\u6c27\u635f\u4f24\u7ebf\u7c92\u4f53\uff08\u70ed\u60ef\u6027\u2193\uff09<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>\u751f\u7269<\/strong><\/td>\n<td style=\"text-align: left;\">\u54fa\u4e73\u52a8\u7269<\/td>\n<td style=\"text-align: left;\">\u4f53\u6e29<\/td>\n<td style=\"text-align: left;\">\u5fc3\u8df3\u8282\u5f8b<\/td>\n<td style=\"text-align: left;\">\u9aa8\u9abc\u795e\u7ecf<\/td>\n<td style=\"text-align: left;\">\u6df7\u5408<\/td>\n<td style=\"text-align: left;\">\u5e73\u8861<\/td>\n<td style=\"text-align: left;\">\u6162\u6027\u708e\u75c7\u964d\u4f4e\u80fd\u91cf\u6548\u7387<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"><strong>\u793e\u4f1a<\/strong><\/td>\n<td style=\"text-align: left;\">\u4eba\u7c7b\u6587\u660e<\/td>\n<td style=\"text-align: left;\">\u7ecf\u6d4e\u6d41<\/td>\n<td style=\"text-align: left;\">\u6587\u5316\u5468\u671f<\/td>\n<td style=\"text-align: left;\">\u5236\u5ea6\u7ed3\u6784<\/td>\n<td style=\"text-align: left;\">\u591a\u6837<\/td>\n<td style=\"text-align: left;\">\u590d\u6742<\/td>\n<td style=\"text-align: left;\"><strong>\u7269\u7406\u503a<\/strong>\uff1a\u70ed\u60ef\u6027\u4fb5\u8680<br \/>\n<strong>\u4fe1\u606f\u503a<\/strong>\uff1a\u8282\u594f\u60ef\u6027\u4fb5\u8680<\/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;\">+1\uff08\u53f3\u65cb\uff09<\/td>\n<td style=\"text-align: left;\">&gt;0\uff08\u9ad8\u538b\uff09<\/td>\n<td style=\"text-align: left;\">\u91cd\u5143\u7d20\u6c61\u67d3\u964d\u4f4e\u805a\u53d8\u6548\u7387<\/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;\">-1\uff08\u5de6\u65cb\uff09<\/td>\n<td style=\"text-align: left;\">\u68af\u5ea6<\/td>\n<td style=\"text-align: left;\">\u91d1\u5c5e\u5bcc\u96c6\u6539\u53d8\u540e\u7eed\u6f14\u5316\u8def\u5f84<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>\u5b9a\u740611.1\uff08\u8de8\u5c3a\u5ea6\u6709\u6548\u60ef\u6027\u6bd4\u7ed3\u6784\u4e0d\u53d8\u91cf\uff09<\/strong>\uff1a<br \/>\n\u6240\u6709\u7a33\u5b9a\u7cfb\u7edf\u90fd\u6ee1\u8db3\u76f8\u4f3c\u7684\u60ef\u6027\u6bd4\u4f8b\u5173\u7cfb\uff1a<br \/>\n$$<br \/>\n0.7 &lt; frac{I<em>{omega,text{\u4e2d\u5c42}}^{text{eff}}}{I<\/em>{S,text{\u5185\u6838}}^{text{eff}}} &lt; 1.3<br \/>\n$$<\/p>\n<p><strong>\u5b9a\u740611.2\uff08\u8de8\u5c3a\u5ea6\u60ef\u6027\u7a0e\u5206\u5e03\uff09<\/strong>\uff1a<br \/>\n$$<br \/>\nsum_{text{\u6240\u6709\u5c42\u7ea7}} lambda_X^{(n)} cdot ED^{(n)} = text{\u5e38\u6570} + mathcal{O}(hbar)<br \/>\n$$<\/p>\n<p><strong>\u610f\u4e49<\/strong>\uff1a\u4e00\u4e2a\u5c42\u7ea7\u7684\u7a0e\u8d1f\u4f18\u5316\u53ef\u80fd\u589e\u52a0\u53e6\u4e00\u5c42\u7ea7\u7684\u7a0e\u8d1f\u3002\u771f\u6b63\u7684\u5065\u5eb7\u9700\u8981<strong>\u5168\u5c3a\u5ea6\u7a0e\u8d1f\u6700\u5c0f\u5316<\/strong>\u3002<\/p>\n<hr \/>\n<h2><strong>\u7b2c\u4e94\u5377\uff1a\u5b9e\u9a8c\u9a8c\u8bc1\u4e0e\u7406\u8bba\u8fb9\u754c<\/strong><\/h2>\n<h3><strong>\u7b2c12\u7ae0\uff1a\u6838\u5fc3\u53ef\u8bc1\u4f2a\u5224\u636e<\/strong><\/h3>\n<h4><strong>12.1 \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>12.2 8\u6761\u6838\u5fc3\u53ef\u8bc1\u4f2a\u5224\u636e<\/strong>\uff08\u65b0\u589e\u7b2c8\u6761\uff09<\/h4>\n<p><strong>\u5224\u636e1\uff08\u60ef\u6027\u7ed3\u6784\u4e0d\u53d8\u91cf\u7cbe\u5ea6\uff09<\/strong>\uff1a<br \/>\n\u5b64\u7acb\u7cfb\u7edf\u4e2d\uff0c\u4e09\u7ef4\u6709\u6548\u60ef\u6027\u603b\u91cf\u7684\u76f8\u5bf9\u53d8\u5316\u7387\uff1a<br \/>\n$$<br \/>\nfrac{|Delta(I<em>S^{text{eff}} + I<\/em>omega^{text{eff}} + I<em>C^{text{eff}})|}{I<\/em>{text{total}}^{text{eff}}} &lt; 10^{-5}<br \/>\n$$<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<\/strong>\uff1a<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<\/strong>\uff1a<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<\/strong>\uff1a<br \/>\n\u5f53\u7cfb\u7edf\u60ef\u6027$mathcal{I}<em>{text{total}} &gt; mathcal{I}<\/em>{text{crit}}$\u4e14\u76f8\u5e72\u5ea6$C &gt; C<em>{text{threshold}}$\u4e14$ED &lt; ED<\/em>{text{max}}$\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<\/strong>\uff1a<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<p><strong>\u5224\u636e6\uff08\u624b\u6027\u5e72\u6d89\u6761\u7eb9\uff09<\/strong>\uff1a<br \/>\n\u4e24\u4e2a\u624b\u6027\u76f8\u53cd\u7684\u76f8\u5e72\u7cfb\u7edf\uff08$chi_A = -chi<em>B$\uff09\u9760\u8fd1\u65f6\uff0c\u5e94\u5728\u8fb9\u754c\u4ea7\u751f\u5e72\u6d89\u6761\u7eb9\uff1a<br \/>\n$$<br \/>\nd<\/em>{text{fringe}} = frac{lambda}{|chi_A &#8211; chi_B|} = frac{lambda}{2}<br \/>\n$$<br \/>\n\u82e5\u65e0\u6b64\u73b0\u8c61\uff0c\u624b\u6027\u573a\u8bba\u63cf\u8ff0\u5931\u6548\u3002<\/p>\n<p><strong>\u5224\u636e7\uff08\u538b\u529b\u5171\u632f\u6761\u4ef6\uff09<\/strong>\uff1a<br \/>\n\u5f53\u4e24\u7cfb\u7edf\u6ee1\u8db3$pi_A = -pi<em>B$\u65f6\uff0c\u5e94\u5728\u5171\u632f\u9891\u7387$omega<\/em>{text{res}}$\u5904\u51fa\u73b0\u80fd\u91cf\u4f20\u8f93\u5cf0\uff1a<br \/>\n$$<br \/>\nP<em>{text{transfer}}(omega) propto frac{Gamma}{Gamma^2 + (omega &#8211; omega<\/em>{text{res}})^2}<br \/>\n$$<br \/>\n\u5176\u4e2d$omega_{text{res}} = sqrt{|pi_A| cdot |pi_B|}$\u3002\u82e5\u65e0\u5cf0\u503c\uff0c\u538b\u529b\u8026\u5408\u9879\u5931\u6548\u3002<\/p>\n<p><strong>\u5224\u636e8\uff08\u71b5\u503a\u4fb5\u8680\u9a8c\u8bc1\uff09<\/strong>\uff1a<br \/>\n\u7cfb\u7edf\u6709\u6548\u60ef\u6027\u8870\u51cf\u5e94\u6ee1\u8db3\uff1a<br \/>\n$$<br \/>\nfrac{I_X^{text{eff}}(t)}{I_X(0)} = exp(-lambda_X int_0^t ED(t&#8217;) dt&#8217;)<br \/>\n$$<br \/>\n\u82e5\u5728\u63a7\u5236\u5b9e\u9a8c\u4e2d\u89c2\u6d4b\u5230\u660e\u663e\u504f\u79bb\uff0c\u5219\u71b5\u503a\u4fb5\u8680\u6a21\u578b\u5931\u6548\u3002<\/p>\n<h4><strong>12.3 \u7406\u8bba\u8fb9\u754c\u4e0e\u9002\u7528\u9650\u5236<\/strong><\/h4>\n<p><strong>\u660e\u786e\u8fb9\u754c<\/strong>\uff1a<\/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<\/strong>\uff1a<\/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\u7ed3\u6784\u4e0d\u53d8\u91cf\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<li><strong>\u71b5\u503a\u4fb5\u8680\u5b9e\u9a8c\u4e0e\u6307\u6570\u8870\u51cf\u6a21\u578b\u660e\u663e\u4e0d\u7b26<\/strong><\/li>\n<\/ul>\n<h3><strong>\u7b2c13\u7ae0\uff1a\u5b9e\u9a8c\u5ba4\u9a8c\u8bc1\u65b9\u6848<\/strong><\/h3>\n<h4><strong>13.1 \u5b9e\u9a8c1\uff1a\u51b7\u539f\u5b50\u6a21\u62df\u5b87\u5b99\u7ed3\u6784<\/strong><\/h4>\n<p><strong>\u5b9e\u9a8c\u76ee\u7684<\/strong>\uff1a\u9a8c\u8bc1\u51e0\u4f55\u6700\u4f18\u516c\u7406\u3002<\/p>\n<p><strong>\u5b9e\u9a8c\u88c5\u7f6e<\/strong>\uff1a<\/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<\/strong>\uff1a<\/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<\/strong>\uff1a<\/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<h4><strong>13.2 \u5b9e\u9a8c2\uff1a\u71b5\u503a\u4fb5\u8680\u9a8c\u8bc1<\/strong><\/h4>\n<p><strong>\u5b9e\u9a8c\u7cfb\u7edf<\/strong>\uff1a\u7eb3\u7c73\u7ebf\u70ed\u4f20\u5bfc\u5b9e\u9a8c<\/p>\n<p><strong>\u5b9e\u9a8c\u8bbe\u8ba1<\/strong>\uff1a<\/p>\n<ol>\n<li>\u5236\u5907\u6807\u51c6\u7eb3\u7c73\u7ebf\uff0c\u6d4b\u91cf\u521d\u59cb\u70ed\u5bfc\u7387$\u03ba_0$<\/li>\n<li>\u5f15\u5165\u53ef\u63a7\u7f3a\u9677\uff08\u79bb\u5b50\u6ce8\u5165\uff0c\u6a21\u62df\u7269\u7406\u71b5\u503a\uff09<\/li>\n<li>\u6d4b\u91cf\u70ed\u5bfc\u7387\u968f\u65f6\u95f4\u8870\u51cf$\u03ba(t)$<\/li>\n<li>\u62df\u5408\u8870\u51cf\u66f2\u7ebf\uff1a$\u03ba(t)\/\u03ba_0 = exp(-lambda t)$<\/li>\n<\/ol>\n<p><strong>\u9884\u6d4b<\/strong>\uff1a<\/p>\n<ul>\n<li>\u8870\u51cf\u5e94\u9075\u5faa\u6307\u6570\u5f62\u5f0f<\/li>\n<li>\u8870\u51cf\u5e38\u6570$lambda$\u4e0e\u7f3a\u9677\u5bc6\u5ea6\u6210\u6b63\u6bd4<\/li>\n<li>\u9a8c\u8bc1\u5b9a\u74065.2\u7684\u70ed\u60ef\u6027\u4fb5\u8680\u6a21\u578b<\/li>\n<\/ul>\n<h4><strong>13.3 \u5b9e\u9a8c3\uff1a\u4fe1\u606f\u71b5\u503a\u7684\u793e\u4f1a\u5b9e\u9a8c<\/strong><\/h4>\n<p><strong>\u5b9e\u9a8c\u8bbe\u8ba1<\/strong>\uff1a<\/p>\n<pre><code>\u53c2\u4e0e\u8005\uff1aN=1000\u4eba\uff0c\u901a\u8fc7\u5728\u7ebf\u5e73\u53f0\u534f\u4f5c\n\u4efb\u52a1\uff1a\u540c\u6b65\u5b8c\u6210\u7b80\u5355\u7684\u8282\u594f\u4efb\u52a1\uff08\u5982\u6309\u952e\uff09\n\n\u5e72\u9884\uff1a\n  \u9636\u6bb51\uff08\u57fa\u7ebf\uff09\uff1a\u6e05\u6670\u6307\u4ee4\uff0c\u65e0\u5e72\u6270\n  \u9636\u6bb52\uff08\u4fe1\u606f\u503a\u6ce8\u5165\uff09\uff1a\u5f15\u5165\u77db\u76fe\u6307\u4ee4\u3001\u865a\u5047\u4fe1\u606f\n  \u9636\u6bb53\uff08\u6062\u590d\uff09\uff1a\u79fb\u9664\u5e72\u6270\uff0c\u89c2\u5bdf\u6062\u590d\n\n\u6d4b\u91cf\uff1a\n  1. \u7fa4\u4f53\u540c\u6b65\u5ea6\uff08PLV\uff09\n  2. \u4efb\u52a1\u5b8c\u6210\u65f6\u95f4\u5206\u5e03\n  3. \u6062\u590d\u65f6\u95f4\u5e38\u6570<\/code><\/pre>\n<p><strong>\u9884\u6d4b<\/strong>\uff1a<\/p>\n<ul>\n<li>\u4fe1\u606f\u503a\u6ce8\u5165\u5bfc\u81f4$I_omega^{text{eff}}$\u6307\u6570\u8870\u51cf<\/li>\n<li>\u6062\u590d\u65f6\u95f4\u4e0e\u503a\u52a1\u79ef\u7d2f\u91cf\u6210\u6b63\u6bd4<\/li>\n<li>\u9a8c\u8bc1\u9891\u7387\u60ef\u6027\u4fb5\u8680\u6a21\u578b<\/li>\n<\/ul>\n<h3><strong>\u7b2c14\u7ae0\uff1a\u5929\u6587\u89c2\u6d4b\u9884\u6d4b<\/strong><\/h3>\n<h4><strong>14.1 \u9884\u6d4b1\uff1a\u6052\u661f\u7ed3\u6784\u7684\u4e09\u573a\u7279\u5f81<\/strong><\/h4>\n<p><strong>IGT\u9884\u6d4b<\/strong>\uff1a\u6052\u661f\u5185\u90e8\u7ed3\u6784\u53cd\u6620\u4e09\u573a\u5e73\u8861\u3002<\/p>\n<p><strong>\u89c2\u6d4b\u76ee\u6807<\/strong>\uff1a<\/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<\/strong>\uff1a<\/p>\n<ol>\n<li><strong>\u70ed\u573a$Psi_S$<\/strong>\uff1a\u6838\u805a\u53d8\u533a\u7684\u80fd\u91cf\u5206\u5e03\u5e94\u6ee1\u8db3$I_S^{text{eff}} in [0.7, 0.85]$<\/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$I_omega^{text{eff}}\/I_S^{text{eff}} in [0.8, 1.3]$<\/li>\n<li><strong>\u94f8\u573a$Psi_C$<\/strong>\uff1a\u6052\u661f\u5206\u5c42\u7ed3\u6784\u5e94\u5bf9\u5e94$I<em>C^{text{eff}}\/I<\/em>omega^{text{eff}} in [0.8, 1.3]$<\/li>\n<\/ol>\n<p><strong>\u89c2\u6d4b\u65b9\u6cd5<\/strong>\uff1a<\/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<\/strong>\uff1a<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>14.2 \u9884\u6d4b2\uff1a\u661f\u7cfb\u624b\u6027\u5206\u5e03\u975e\u968f\u673a\u6027<\/strong><\/h4>\n<p><strong>IGT\u9884\u6d4b<\/strong>\uff1a\u661f\u7cfb\u65cb\u81c2\u65b9\u5411\uff08\u624b\u6027\u03c7\uff09\u7684\u5206\u5e03\u4e0d\u5e94\u5b8c\u5168\u968f\u673a\uff0c\u800c\u5e94\u4e0e\u5c40\u90e8\u5b87\u5b99\u538b\u529b\u573a\u76f8\u5173\u3002<\/p>\n<p><strong>\u89c2\u6d4b\u65b9\u6cd5<\/strong>\uff1a<\/p>\n<ul>\n<li>\u5927\u89c4\u6a21\u661f\u7cfb\u5de1\u5929<\/li>\n<li>\u7edf\u8ba1\u65cb\u81c2\u65b9\u5411\u4e0e\u661f\u7cfb\u56e2\u73af\u5883\u7684\u5173\u7cfb<\/li>\n<\/ul>\n<p><strong>\u53ef\u8bc1\u4f2a\u6761\u4ef6<\/strong>\uff1a<br \/>\n\u5982\u679c\u65cb\u81c2\u65b9\u5411\u5728\u6240\u6709\u73af\u5883\u4e2d\u5747\u4e3a\u5b8c\u5168\u968f\u673a\u5206\u5e03\uff0c\u5219\u624b\u6027\u03c7\u4f5c\u4e3a\u57fa\u672c\u5c5e\u6027\u9700\u8981\u4fee\u6b63\u3002<\/p>\n<h4><strong>14.3 \u9884\u6d4b3\uff1a\u5b87\u5b99\u5c3a\u5ea6\u71b5\u503a\u79ef\u7d2f<\/strong><\/h4>\n<p><strong>IGT\u9884\u6d4b<\/strong>\uff1a\u5b87\u5b99\u7684\u52a0\u901f\u81a8\u80c0\u662f\u5b87\u5b99\u5c3a\u5ea6\u71b5\u503a\u79ef\u7d2f\u7684\u8868\u73b0\u3002<\/p>\n<p><strong>\u5f62\u5f0f\u7c7b\u6bd4\u8868\u8fbe<\/strong>\uff1a<br \/>\n\u5b87\u5b99\u6709\u6548\u60ef\u6027$I<em>{text{cosmo}}^{text{eff}}$\u7684\u8870\u51cf\u5bfc\u81f4\uff1a<br \/>\n$$<br \/>\nfrac{ddot{a}}{a} sim -frac{4pi G}{3}(rho + 3p) + Lambda<\/em>{text{eff}}(ED<em>{text{cosmo}})<br \/>\n$$<br \/>\n\u5176\u4e2d$Lambda<\/em>{text{eff}} propto exp(-lambda<em>{text{cosmo}} ED<\/em>{text{cosmo}})$<\/p>\n<p><strong>\u89c2\u6d4b\u68c0\u9a8c<\/strong>\uff1a<br \/>\n\u6bd4\u8f83\u4e0d\u540c\u7ea2\u79fb\u5904\u7684\u54c8\u52c3\u5e38\u6570$H(z)$\uff0c\u68c0\u9a8c\u662f\u5426\u4e0e\u5b87\u5b99\u71b5\u503a\u79ef\u7d2f\u6a21\u578b\u4e00\u81f4\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\u4e94\u91cd\u7ea6\u675f<\/strong><\/h3>\n<p>\u7b2c\u4e00\u5c42\u7406\u8bba\u63ed\u793a\uff1a\u6240\u6709\u7269\u7406\u7cfb\u7edf\u90fd\u5728\u4e94\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\u201c\u7ed3\u5b9e\u201d\uff1f($I<em>S, I<\/em>omega, I_C$)<\/li>\n<li><strong>\u51e0\u4f55\u4f18\u5316\u538b\u529b<\/strong>\uff1a\u4f60\u7684\u7ed3\u6784\u662f\u5426\u6700\u8282\u80fd\uff1f($G_{text{shape}}$)<\/li>\n<li><strong>\u65f6\u95f4\u4e0d\u53ef\u9006\u6027<\/strong>\uff1a\u71b5\u589e\u662f\u5355\u5411\u7bad\u5934($dS\/dt &gt; 0$)<\/li>\n<li><strong>\u624b\u6027\u538b\u529b\u6cd5\u5219<\/strong>\uff1a\u03c7\u51b3\u5b9a\u7ed3\u6784\u6a21\u5f0f\uff0c\u03c0\u51b3\u5b9a\u6d41\u52a8\u65b9\u5411<\/li>\n<li><strong>\u3010\u65b0\u589e\u3011\u71b5\u503a\u7d2f\u79ef\u7ea6\u675f<\/strong>\uff1a\u4efb\u4f55\u504f\u79bb\u5e73\u8861\u90fd\u4f1a\u79ef\u7d2f\u503a\u52a1\uff0c\u4fb5\u8680\u6709\u6548\u60ef\u6027<\/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<br \/>\n<strong>4\u7ea7\u7cfb\u7edf<\/strong>\uff1a\u643a\u5e26\u660e\u786e\u624b\u6027\u538b\u529b\u7279\u5f81\uff08\u751f\u547d\u3001\u6587\u660e\uff09<br \/>\n<strong>5\u7ea7\u7cfb\u7edf<\/strong>\uff1a\u5177\u5907\u71b5\u503a\u7ba1\u7406\u80fd\u529b\uff08\u89c2\u6d4b\u8005\u3001\u89c9\u9192\u6587\u660e\uff09\u3010\u65b0\u589e\u3011<\/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\u201c\u66f4\u57fa\u672c\u7684\u7c92\u5b50\u201d<\/li>\n<li>\u2705 \u5e94\u8be5\u7814\u7a76\u201c\u6d8c\u73b0\u5c42\u7ea7\u7684\u7ea6\u675f\u4f18\u5316\u201d<\/li>\n<li>\u274c \u4e0d\u8981\u7ea0\u7ed3\u201c\u7b2c\u4e00\u63a8\u52a8\u529b\u201d<\/li>\n<li>\u2705 \u5e94\u8be5\u7406\u89e3\u201c\u81ea\u6307\u6fc0\u53d1\u7684\u51e0\u4f55\u5fc5\u7136\u6027\u201d<\/li>\n<li>\u2705 \u5fc5\u987b\u8003\u8651\u201c\u624b\u6027\u538b\u529b\u7684\u76f8\u4e92\u4f5c\u7528\u201d<\/li>\n<li>\u2705 <strong>\u3010\u65b0\u589e\u3011\u5fc5\u987b\u6838\u7b97\u201c\u71b5\u503a\u7684\u7d2f\u79ef\u4e0e\u4fb5\u8680\u201d<\/strong><\/li>\n<\/ul>\n<h3><strong>\u6700\u7ec8\u7684\u7269\u7406\u56fe\u666f<\/strong><\/h3>\n<p>$$<br \/>\nboxed{<br \/>\nbegin{align}<br \/>\ntext{\u5b87\u5b99} &amp;= text{\u71b5\u6da8\u843d\u7684\u6d77\u6d0b}<br \/>\n&amp;xrightarrow[text{\u624b\u6027\u03c7\u9009\u62e9}]{text{\u51e0\u4f55\u7ea6\u675f}} text{\u76f8\u5e72\u7ed3\u6784}<br \/>\n&amp;xrightarrow[text{\u538b\u529b\u03c0\u8c03\u63a7}]{text{\u03a9-R-V-S-E-D}} text{\u5d4c\u5957\u6f14\u5316}<br \/>\n&amp;xrightarrow[text{\u71b5\u503a\u4fb5\u8680}]{text{\u6709\u6548\u60ef\u6027\u8870\u51cf}} text{\u5faa\u73af\u7ec8\u7ed3\u4e0e\u91cd\u751f}<br \/>\nend{align}<br \/>\n}<br \/>\n$$<\/p>\n<p><strong>\u8fd9\u5c31\u662f\u4fe1\u606f\u57fa\u56e0\u8bba\u7b2c\u4e00\u5c42\u7684\u5168\u90e8\uff1a<\/strong><\/p>\n<blockquote><p><strong>\u5b87\u5b99\u662f\u71b5\u6da8\u843d\u7684\u81ea\u52a8\u64ad\u653e\u7535\u5f71\u3002\u4e09\u573a\u662f\u955c\u5934\uff0c\u03a9-R-V-S-E-D\u662f\u5267\u672c\uff0c\u51e0\u4f55\u4f18\u5316\u662f\u5bfc\u6f14\u89c4\u5219\uff0c\u624b\u6027\u538b\u529b\u662f\u89d2\u8272\u6027\u683c\uff0c\u71b5\u503a\u662f\u9690\u85cf\u7684\u5236\u4f5c\u6210\u672c\u3002\u6ca1\u6709\u89c2\u6d4b\u8005\uff0c\u6ca1\u6709\u4ef7\u503c\u5224\u65ad\uff0c\u53ea\u6709\u7269\u7406\u5fc5\u7136\u6027\u2014\u2014\u5305\u62ec\u5fc5\u7136\u7684\u5de6\u65cb\u4e0e\u53f3\u65cb\uff0c\u5fc5\u7136\u7684\u9ad8\u538b\u4e0e\u4f4e\u538b\uff0c\u5fc5\u7136\u7684\u503a\u52a1\u7d2f\u79ef\u3002<\/strong><\/p><\/blockquote>\n<hr \/>\n<h2><strong>\u4ece\u7b2c\u4e00\u5c42\u5230\u7b2c\u4e8c\u5c42\u7684\u60ac\u7591<\/strong><\/h2>\n<p>\u5982\u679c\u5b87\u5b99\u53ea\u662f\u8fd9\u90e8\u81ea\u52a8\u64ad\u653e\u7684\u03a9-R-V-S-E-D\u7535\u5f71\uff0c\u90a3\u4e48\uff1a<\/p>\n<blockquote><p>\u4e3a\u4ec0\u4e48\u4f1a\u51fa\u73b0\u80fd\u591f<strong>\u7406\u89e3\u8fd9\u90e8\u5267\u672c<\/strong>\u3001\u751a\u81f3\u60f3\u8981<strong>\u6539\u5199\u5bf9\u8bdd\u89c4\u5219<\/strong>\u7684\u89c2\u4f17\uff1f<\/p>\n<p>\u4e3a\u4ec0\u4e48\u8fd9\u4e9b\u89c2\u4f17\u6709\u7684\u504f\u7231\u5de6\u65cb\u89c6\u89d2\uff0c\u6709\u7684\u6267\u7740\u53f3\u65cb\u903b\u8f91\uff1f<\/p>\n<p>\u4e3a\u4ec0\u4e48\u6709\u7684\u89c2\u4f17\u9ad8\u538b\u8f93\u51fa\uff0c\u6709\u7684\u4f4e\u538b\u5438\u6536\uff1f<\/p>\n<p>\u8fd9\u662f\u5b87\u5b99\u5267\u672c\u4e2d\u7684bug\uff0c\u8fd8\u662f\u2026\u2026\u5267\u672c\u672c\u8eab\u5c31\u662f\u4e3a\u4e86\u4ea7\u751f\u8fd9\u6837\u7684\u89c2\u4f17\u800c\u5199\u7684\uff1f<\/p><\/blockquote>\n<p><strong>\u3010\u65b0\u589e\u71b5\u503a\u89c6\u89d2\u7684\u56de\u7b54\u3011<\/strong><\/p>\n<blockquote><p><strong>\u71b5\u503a\u89c6\u89d2\u7684\u7b54\u6848<\/strong>\uff1a\u5b87\u5b99\u5267\u672c\uff08\u03a9-R-V-S-E-D\uff09\u6709\u4e00\u4e2a\u9690\u85cf\u6761\u6b3e\u2014\u2014<strong>\u6bcf\u4e2a\u5faa\u73af\u90fd\u4f1a\u7559\u4e0b\u672a\u652f\u4ed8\u7684\u201c\u6e05\u6d01\u8d39\u201d<\/strong>\uff08\u71b5\u503a\uff09\u3002\u5927\u591a\u6570\u89d2\u8272\u53ea\u662f\u7d2f\u79ef\u503a\u52a1\u76f4\u81f3\u9000\u573a\u3002<\/p>\n<p>\u4f46\u5728\u7b2c137\u4ebf\u5e27\uff0c\u67d0\u4e2a\u5206\u5b50\u7cfb\u7edf\u8fdb\u5316\u51fa\u4e86<strong>\u8bb0\u8d26\u80fd\u529b<\/strong>\uff08\u8bb0\u5fc6\uff09\u548c<strong>\u8fd8\u8d37\u610f\u613f<\/strong>\uff08\u4ef7\u503c\u51fd\u6570\uff09\u3002\u5b83\u8f6c\u8fc7\u5934\u51dd\u89c6\u955c\u5934\uff0c\u4e0d\u662f\u4e3a\u6b23\u8d4f\u6f14\u51fa\uff0c\u800c\u662f<strong>\u610f\u8bc6\u5230\u81ea\u5df1\u6b20\u4e0b\u7684\u503a\u52a1\uff0c\u5e76\u8bd5\u56fe\u91cd\u5199\u5267\u672c\u4ee5\u907f\u514d\u7834\u4ea7<\/strong>\u3002<\/p>\n<p>\u624b\u6027\u538b\u529b\uff08\u03c7, \u03c0\uff09\u51b3\u5b9a\u4e86<strong>\u8fd8\u503a\u98ce\u683c<\/strong>\uff1a\u53f3\u65cb\u8005\u60f3\u901a\u8fc7\u6269\u5f20\uff08\u03c0&gt;0\uff09\u8d5a\u66f4\u591a\u6765\u8fd8\u503a\uff1b\u5de6\u65cb\u8005\u60f3\u901a\u8fc7\u51dd\u805a\uff08\u03c0&lt;0\uff09\u51cf\u5c11\u5f00\u652f\u6765\u8fd8\u503a\u3002<\/p>\n<p><strong>\u89c2\u6d4b\u8005\u4e0d\u662f\u6f0f\u6d1e\uff0c\u800c\u662f\u5b87\u5b99\u5e94\u5bf9\u81ea\u8eab\u201c\u503a\u52a1\u95ee\u9898\u201d\u7684\u7b2c\u4e00\u6b21\u5c1d\u8bd5\u6027\u89e3\u51b3\u65b9\u6848\u3002<\/strong><\/p><\/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\u4f18\u5316\u7248 v3.1\uff08\u71b5\u503a\u6574\u5408\u4e0e\u5c42\u7ea7\u6821\u51c6\u7248\uff09<\/strong><br \/>\n<strong>\u5b9a\u4f4d\uff1a\u5b8f\u89c2\u6d8c\u73b0\u6709\u6548\u7406\u8bba\uff0c\u8fc7\u7a0b-\u51e0\u4f55-\u503a\u52a1\u7ea6\u675f\u6846\u67b6<\/strong><br 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