{"id":46948,"date":"2023-12-04T21:45:24","date_gmt":"2023-12-04T13:45:24","guid":{"rendered":"https:\/\/swarma.org\/?p=46948"},"modified":"2023-12-04T21:45:24","modified_gmt":"2023-12-04T13:45:24","slug":"nature-physics%e8%af%84%e8%ae%ba%ef%bc%9a%e9%87%8d%e6%95%b4%e5%8c%96%e7%be%a450%e5%b9%b4%ef%bc%8c%e5%ba%94%e7%94%a8%e4%ba%8e%e9%9d%9e%e5%b9%b3%e8%a1%a1%e7%b3%bb%e7%bb%9f%e5%89%8d%e6%99%af%e5%b9%bf","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=46948","title":{"rendered":"Nature Physics\u8bc4\u8bba\uff1a\u91cd\u6574\u5316\u7fa450\u5e74\uff0c\u5e94\u7528\u4e8e\u975e\u5e73\u8861\u7cfb\u7edf\u524d\u666f\u5e7f\u9614"},"content":{"rendered":"
\n
\n
\n
\n

<\/p>\n<\/section>\n

\n
\n
\n
\n
\n
\n

<\/section>\n<\/section>\n
\n
\n

\u5bfc\u8bed<\/strong><\/p>\n<\/section>\n<\/section>\n

\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\u4ece\u539f\u5b50\u5230\u751f\u547d\u5230\u6d69\u701a\u5b87\u5b99\uff0c\u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u8bb8\u591a\u73b0\u8c61\u6d89\u53ca\u5230\u5e7f\u9614\u7684\u5c3a\u5ea6\u3002\u91cd\u6574\u5316\u7fa4\uff08renormalization group\uff09\u662f\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u8003\u5bdf\u7269\u7406\u7cfb\u7edf\u53d8\u5316\u7684\u6570\u5b66\u5de5\u5177\uff0c\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u7cfb\u7edf\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u7684\u884c\u4e3a\u3002\u4e3a\u4e86\u7eaa\u5ff5\u7269\u7406\u5b66\u5bb6 Kenneth Wilson \u63d0\u51fa\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u5927\u7ea650\u5e74\uff0c\u8fd1\u671f Nature Physics<\/em> \u63a8\u51fa\u8bc4\u8bba\u6587\u7ae0\u5408\u96c6\uff0c\u5728\u5176\u4e2d\u4e00\u7bc7\u6587\u7ae0\u4e2d\uff0c\u7f8e\u56fd IBM T. J. Watson \u7814\u7a76\u4e2d\u5fc3\u7814\u7a76\u5458\u6d82\u8c6b\u6d77\u4ecb\u7ecd\u4e86\u5229\u7528\u91cd\u6574\u5316\u65b9\u6cd5\u7814\u7a76\u975e\u5e73\u8861\u96c6\u7fa4\uff08flocking\uff09\u7684\u7814\u7a76\uff0c\u5e76\u8ba4\u4e3a\u5c06\u7c97\u7c92\u5316\u548c\u91cd\u6574\u5316\u7fa4\u7684\u57fa\u672c\u601d\u60f3\u5f15\u5165\u6d3b\u6027\u7cfb\u7edf\u548c\u751f\u547d\u7cfb\u7edf\u7684\u7814\u7a76\u4e2d\uff0c\u662f\u7269\u7406\u5b66\u548c\u751f\u7269\u5b66\u4e2d\u6700\u6709\u524d\u666f\u7684\u65b9\u5411\u4e4b\u4e00\u3002<\/span><\/strong><\/span><\/strong><\/section>\n
<\/span><\/strong><\/section>\n<\/section>\n
\n
<\/span><\/strong><\/section>\n
<\/span><\/strong><\/section>\n<\/section>\n
\n
<\/span><\/section>\n

<\/section>\n
\u7814\u7a76\u9886\u57df\uff1a\u7edf\u8ba1\u7269\u7406\uff0c\u975e\u5e73\u8861\u7cfb\u7edf\uff0c\u91cd\u6574\u5316\u7fa4\uff0c\u96c6\u7fa4\u884c\u4e3a\uff0c\u968f\u673a\u52a8\u529b\u5b66<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n<\/section>\n
\n
<\/span><\/strong><\/section>\n<\/section>\n
\n
<\/span><\/strong><\/strong><\/strong><\/span><\/strong><\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/strong><\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n
\n
<\/section>\n<\/section>\n
\n
<\/span><\/strong><\/section>\n
\u6d82\u8c6b\u6d77<\/span><\/span><\/span> <\/span>| \u4f5c\u8005<\/span><\/strong><\/span><\/strong><\/section>\n
\u9ec4\u6cfd\u8c6a<\/span><\/span> <\/span>| \u8bd1\u8005<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n
\u6881\u91d1<\/span><\/span> <\/span>| \u5ba1\u6821<\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/section>\n
<\/span><\/strong><\/span><\/strong><\/section>\n<\/section>\n

<\/section>\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n

<\/p>\n

\n
\n
\n
\u8bba\u6587\u9898\u76ee\uff1a<\/span><\/section>\n
The renormalization group for non-equilibrium systems<\/span><\/section>\n
\u8bba\u6587\u5730\u5740\uff1a<\/span><\/section>\n
https:\/\/www.nature.com\/articles\/s41567-023-02196-z<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n

<\/section>\n
Ken Wilson \u5728\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u65b9\u9762\u7684\u5de5\u4f5c\u6e90\u4e8e\u5bf9\u5e73\u8861\u7cfb\u7edf\u4e2d\u4e34\u754c\u73b0\u8c61\u7684\u7814\u7a76<\/span>\uff08\u6709\u5173Wilson\u5bf9\u8be5\u4e3b\u9898\u7684\u8bc4\u8bba\uff0c\u8bf7\u53c2\u89c1\u53c2\u8003\u6587\u732e[1]\uff09<\/span>\u3002\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u4ea7\u751f\u4e86\u5373\u523b\u548c\u6301\u4e45\u7684\u5f71\u54cd\u3002\u7136\u800c\uff0c\u57281982\u5e74\u5e95\u8bfa\u8d1d\u5c14\u5956\u9881\u5956\u5178\u793c\u7684\u6f14\u8bb2\u4e2d\uff0cKen Wilson \u6307\u51fa\uff1a\u201c\u5728\u6211\u770b\u6765\uff0c\u4f7f\u7528\u91cd\u6574\u5316\u7fa4\u548c\u5c55\u5f00\u5b8c\u6210\u7684\u5927\u91cf\u7814\u7a76\u53ea\u662f\u4e00\u4e2a\u5f00\u59cb\uff0c\u672a\u6765\u4e8c\u5341\u5e74<\/span>\uff08\u6216\u8005\u53ef\u80fd\u9700\u8981\u4e0b\u4e00\u4e2a\u4e16\u7eaa\uff09<\/span>\u4eba\u4eec\u5c06\u53d1\u73b0\u66f4\u5927\u8303\u56f4\u7684\u5e94\u7528\u7814\u7a76\u7684\u3002\u201d\u5728\u8fd9\u7bc7\u8bc4\u8bba\u4e2d\uff0c\u6211\u5c06\u63cf\u8ff0\u6211\u81ea\u5df1\u5728\u53d1\u5c55\u4e00\u79cd\u8fd9\u6837\u7684\u5e94\u7528\u65b9\u9762\u7684\u5b9e\u8df5\uff1a\u975e\u5e73\u8861\u968f\u673a\u52a8\u529b\u7cfb\u7edf<\/strong><\/span>\uff08non-equilibrium stochastic dynamical systems\uff09<\/span>\u7684\u7814\u7a76\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

1. \u91cd\u6574\u5316\u7fa4\u7528\u4e8e\u7814\u7a76\u96c6\u7fa4\u73b0\u8c61<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

Leo Kadanoff \u548c Ken Wilson \u5bf9\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u7684\u6700\u521d\u53d1\u5c55\u662f\u57fa\u4e8e\u5e73\u8861\u7cfb\u7edf\u7684\u3002\u5728\u8fd9\u4e9b\u60c5\u51b5\u4e0b\u53ef\u4ee5\u5199\u51fa\u63a7\u5236\u7cfb\u7edf\u7edf\u8ba1\u7279\u6027\u7684\u54c8\u5bc6\u987f\u91cf\u3002<\/span><\/section>\n

<\/section>\n
\u57fa\u672c\u601d\u60f3\u662f\u5728\u7c97\u7c92\u5316\u6c34\u5e73\u4e0a\u8003\u8651\u591a\u4f53\u7cfb\u7edf\uff0c\u5373\u5728\u4e00\u4e2a\u66f4\u5927\u7684\u957f\u5ea6\u5c3a\u5ea6\u4e0a\u5bf9\u5fae\u89c2\u81ea\u7531\u5ea6\u505a\u5e73\u5747\u3002Kadanoff\u63d0\u51fa [2]\uff0c\u7ecf\u8fc7\u9002\u5f53\u7684\u7f29\u653e\u540e\uff0c\u7c97\u7c92\u5316\u7cfb\u7edf\u53ef\u4ee5\u7528\u4e0e\u521d\u59cb\u6a21\u578b\u76f8\u540c\u5f62\u5f0f\u7684\u54c8\u5bc6\u987f\u91cf\u548c\u4e00\u7ec4\u91cd\u6574\u5316\u53c2\u6570\u63cf\u8ff0\u3002\u53c2\u6570\u4ece\u66f4\u7cbe\u7ec6\u7684\u5c3a\u5ea6\u5230\u66f4\u7c97\u7cd9\u7684\u5c3a\u5ea6\u7684\u53d8\u6362\u6784\u6210\u91cd\u6574\u5316\u7fa4<\/strong><\/span>\uff08renormalization group\uff09<\/span>\u3002<\/span><\/section>\n

<\/section>\n
\u53cd\u590d\u5e94\u7528\u8fd9\u79cd\u7c97\u7c92\u5316\u8fc7\u7a0b\u4f1a\u4ea7\u751f\u6240\u8c13\u7684\u53c2\u6570\u6d41\u3002\u8fd9\u4e2a\u6d41\u5177\u6709\u4e0d\u52a8\u70b9<\/span>\uff08fixed point\uff09<\/span>\u2014\u2014\u5728\u91cd\u6574\u5316\u4e0b\u4fdd\u6301\u4e0d\u53d8\u7684\u7279\u6b8a\u503c\u3002\u8fd9\u4e9b\u53c2\u6570\u5bf9\u5e94\u4e8e\u8be5\u7cfb\u7edf\u9075\u5faa\u7684\u666e\u9002\u6807\u5ea6\u5f8b\u7684\u4e34\u754c\u70b9\u3002\u5177\u6709\u76f8\u540c\u6807\u5ea6\u5f8b\u7684\u7cfb\u7edf\u88ab\u8ba4\u4e3a\u5c5e\u4e8e\u540c\u4e00\u4e2a\u666e\u9002\u7c7b<\/strong><\/span>\uff08universality class\uff09<\/span>\u3002<\/span><\/section>\n

<\/section>\n
<\/section>\n
\u56fe1. \u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u793a\u610f\u56fe<\/span><\/section>\n

<\/section>\n
\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u4e2d\u7684\u53e6\u4e00\u4e2a\u5173\u952e\u601d\u60f3\u662f\u4e0a\u4e34\u754c\u7ef4\u6570\u7684\u5b58\u5728\u3002\u8d85\u8fc7\u8fd9\u4e2a\u7ef4\u5ea6\uff0c\u4e0e\u5e73\u5747\u573a\u7406\u8bba\u76f8\u5bf9\u5e94\u7684\u4e0d\u52a8\u70b9\u662f\u7a33\u5b9a\u7684\uff0c\u8fd9\u610f\u5473\u7740\u5b83\u6b63\u786e\u5730\u6355\u6349\u5230\u4e86\u4e34\u754c\u884c\u4e3a\u3002\u5bf9\u4e8e\u8f83\u4f4e\u7684\u7ef4\u5ea6\uff0c\u53ef\u4ee5\u901a\u8fc7\u5fae\u6270\u6c42\u89e3\u9636\u7684\u91cd\u6574\u5316\u7fa4\u65b9\u7a0b\u6765\u5f97\u5230\u9636\u7684\u6807\u5ea6\u6307\u6570\uff0c\u4ece\u800c\u627e\u5230\u4e34\u754c\u884c\u4e3a\u7684\u8fd1\u4f3c\u503c [3]\u3002<\/span><\/section>\n

<\/section>\n
\u968f\u540e\u7684\u7814\u7a76\u5f88\u5feb\u5c06\u91cd\u6574\u5316\u7fa4\u7684\u5e94\u7528\u6269\u5c55\u5230\u4e86\u4e34\u754c\u73b0\u8c61\u7684\u52a8\u529b\u5b66\u7814\u7a76\u4e2d[4,5]<\/span>\uff08\u76f8\u5173\u7814\u7a76\u7684\u5168\u9762\u7efc\u8ff0\uff0c\u8bf7\u53c2\u89c1\u53c2\u8003\u6587\u732e[6]\uff09<\/span>\u3002\u867d\u7136\u91cd\u6574\u5316\u7fa4\u6700\u521d\u662f\u5728\u5e73\u8861\u7cfb\u7edf\u4e2d\u53d1\u5c55\u8d77\u6765\u7684\uff0c\u4f46\u5f88\u660e\u663e\uff0c\u52a8\u6001\u91cd\u6574\u5316\u7fa4\u53ef\u88ab\u7528\u4e8e\u7814\u7a76\u6ca1\u6709\u54c8\u5bc6\u987f\u91cf\u6216\u5176\u4ed6\u80fd\u91cf\u6cdb\u51fd\u7684\u975e\u5e73\u8861\u7cfb\u7edf\u7684\u968f\u673a\u52a8\u529b\u5b66<\/strong>\u3002\u8fd9\u662f\u91cd\u6574\u5316\u7fa4\u7684\u4e00\u4e2a\u975e\u5e38\u4ee4\u4eba\u5174\u594b\u7684\u7279\u70b9\uff0c\u56e0\u4e3a\u81ea\u7136\u754c\u4e2d\u7684\u5927\u591a\u6570\u7cfb\u7edf\u90fd\u53d7\u5916\u529b\u9a71\u52a8\u800c\u8fdc\u79bb\u5e73\u8861\u6001\uff0c\u4f46\u5b83\u4eec\u8868\u73b0\u51fa\u4e0e\u5728\u5e73\u8861\u4e34\u754c\u73b0\u8c61\u4e2d\u89c2\u5bdf\u5230\u7684\u7c7b\u4f3c\u7684\u9c81\u68d2\u7684\u6807\u5ea6\u884c\u4e3a\u3002<\/span><\/section>\n

<\/section>\n
\u4e00\u4e2a\u8fd9\u6837\u7684\u4f8b\u5b50\u662f\u7528\u4e8e\u63cf\u8ff0\u754c\u9762\u751f\u957f\u7684 Kardar-Parisi-Zhang<\/span> (KPZ) <\/span>\u65b9\u7a0b [7]\u3002\u5728KPZ\u65b9\u7a0b\u7684\u60c5\u51b5\u4e0b\uff0c\u91cd\u6574\u5316\u7fa4\u5df2\u88ab\u6210\u529f\u5730\u7528\u4e8e\u7406\u89e3\u5176\u6807\u5ea6\u884c\u4e3a [7-9]\u3002\u4ece\u4e2a\u4eba\u89d2\u5ea6\u6765\u8bf4\uff0c\u7814\u7a76KPZ\u65b9\u7a0b\u53ca\u5176\u53d8\u5316\u4f7f\u6211\u6709\u673a\u4f1a\u5b66\u4e60\u548c\u6b23\u8d4f\u91cd\u6574\u5316\u80cc\u540e\u7f8e\u5999\u7684\u76f4\u89c9\u548c\u5f3a\u5927\u7684\u6280\u672f[10,11]\u3002\u540e\u6765\uff0c\u6211\u4e0eJohn Toner\u5408\u4f5c\uff0c\u53d1\u5c55\u4e86\u4e00\u4e2a\u5173\u4e8e\u96c6\u7fa4\u7684\u6d41\u4f53\u52a8\u529b\u5b66\u7406\u8bba\uff0c\u5176\u4e2d\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u53d1\u6325\u4e86\u5173\u952e\u4f5c\u7528\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

2. \u91cd\u6574\u5316\u7fa4\u7528\u4e8e\u7814\u7a76\u96c6\u7fa4\u73b0\u8c61<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u6700\u5bb9\u6613\u8fa8\u522b\u7684\u96c6\u7fa4\u73b0\u8c61\u51fa\u73b0\u5728\u9e1f\u7fa4\u548c\u9c7c\u7fa4\u4e2d<\/span>\uff08\u56fe2a\uff0cb\uff09<\/span>\u3002\u4f46\u662f\uff0c\u8fd9\u79cd\u96c6\u4f53\u8fd0\u52a8\u4e5f\u53ef\u4ee5\u5728\u8f83\u5c0f\u7684\u957f\u5ea6\u5c3a\u5ea6\u4e0a\u51fa\u73b0\uff0c\u4f8b\u5982\u5728\u83cc\u7fa4<\/span>\uff08\u56fe2c\uff09<\/span>\u6216\u9a6c\u8fbe\u86cb\u767d\u548c\u5fae\u7ba1\u7684\u6df7\u5408\u7269\u4e2d\u3002<\/span><\/section>\n

<\/section>\n
<\/section>\n

\u56fe2. \u5927\u81ea\u7136\u4e2d\u7684\u96c6\u7fa4\u73b0\u8c61\u3002\u96c6\u7fa4\u884c\u4e3a\u8de8\u8d8a\u5de8\u5927\u7684\u957f\u5ea6\u8303\u56f4\uff0c\u4ece\uff08a\uff09\u9c7c\u7fa4\u548c\uff08b\uff09\u9e1f\u7fa4\u4e2d\u7684\u6570\u5341\u7c73\u5230\u6570\u767e\u7c73\uff0c\u518d\u5230\uff08c\uff09\u83cc\u7fa4\u4e2d\u7684\u5fae\u7c73\u7ea7\u522b\u3002<\/span><\/p>\n


<\/section>\n
\u5c3d\u7ba1\u96c6\u7fa4\u51fa\u73b0\u5728\u8bb8\u591a\u65e5\u5e38\u60c5\u5883\u4e2d\uff0c\u4f46\u76f4\u5230\u8fc7\u53bb29\u5e74\uff0c\u5b83\u7684\u8bb8\u591a\u666e\u904d\u7279\u5f81\u624d\u88ab\u53d1\u73b0\u548c\u7406\u89e3\u3002\u8fd9\u79cd\u7406\u89e3\u5728\u5f88\u5927\u7a0b\u5ea6\u4e0a\u6765\u81ea\u7edf\u8ba1\u7269\u7406\u7684\u601d\u60f3\uff0c\u8fd9\u4e9b\u601d\u60f3\u88ab\u5e94\u7528\u5728\u7531 Tamas Vicsek \u53ca\u5176\u5408\u4f5c\u8005\uff0cJohn Toner\u548c\u6211\uff0c\u8fdb\u884c\u7684\u4e00\u7cfb\u5217\u7814\u7a76\u4e2d\u3002<\/span><\/section>\n

<\/section>\n
John \u548c\u6211\u57281994\u5e74\u672b\u5f00\u59cb\u4e86\u96c6\u7fa4\u7406\u8bba\u7684\u7814\u7a76\uff0c\u90a3\u662f Tamas Vicsek \u8bbf\u95ee\u4f4d\u4e8e\u7ebd\u7ea6\u7ea6\u514b\u9547\u9ad8\u5730\u7684 IBM Watson \u5b9e\u9a8c\u5ba4\u671f\u95f4\u3002Vicsek \u4e3e\u529e\u4e86\u4e00\u4e2a\u5173\u4e8e\u6d3b\u6027\u81ea\u9a71\u52a8\u667a\u80fd\u4f53<\/span>\uff08active self-driven agents\uff09<\/span>\u96c6\u7fa4\u6a21\u578b<\/span>\uff08\u79f0\u4f5c boid [12]\uff09<\/span>\u7684\u7814\u8ba8\u4f1a\u3002\u6bcf\u4e00\u4e2a boid \u4ee5\u6052\u5b9a\u901f\u5ea6\u79fb\u52a8\uff0c\u5176\u79fb\u52a8\u65b9\u5411\u7531\u5176\u90bb\u5c45\u8fd0\u52a8\u65b9\u5411\u7684\u5e73\u5747\u503c\u52a0\u4e0a\u4e00\u4e9b\u566a\u58f0\u51b3\u5b9a\u3002\u5728\u4ed6\u4eec\u5bf9\u6a21\u578b\u7684\u4e8c\u7ef4\u6a21\u62df\u4e2d\uff0cVicsek \u53ca\u5176\u5408\u4f5c\u8005\u7814\u7a76\u4e86\u5f53\u964d\u4f4e\u566a\u58f0\u6c34\u5e73\u6216\u589e\u52a0\u7269\u4f53\u5bc6\u5ea6\u65f6\u4f1a\u53d1\u751f\u4ec0\u4e48\u3002\u4ed6\u4eec\u89c2\u5bdf\u5230\u4e86\u4ece\u65e0\u5e8f\u76f8\u5230\u6709\u5e8f\u76f8\u7684\u76f8\u53d8\uff0c\u5728\u65e0\u5e8f\u76f8\u4e2d\uff0c\u667a\u80fd\u4f53\u5728\u6ca1\u6709\u957f\u7a0b\u5e8f\u7684\u60c5\u51b5\u4e0b\u6cbf\u968f\u673a\u65b9\u5411\u79fb\u52a8\uff0c\u5728\u6709\u5e8f\u76f8\u4e2d\uff0c\u5b83\u4eec\u4e00\u81f4\u5730\u805a\u96c6\u6210\u4e00\u4e2a\u96c6\u7fa4\u3002<\/span><\/section>\n

<\/section>\n
\u5728\u62a5\u544a\u7684\u6700\u540e\uff0cVicsek \u62b1\u6028\u8bf4\uff0c\u4ed6\u65e0\u6cd5\u53d1\u8868\u4ed6\u7684\u7814\u7a76\u6210\u679c\uff0c\u56e0\u4e3a\u5ba1\u7a3f\u4eba\u575a\u6301\u8ba4\u4e3a\u5177\u6709\u957f\u7a0b\u5e8f\u7684\u96c6\u7fa4\u72b6\u6001\u5728\u4e8c\u7ef4\u60c5\u51b5\u4e0b\u662f\u4e0d\u53ef\u80fd\u7684\uff0c\u56e0\u4e3a\u5b83\u8fdd\u80cc\u4e86Mermin-Wagner\u5b9a\u7406[13]\u3002\u8be5\u5b9a\u7406\u6307\u51fa\uff0c\u5728\u4e8c\u7ef4\u6216\u66f4\u4f4e\u7ef4\u5ea6\u7684\u6a21\u578b\u4e2d\uff0c\u5177\u6709\u77ed\u7a0b\u76f8\u4e92\u4f5c\u7528\u7684\u6709\u9650\u6e29\u5ea6\u7cfb\u7edf\u7684\u8fde\u7eed\u5bf9\u79f0\u6027\u65e0\u6cd5\u88ab\u7834\u574f\u3002<\/span><\/section>\n

<\/section>\n
\u8fd9\u4e2a\u7ed3\u679c\u4f3c\u4e4e\u610f\u5473\u7740\u4efb\u4f55\u6709\u9650\u7684\u566a\u97f3\u90fd\u4f1a\u4ea7\u751f\u6da8\u843d\uff0c\u7834\u574f\u5177\u6709\u8fde\u7eed\u5bf9\u79f0\u6027\u548c\u77ed\u7a0b\u76f8\u4e92\u4f5c\u7528\u7684\u7cfb\u7edf\u7684\u957f\u7a0b\u5e8f\u3002Vicsek \u6a21\u578b\u5c31\u5c5e\u4e8e\u8fd9\u4e00\u7c7b\uff0c\u6709\u5e8f\u6001\u7684\u5355\u4e2a\u96c6\u7fa4\u65b9\u5411\u7834\u574f\u4e86\u6a21\u578b\u7684\u65cb\u8f6c\u5bf9\u79f0\u6027\u3002\u4ee5\u6b64\u770b\u6765\uff0c\u81f3\u5c11\u5728\u4e24\u7ef4\uff0c\u81ea\u53d1\u5f62\u6210\u7684\u96c6\u7fa4\u6ce8\u5b9a\u4f1a\u6d88\u5931\u3002<\/span><\/section>\n

<\/section>\n
\u5728Vicsek\u7684\u7814\u8ba8\u4f1a\u4e0a\uff0c\u4f5c\u4e3a\u542c\u4f17\u7684John\u548c\u6211\u90fd\u63d0\u51fa\u4e86\u5f88\u591a\u95ee\u9898\u3002Vicsek\u7684\u6a21\u62df\u7ed3\u679c\u4ee4\u6211\u4eec\u611f\u5230\u56f0\u60d1\uff0c\u6211\u4eec\u51b3\u5b9a\u7acb\u5373\u5171\u540c\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u2014\u2014\u4e5f\u8bb8\u7d27\u8feb\u6027\u6765\u81ea\u4e8e\u5e0c\u671b\u5c06 boid \u96c6\u7fa4\u4ece\u5728\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u770b\u4f3c\u4e0d\u53ef\u907f\u514d\u5730\u5206\u5f00\u7684\u547d\u8fd0\u4e2d\u62ef\u6551\u51fa\u6765\u3002\u5f53John\u548c\u6211\u5728\u7b2c\u4e8c\u5929\u91cd\u805a\u65f6\uff0c\u6211\u4eec\u5df2\u7ecf\u638c\u63e1\u4e86\u7c97\u7c92\u5316\u6d41\u4f53\u52a8\u529b\u5b66\u7406\u8bba\u7684\u57fa\u672c\u8981\u7d20\u3002\u5728\u63a5\u4e0b\u6765\u7684\u51e0\u4e2a\u6708\u91cc\uff0c\u6211\u4eec\u4e0eVicsek\u4fdd\u6301\u7740\u8054\u7cfb\uff0c\u5728\u96c6\u7fa4\u7406\u8bba\u4e0a\u53d6\u5f97\u66f4\u591a\u8fdb\u5c55\uff0cVicsek\u7684\u8bba\u6587\u6700\u7ec8\u57281995\u5e74\u53d1\u8868[14]\u3002\u5927\u5bb6\u4e0d\u7981\u731c\u6d4b\uff0c\u6211\u4eec\u7684\u5de5\u4f5c\u53ef\u80fd\u5bf9\u6b64\u6709\u4e00\u5b9a\u5e2e\u52a9\u3002<\/span><\/section>\n

<\/section>\n
John\u548c\u6211\u53d1\u5c55\u7684\u96c6\u7fa4\u6d41\u4f53\u52a8\u529b\u5b66\u7406\u8bba<\/strong>\u57fa\u4e8e boid \u7684\u901f\u5ea6\u573a\uff08v\uff09\u7684\u53cc\u91cd\u4f5c\u7528\u3002\u9996\u5148\uff0c\u6a21\u578b\u7684\u76f8\u4e92\u4f5c\u7528\u8bd5\u56fe\u8ba9 boid \u7684\u901f\u5ea6\u4e0e\u5176\u90bb\u5c45\u7684\u901f\u5ea6\u4fdd\u6301\u4e00\u81f4\uff0c\u8fd9\u53ef\u4ee5\u7528\u63cf\u8ff0\u78c1\u6027\u6750\u6599\u7684\u4e00\u4e2a\u88ab\u79f0\u4e3a\u77e2\u91cf \u03d54<\/sup><\/span> \u7406\u8bba\u7684\u6a21\u578b\u6765\u63cf\u8ff0\u3002\u5176\u6b21\uff0c\u901f\u5ea6\u77e2\u91cf\u8fd8\u8868\u5f81\u4e86 boid \u7684\u7269\u7406\u8fd0\u52a8\uff0c\u5b83\u65e2\u8f93\u8fd0 boid \u7684\u4e3b\u4f53\u53c8\u8f93\u8fd0 boid \u7684\u901f\u5ea6\u3002\u8fd9\u79cd\u8f93\u8fd0\u548c\u6d41\u52a8\u53ef\u4ee5\u901a\u8fc7Navier-Stokes\u65b9\u7a0b\u6765\u63cf\u8ff0\u3002<\/span><\/section>\n

<\/section>\n
\u7ed3\u5408\u8fd9\u4e24\u4e2a\u8981\u7d20\uff0c\u6211\u4eec\u5199\u4e0b\u4e86\u4e00\u4e2a\u52a8\u529b\u5b66\u573a\u65b9\u7a0b\uff0c\u5176\u4e2d\u65e2\u6709\u8f93\u8fd0\u7684\u5bf9\u6d41\u9879 ((v\u00b7\u2207)v) \uff0c\u4e5f\u6709\u6d77\u68ee\u5821\u81ea\u65cb\u7684\u6807\u51c6 \u03d54<\/sup><\/span> \u7c7b\u578b\u9879\u3002\u540e\u6765\uff0c\u6211\u4eec\u6269\u5c55\u4e86\u8be5\u65b9\u7a0b\uff0c\u4f7f\u5176\u5305\u542b\u6240\u6709\u53ef\u80fd\u7684\u76f8\u5173\u9879\uff0c\u8fd9\u4e9b\u9879\u4fdd\u6301\u4e86\u901f\u5ea6\u548c\u7a7a\u95f4\u7684\u65cb\u8f6c\u5bf9\u79f0\u6027\uff0c\u800c\u4e0d\u65bd\u52a0\u4f3d\u5229\u7565\u4e0d\u53d8\u6027\u3002\u4f3d\u5229\u7565\u4e0d\u53d8\u6027\u56e0\u4e3a boid \u7fa4\u79fb\u52a8\u7684\u4ecb\u8d28<\/span>\uff08\u7a7a\u6c14\u6216\u6c34\uff09<\/span>\u662f\u552f\u4e00\u7684\u53c2\u8003\u7cfb\u800c\u88ab\u7834\u574f\u3002\u8fd9\u4e2a\u63cf\u8ff0\u96c6\u7fa4\u6d41\u4f53\u52a8\u529b\u5b66\u7279\u6027\u7684\u65b9\u7a0b\u73b0\u5728\u88ab\u79f0\u4e3aToner-Tu\u65b9\u7a0b\u3002\u503c\u5f97\u5f3a\u8c03\u7684\u662f\uff0c\u7531\u4e8e\u901f\u5ea6\u573a\u7684\u53cc\u91cd\u4f5c\u7528\uff0c\u96c6\u7fa4\u7cfb\u7edf\u672c\u8d28\u4e0a\u662f\u8fdc\u79bb\u5e73\u8861\u6001\u7684\uff0c\u56e0\u4e3a\u6ca1\u6709\u80fd\u91cf\u6cdb\u51fd\u53ef\u4ee5\u65e2\u63cf\u8ff0 boid \u52a8\u529b\u5b66\u7684\u65b9\u5411\u4e00\u81f4\u6027\u53c8\u63cf\u8ff0\u5176\u7269\u7406\u8fd0\u52a8\u3002<\/span><\/section>\n

<\/section>\n
\u6211\u4eec\u7528\u91cd\u6574\u5316\u7fa4\u6280\u672f\u5bf9\u6d41\u4f53\u52a8\u529b\u5b66\u7406\u8bba\u7684\u5206\u6790\u5728Vicsek\u7684\u8bba\u6587[14]\u53d1\u8868\u7684\u51e0\u4e2a\u6708\u540e\u53d1\u8868[15]\u3002\u5728\u6240\u6709 boid \u90fd\u671d\u7740\u540c\u4e00\u4e2a\u65b9\u5411\u79fb\u52a8\u7684\u6709\u5e8f\u76f8\u4e2d\uff0c\u53ef\u4ee5\u901a\u8fc7\u8ba1\u7b97\u6709\u5e8f\u6001\u5468\u56f4\u7684\u6da8\u843d\u5e45\u5ea6\u6765\u8bc4\u4f30\u7cfb\u7edf\u7684\u7a33\u5b9a\u6027\u3002\u5bf9\u79f0\u6027\u7684\u7834\u7f3a\u610f\u5473\u7740\u5b58\u5728\u88ab\u79f0\u4e3aGoldstone\u6a21<\/span>\uff08Goldstone mode\uff09<\/span>\u7684\u957f\u6ce2\u957f\u3001\u4f4e\u80fd\u91cf\u7684\u81ea\u7531\u5ea6\uff0c\u8fd9\u4e9b\u81ea\u7531\u5ea6\u53ef\u4ee5\u88ab\u566a\u58f0\u6e90\u6fc0\u53d1\u3002<\/span><\/section>\n

<\/section>\n
\u7531\u4e8eGoldstone\u6a21\u7684\u5b58\u5728\uff0c\u6709\u5e8f\u6001\u5468\u56f4\u7684\u901f\u5ea6\u6da8\u843d\u7684\u65b9\u5dee\u5305\u542b\u4e00\u4e2a\u6807\u5ea6\u4e3a L2\u03c7<\/span><\/sup><\/span> \u7684\u9879\uff0c\u5176\u4e2dL\u662f\u7cfb\u7edf\u7684\u957f\u5ea6\u5c3a\u5ea6\u3002\u6211\u4eec\u53d1\u73b0\uff0c\u5728\u975e\u7ebf\u6027\u5bf9\u6d41\u9879\u4e0d\u5b58\u5728\u7684\u60c5\u51b5\u4e0b\uff0c\u03c7<\/span>=1-d\/2\uff0c\u5176\u4e2dd\u662f\u7cfb\u7edf\u7684\u7ef4\u6570\u3002\u5728\u4e09\u7ef4\u4ee5\u4e0b\uff0c\u6da8\u843d\u968f\u7740\u7cfb\u7edf\u5c3a\u5bf8\u7684\u589e\u52a0\u800c\u589e\u957f\uff0c\u6709\u5e8f\u6001\u4e0d\u7a33\u5b9a\uff0c\u7b26\u5408 Mermin-Wagner \u5b9a\u7406\u7684\u9884\u6d4b\u3002<\/span><\/section>\n

<\/section>\n
\u7136\u800c\uff0c\u96c6\u7fa4\u7cfb\u7edf\u4e2d boid \u7fa4\u7684\u8fd0\u52a8\u4f7f\u95ee\u9898\u4e0e\u53d7 Mermin-Wagner \u5b9a\u7406\u7ea6\u675f\u7684\u5e73\u8861\u6a21\u578b\u5b8c\u5168\u4e0d\u540c\u3002\u7279\u522b\u5730\uff0c\u6211\u4eec\u53d1\u73b0\u5bf9\u6d41\u9879\u5f71\u54cd\u4e86\u6a21\u578b\u7684\u91cd\u6574\u5316\u7fa4\u6d41\uff0c\u5e76\u4e14\u6307\u6570\u03c7<\/span>\u504f\u79bb\u4e86\u5176\u5728\u7ebf\u6027\u7406\u8bba\u4e2d\u7684\u503c\u3002\u4e8b\u5b9e\u4e0a\uff0c\u901a\u8fc7\u4f7f\u7528\u6a21\u578b\u7684\u67d0\u4e9b\u5e94\u8be5\u9002\u7528\u4e8ed = 2 \u7684\u4e0d\u53d8\u6027\u8d28\uff0c\u6211\u4eec\u80fd\u591f\u5f97\u5230\u4e00\u4e2a\u7cbe\u786e\u7684\u8868\u8fbe\u5f0f<\/span>\u3002<\/span><\/section>\n

<\/section>\n
\u6211\u4eec\u7684\u7ed3\u679c\u8868\u660e\uff0c\u5f53 d = 2 \u65f6\uff0c\u03c7 = \u22121\/5 < 0\uff0c\u957f\u7a0b\u6709\u5e8f\u6001\u5468\u56f4\u7684\u6da8\u843d\u5728\u70ed\u529b\u5b66\u6781\u9650\u4e0b\u4ecd\u7136\u662f\u6709\u9650\u7684\uff0c\u96c6\u4f53\u96c6\u7fa4\u884c\u4e3a\u5728\u4e8c\u7ef4\u4e2d\u662f\u7a33\u5b9a\u7684\u3002\u968f\u540e\uff0c\u6211\u4eec\u5e94\u7528\u96c6\u7fa4\u7684\u6d41\u4f53\u52a8\u529b\u5b66\u7406\u8bba\u7814\u7a76\u4e86\u5176\u4ed6\u91cd\u8981\u7684\u6d8c\u73b0\u73b0\u8c61\uff0c\u4f8b\u5982\u58f0\u6ce2[16]\u548c\u96c6\u7fa4\u7684\u5de8\u5927\u6570\u91cf\u6da8\u843d[17]\u3002\u6700\u8fd1\uff0c\u52a8\u529b\u5b66\u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u5df2\u88ab\u7528\u4e8e\u7814\u7a76\u5728\u6dec\u706b\u65e0\u5e8f<\/span>\uff08quenched disorder\uff09<\/span>[18]\u548c\u81ea\u7136\u96c6\u7fa4<\/span>\uff08natural swarms\uff09<\/span>\u4e2d\u7684\u96c6\u7fa4\u884c\u4e3a[19]\u3002\u96c6\u7fa4\u6a21\u578b\u5728\u7269\u7406\u5b66\u4ee5\u5916\u7684\u9886\u57df\u4e5f\u4ea7\u751f\u4e86\u5f71\u54cd\uff0c\u4ece\u673a\u5668\u4eba\u5b66[20]\u5230\u4ea4\u901a[21]\u7b49\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n

\n
\n
\n
\n
\n

<\/section>\n

<\/section>\n
\n
<\/svg><\/section>\n<\/section>\n<\/section>\n
\n

3. \u5f15\u5165\u975e\u5e73\u8861\u751f\u7269\u7cfb\u7edf<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n

\u9664\u96c6\u7fa4\u5916\uff0c\u57fa\u4e8e\u91cd\u6574\u5316\u7fa4\u7684\u65b9\u6cd5\u7684\u591a\u529f\u80fd\u6027\u548c\u5f3a\u5927\u6027\u5df2\u5728\u8bf8\u5982\u6d3b\u6027\u7269\u8d28\u548c\u751f\u547d\u7cfb\u7edf\u5728\u5185\u7684\u4e0d\u540c\u975e\u5e73\u8861\u7cfb\u7edf\u4e2d\u5f97\u5230\u4e86\u8bc1\u660e\u3002\u4f8b\u5982\uff0c\u5b83\u5df2\u7ecf\u88ab\u7528\u4e8e\u5f00\u53d1[22]\u4e00\u79cd\u7c97\u7c92\u5316\u65b9\u6cd5\uff0c\u6765\u7814\u7a76\u5927\u578b\u795e\u7ecf\u5143\u7f51\u7edc\u4e2d\u7684\u795e\u7ecf\u6d3b\u52a8\uff0c\u8be5\u65b9\u6cd5\u63ed\u793a\u4e86\u5927\u8111\u4e0d\u540c\u90e8\u4f4d\u795e\u7ecf\u5143\u653e\u7535\u6a21\u5f0f\u7684\u51c6\u666e\u9002\u6807\u5ea6\u884c\u4e3a[23]\u3002\u6211\u4eec\u6700\u8fd1\u7684\u5de5\u4f5c\u4e2d\u6784\u5efa\u4e86\u4e00\u79cd\u6001\u7a7a\u95f4\u65b9\u6cd5\uff0c\u6765\u7406\u89e3\u975e\u5e73\u8861\u53cd\u5e94\u7f51\u7edc\u4e2d\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u7684\u80fd\u91cf\u8017\u6563\u7387\u7684\u9006\u5e42\u5f8b\u6807\u5ea6[24,25]\u3002<\/span><\/section>\n

<\/section>\n
<\/section>\n
\u56fe3. \u91cd\u6574\u5316\u7fa4\u65b9\u6cd5\u7528\u4e8e\u795e\u7ecf\u79d1\u5b66\u7814\u7a76\u3002\uff5c\u6765\u6e90\uff1aTiberi et al.<\/span><\/section>\n

<\/section>\n
\u975e\u5e73\u8861\u751f\u7269\u7cfb\u7edf\u7ecf\u5e38\u8868\u73b0\u51fa\u4e0e\u5e73\u8861\u6001\u751f\u7269\u7cfb\u7edf\u622a\u7136\u4e0d\u540c\u7684\u610f\u60f3\u4e0d\u5230\u7684\u884c\u4e3a\u3002\u7136\u800c\uff0c\u4e0e\u5e73\u8861\u6001\u7edf\u8ba1\u7269\u7406\u6a21\u578b\u4e00\u6837\uff0c\u5b83\u4eec\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0a\u8868\u73b0\u51fa\u96c6\u4f53\u884c\u4e3a\u3002\u6211\u76f8\u4fe1\u5c06\u7c97\u7c92\u5316\u548c\u91cd\u6574\u5316\u7fa4\u7684\u57fa\u672c\u601d\u60f3\u5f15\u5165\u6d3b\u6027\u7cfb\u7edf\u548c\u751f\u547d\u7cfb\u7edf\u7684\u7814\u7a76\u4e2d\uff0c\u662f\u7269\u7406\u5b66\u548c\u751f\u7269\u5b66\u4e2d\u6700\u6709\u524d\u666f\u7684\u7814\u7a76\u65b9\u5411\u4e4b\u4e00<\/strong>\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n
\n
\n
\n

\u6838\u5fc3\u6982\u5ff5<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n


<\/span><\/section>\n
\u91cd\u6574\u5316\u7fa4<\/strong><\/span><\/section>\n

<\/strong><\/span><\/section>\n
\u5728\u7406\u8bba\u7269\u7406\u4e2d\uff0c\u91cd\u6574\u5316\u7fa4<\/span>\uff08renormalization group\uff0c\u7b80\u79f0RG\uff09<\/span>\u662f\u4e00\u4e2a\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u8003\u5bdf\u7269\u7406\u7cfb\u7edf\u53d8\u5316\u7684\u6570\u5b66\u5de5\u5177\u3002\u6807\u5ea6\u4e0a\u7684\u53d8\u5316\u79f0\u4e3a\u201c\u6807\u5ea6\u53d8\u6362\u201d\u3002\u91cd\u6574\u5316\u7fa4\u4e0e\u201c\u6807\u5ea6\u4e0d\u53d8\u6027\u201d\u548c\u201c\u5171\u5f62\u4e0d\u53d8\u6027\u201d\u5173\u7cfb\u7d27\u5bc6\uff0c\u90fd\u4e0e\u81ea\u76f8\u4f3c\u6709\u5173\u3002\u5728\u91cd\u6574\u5316\u7406\u8bba\u4e2d\uff0c\u7cfb\u7edf\u5728\u67d0\u4e00\u4e2a\u6807\u5ea6\u4e0a\u81ea\u76f8\u4f3c\u4e8e\u4e00\u4e2a\u66f4\u5c0f\u7684\u6807\u5ea6\uff0c\u4f46\u63cf\u8ff0\u5b83\u4eec\u7ec4\u6210\u7684\u53c2\u91cf\u503c\u4e0d\u76f8\u540c\u3002\u7cfb\u7edf\u7684\u7ec4\u6210\u53ef\u4ee5\u662f\u539f\u5b50\uff0c\u57fa\u672c\u7c92\u5b50\uff0c\u81ea\u65cb\u7b49\u3002\u7cfb\u7edf\u7684\u53d8\u91cf\u662f\u4ee5\u7cfb\u7edf\u7ec4\u6210\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u6765\u63cf\u8ff0\u3002<\/span><\/section>\n

<\/section>\n
\u70ed\u529b\u5b66\u5e73\u8861\u6001<\/strong><\/span><\/section>\n

<\/strong><\/span><\/section>\n
\u70ed\u529b\u5b66\u5e73\u8861\u6001\u6307\u4e00\u4e2a\u70ed\u529b\u5b66\u7cfb\u7edf\u5728\u6ca1\u6709\u5916\u754c\u5f71\u54cd\u7684\u6761\u4ef6\u4e0b\uff0c\u7cfb\u7edf\u5404\u90e8\u5206\u7684\u5b8f\u89c2\u5c5e\u6027<\/span>\uff08\u5982\u7269\u8d28\u7684\u91cf\u3001\u80fd\u91cf\u3001\u4f53\u79ef\u7b49\uff09<\/span>\u5728\u957f\u65f6\u95f4\u5185\u4e0d\u53d1\u751f\u4efb\u4f55\u53d8\u5316\u7684\u72b6\u6001\u3002<\/span><\/section>\n

<\/section>\n
\u4e34\u754c\u7ef4\u6570<\/strong><\/span><\/section>\n

<\/strong><\/span><\/section>\n
\u5728\u7269\u7406\u5b66\u4e2d\u76f8\u53d8\u7684\u91cd\u6574\u5316\u7fa4\u5206\u6790\u4e2d\uff0c\u4e34\u754c\u7ef4\u6570\u662f\u76f8\u53d8\u7279\u5f81\u53d1\u751f\u53d8\u5316\u7684\u7a7a\u95f4\u7ef4\u5ea6\u3002\u5728\u4e34\u754c\u7ef4\u6570\u4ee5\u4e0b\u6ca1\u6709\u76f8\u53d8\u3002\u5728\u4e34\u754c\u7ef4\u6570\u4ee5\u4e0a\uff0c\u8be5\u7406\u8bba\u7684\u4e34\u754c\u6307\u6570\u4e0e\u5e73\u5747\u573a\u8bba\u4e2d\u7684\u4e34\u754c\u6307\u6570\u76f8\u540c\u3002V.Ginzburg\u63d0\u51fa\u4e86\u4e00\u4e2a\u5728\u5e73\u5747\u573a\u8bba\u4e2d\u83b7\u5f97\u4e34\u754c\u7ef4\u6570\u7684\u4f18\u7f8e\u51c6\u5219\u3002<\/span><\/section>\n

<\/section>\n
Kardar-Parisi-Zhang\u65b9\u7a0b<\/strong><\/span><\/section>\n

<\/strong><\/span><\/section>\n
\u5728\u6570\u5b66\u4e2d\uff0cKardar\u2013Parisi\u2013Zhang<\/span>\uff08KPZ\uff09<\/span>\u65b9\u7a0b\u662f\u4e00\u4e2a\u975e\u7ebf\u6027\u968f\u673a\u504f\u5fae\u5206\u65b9\u7a0b\uff0c\u7531Mehran Kardar\u3001Giorgio Parisi\u548cYi-Cheng Zhang\u4e8e1986\u5e74\u63d0\u51fa\u3002\u5b83\u63cf\u8ff0\u4e86\u4f5c\u4e3a\u7a7a\u95f4\u548c\u65f6\u95f4\u5750\u6807\u7684\u51fd\u6570\u7684\u9ad8\u5ea6\u573a<\/sub>\u968f\u65f6\u95f4\u7684\u53d8\u5316\u3002<\/span><\/section>\n

<\/span><\/section>\n
<\/section>\n

<\/section>\n
\u5176\u4e2d\uff0c<\/sub>\u662f\u767d\u9ad8\u65af\u566a\u58f0\u3002<\/span><\/section>\n

<\/section>\n
\u901a\u8fc7\u91cd\u6574\u5316\u7fa4\uff0cKPZ\u65b9\u7a0b\u88ab\u63a8\u6d4b\u4e3a\u8bb8\u591a\u8868\u9762\u751f\u957f\u6a21\u578b\u7684\u573a\u8bba\uff0c\u5982Eden\u6a21\u578b\u3001\u5f39\u9053\u6c89\u79ef<\/span>\uff08ballistic deposition\uff09<\/span>\u548c\u5f31\u4e0d\u5bf9\u79f0\u5355\u6b65\u56fa\u4f53\u5bf9\u56fa\u4f53\u8fc7\u7a0b<\/span>\uff08SOS\uff09<\/span>\u6a21\u578b<\/span>\uff08weakly asymmetric single step solid on solid process model\uff09<\/span>\u3002Bertini\u548cGiacomin\u5728SOS\u6a21\u578b\u7684\u60c5\u51b5\u4e0b\u7ed9\u51fa\u4e86\u8fd9\u4e00\u63a8\u6d4b\u7684\u4e00\u4e2a\u4e25\u683c\u8bc1\u660e\u3002<\/span><\/section>\n

<\/section>\n
Mermin-Wagner\u5b9a\u7406<\/strong><\/span><\/section>\n

<\/strong><\/span><\/section>\n
\u5728\u91cf\u5b50\u573a\u8bba\u548c\u7edf\u8ba1\u529b\u5b66\u4e2d\uff0cMermin\u2013Wagner\u5b9a\u7406<\/span>\uff08\u4e5f\u79f0\u4e3aMermin\u2013Wagner\u2013Hohenberg\u5b9a\u7406\u3001Mermin\u2013Wagner\u2013Berezinskii\u5b9a\u7406\u6216Coleman\u5b9a\u7406\uff09<\/span>\u6307\u51fa\uff0c\u5728d\u22642<\/span>\u7ef4\u5ea6\u5177\u6709\u8db3\u591f\u77ed\u7a0b\u76f8\u4e92\u4f5c\u7528\u7684\u7cfb\u7edf\u4e2d\uff0c\u8fde\u7eed\u5bf9\u79f0\u6027\u5728\u6709\u9650\u6e29\u5ea6\u4e0b\u4e0d\u80fd\u81ea\u53d1\u7834\u7f3a\u3002\u76f4\u89c2\u5730\u8bf4\uff0c\u8fd9\u610f\u5473\u7740\u53ef\u4ee5\u5728\u51e0\u4e4e\u6ca1\u6709\u80fd\u91cf\u6d88\u8017\u7684\u60c5\u51b5\u4e0b\u4ea7\u751f\u957f\u7a0b\u6da8\u843d\uff0c\u800c\u4e14\u7531\u4e8e\u5b83\u4eec\u589e\u52a0\u4e86\u71b5\uff0c\u7cfb\u7edf\u503e\u5411\u4e8e\u4ea7\u751f\u3002\u8fd9\u662f\u56e0\u4e3a\uff0c\u5982\u679c\u53d1\u751f\u8fd9\u79cd\u81ea\u53d1\u7684\u5bf9\u79f0\u6027\u7834\u7f3a\uff0c\u90a3\u4e48\u76f8\u5e94\u7684\u65e0\u8d28\u91cfGoldstone\u73bb\u8272\u5b50\u5c06\u5177\u6709\u7ea2\u5916\u53d1\u6563\u7684\u5173\u8054\u51fd\u6570\u3002<\/span><\/section>\n

<\/span><\/section>\n
David Mermin\u3001Herbert Wagner<\/span>\uff081966\uff09<\/span>\u548cPierre Hohenberg<\/span>\uff081967\uff09<\/span>\u5728\u7edf\u8ba1\u529b\u5b66\u4e2d\u4ee5\u53caSidney Coleman<\/span>\uff081973\uff09<\/span>\u5728\u91cf\u5b50\u573a\u8bba\u4e2d\u4e25\u683c\u8bc1\u660e\u4e86d\u22642\u7ef4\u65e0\u9650\u7cfb\u7edf\u4e2d\u4e0d\u5b58\u5728\u81ea\u53d1\u5bf9\u79f0\u6027\u7834\u7f3a\u3002\u8be5\u5b9a\u7406\u4e0d\u9002\u7528\u4e8e\u79bb\u6563\u5bf9\u79f0\u6027\uff0c\u8fd9\u53ef\u4ee5\u5728\u4e8c\u7ef4\u4f0a\u8f9b\u6a21\u578b\u4e2d\u770b\u51fa\u3002<\/span><\/section>\n

<\/section>\n
Vicsek\u6a21\u578b<\/strong><\/span><\/section>\n

<\/strong><\/span><\/section>\n
Vicsek\u6a21\u578b\u662f\u4e00\u79cd\u7528\u4e8e\u63cf\u8ff0\u6d3b\u6027\u7269\u8d28\u7684\u6570\u5b66\u6a21\u578b\u3002\u7269\u7406\u5b66\u5bb6\u7814\u7a76\u6d3b\u6027\u7269\u8d28\u7684\u4e00\u4e2a\u52a8\u673a\u662f\u4e0e\u8be5\u9886\u57df\u76f8\u5173\u7684\u4e30\u5bcc\u73b0\u8c61\u5b66\u3002\u96c6\u4f53\u8fd0\u52a8\u548c\u96c6\u7fa4\u662f\u7814\u7a76\u6700\u591a\u7684\u73b0\u8c61\u4e4b\u4e00\u3002\u5728\u4e3a\u4ece\u5fae\u89c2\u63cf\u8ff0\u4e2d\u6355\u6349\u8fd9\u79cd\u884c\u4e3a\u800c\u5f00\u53d1\u7684\u5927\u91cf\u6a21\u578b\u4e2d\uff0c\u6700\u8457\u540d\u7684\u662fTam\u00e1s-Vicsek\u7b49\u4eba1995\u5e74\u5f15\u5165\u7684\u6a21\u578b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u7269\u7406\u5b66\u5bb6\u5bf9\u8fd9\u4e2a\u6a21\u578b\u975e\u5e38\u611f\u5174\u8da3\uff0c\u56e0\u4e3a\u5b83\u662f\u6700\u5c0f\u7684\u5e76\u4e14\u63cf\u8ff0\u4e86\u4e00\u79cd\u666e\u9002\u6027\u3002\u5b83\u7531\u70b9\u72b6\u81ea\u63a8\u8fdb\u7c92\u5b50\u7ec4\u6210\uff0c\u8fd9\u4e9b\u7c92\u5b50\u4ee5\u6052\u5b9a\u7684\u901f\u5ea6\u6f14\u5316\uff0c\u5e76\u5728\u5b58\u5728\u566a\u97f3\u7684\u60c5\u51b5\u4e0b\u4f7f\u5176\u901f\u5ea6\u4e0e\u90bb\u5c45\u7684\u901f\u5ea6\u4e00\u81f4\u3002\u8fd9\u6837\u7684\u6a21\u578b\u663e\u793a\u4e86\u5bf9\u9f50\u540e\u7684\u9ad8\u5bc6\u5ea6\u7c92\u5b50\u6216\u4f4e\u566a\u58f0\u4e0b\u7684\u96c6\u4f53\u8fd0\u52a8\u3002<\/span><\/section>\n

<\/span><\/section>\n

<\/section>\n
\n
\n
\n

\u5b66\u8005\u7b80\u4ecb<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

<\/section>\n
\u6d82\u8c6b\u6d77<\/span><\/strong>\uff0c1987\u5e74\u6bd5\u4e1a\u4e8e\u4e2d\u56fd\u79d1\u5b66\u6280\u672f\u5927\u5b66\uff0c1991\u5e74\u5728\u52a0\u5dde\u5927\u5b66\u5723\u5730\u4e9a\u54e5\u5206\u6821\u83b7\u5f97\u7269\u7406\u5b66\u535a\u58eb\u5b66\u4f4d\u30021991\u5e74\u81f31994\u5e74\uff0c\u4ed6\u662f\u52a0\u5dde\u7406\u5de5\u5b66\u9662\u7684 Division Prize Fellow\uff0c1994\u5e74\u52a0\u5165IBM\u6c83\u68ee\u7814\u7a76\u4e2d\u5fc3\u62c5\u4efb\u7814\u7a76\u5458\uff0c\u5e76\u4e8e2003-2015\u5e74\u62c5\u4efb\u7406\u8bba\u7ec4\u7ec4\u957f\u3002\u4ed6\u81ea2004\u5e74\u8d77\u62c5\u4efb\u7f8e\u56fd\u7269\u7406\u5b66\u4f1a<\/span>\uff08APS\uff09<\/span>\u4f1a\u58eb\uff0c\u5e76\u4e8e2017\u5e74\u62c5\u4efb\u7f8e\u56fd\u7269\u7406\u5b66\u4f1a\u751f\u7269\u7269\u7406\u90e8\u4e3b\u5e2d\u3002\u4ed6\u4e5f\u662f\u7f8e\u56fd\u79d1\u5b66\u4fc3\u8fdb\u4f1a<\/span>\uff08AAAS\uff09<\/span>\u4f1a\u58eb\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4ed6\u7684\u7814\u7a76\u5174\u8da3\u5305\u62ec\u975e\u5e73\u8861\u7edf\u8ba1\u7269\u7406\u3001\u751f\u7269\u7269\u7406\u3001\u7406\u8bba\u795e\u7ecf\u79d1\u5b66\u4ee5\u53ca\u8fd1\u671f\u7684\u6df1\u5ea6\u5b66\u4e60\u7406\u8bba\u57fa\u7840\u3002\u5176\u4e2d\u5bf9\u751f\u7269\u7269\u7406\u5b66\u7684\u7814\u7a76\u5174\u8da3\u6709\u4e24\u4e2a\u65b9\u9762\uff1a\u901a\u8fc7\u4f7f\u7528\u7269\u7406\u5b66\u7684\u5de5\u5177<\/span>\uff08\u8ba1\u7b97\u5efa\u6a21\u3001\u7edf\u8ba1\u7269\u7406\u3001\u52a8\u529b\u7cfb\u7edf\u5206\u6790\uff09<\/span>\u6765\u7406\u89e3\u91cd\u8981\u7684\u751f\u7269\u73b0\u8c61<\/span>\uff08\u5982\u4fe1\u53f7\u8f6c\u5bfc\uff09<\/span>\uff1b\u4ece\u5bf9\u751f\u7269\u7cfb\u7edf\u7684\u7814\u7a76\u4e2d\u63ed\u793a\u4e00\u822c\u7684\u8bbe\u8ba1\u539f\u7406\u548c\u65b0\u7684\u7269\u7406\u5b66<\/span>\uff08\u5982\u975e\u5e73\u8861\u70ed\u529b\u5b66\u3001\u968f\u673a\u52a8\u529b\u5b66\uff09<\/span>\u3002\u5f53\u524d\u7684\u7814\u7a76\u5174\u8da3\u4e4b\u4e00\u662f\u7406\u89e3\u751f\u547d\u7cfb\u7edf\u4e2d\u4fe1\u606f\u5904\u7406\u7684\u52a8\u529b\u5b66\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u4ed6\u5728\u591a\u4e2a\u9886\u57df\u505a\u51fa\u4e86\u5f00\u521b\u6027\u8d21\u732e\uff0c\u5305\u62ec\u96c6\u7fa4\u7406\u8bba\u3001\u7ec6\u83cc\u8d8b\u836f\u6027<\/span>\uff08bacterial chemotaxis\uff09<\/span>\u7684\u5b9a\u91cf\u6a21\u578b\u3001\u663c\u591c\u8282\u5f8b\u65f6\u949f<\/span>\uff08circadium clock\uff09<\/span>\u4ee5\u53ca\u751f\u7269\u7cfb\u7edf\u4e2d\u7684\u80fd\u91cf-\u901f\u5ea6-\u7cbe\u5ea6\u5173\u7cfb\u3002\u7531\u4e8e\u5728\u7406\u8bba\u7edf\u8ba1\u7269\u7406\u65b9\u9762\u7684\u5de5\u4f5c\uff0c\u4ed6\u4e0eJohn Toner\u548cTamas Vicsek\u4e00\u8d77\u88ab\u7f8e\u56fd\u7269\u7406\u5b66\u4f1a\u6388\u4e882020\u5e74Lars Onsager\u5956\uff1a\u201c\u56e0\u4e3a\u4ed6\u5728\u96c6\u7fa4\u7406\u8bba\u65b9\u9762\u7684\u5f00\u521b\u6027\u5de5\u4f5c\uff0c\u8fd9\u6807\u5fd7\u7740\u6d3b\u6027\u7269\u8d28\u9886\u57df\u7684\u8bde\u751f\uff0c\u5e76\u5bf9\u5176\u53d1\u5c55\u505a\u51fa\u4e86\u5de8\u5927\u8d21\u732e\u3002\u201d<\/span><\/section>\n

<\/section>\n

\u5b66\u8005\u4e3b\u9875\uff1a<\/span><\/p>\n

https:\/\/researcher.draco.res.ibm.com\/researcher\/view.php?person=us-yuhai<\/span><\/p>\n


<\/span><\/section>\n

<\/span><\/section>\n
\n
\n
\n

\u53c2\u8003\u6587\u732e<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n

\n
\n
\n
\n

<\/span><\/p>\n

1. Wilson, K. G. Rev. Mod. Phys. 47, 773\u2013840 (1975).<\/span><\/section>\n
2. Kadanoff, L. P. Phys. Phys. Fiz. 2, 263\u2013272 (1966).<\/span><\/section>\n
3. Wilson, K. G. & Fisher, M. E. Phys. Rev. Lett. 28, 240\u2013243 (1972).<\/span><\/section>\n
4. Halperin, B. I., Hohenberg, P. C. & Ma, S.-k Phys. Rev. Lett. 29, 1548\u20131551 (1972).<\/span><\/section>\n
5. Bausch, R., Janssen, H. K. & Wagner, H. Z. Phys. B Condens. Matter 24, 113\u2013127 (1976).<\/span><\/section>\n
6. Hohenberg, P. C. & Halperin, B. I. Rev. Mod. Phys. 49, 435\u2013479 (1977).<\/span><\/section>\n
7. Kardar, M., Parisi, G. & Zhang, Y.-C. Phys. Rev. Lett. 56, 889\u2013892 (1986).<\/span><\/section>\n
8. Medina, E., Hwa, T., Kardar, M. & Zhang, Y.-C. Phys. Rev. A 39, 3053\u20133075 (1989).<\/span><\/section>\n
9. Canet, L., Chat\u00e9, H., Delamotte, B. & Wschebor, N. Phys. Rev. Lett. 104, 150601 (2010).<\/span><\/section>\n
10. Kessler, D. A., Levine, H. & Tu, Y. Phys. Rev. A 43, 4551\u20134554 (1991).<\/span><\/section>\n
11. Tu, Y. Phys. Rev. Lett. 73, 3109\u20133112 (1994).<\/span><\/section>\n
12. Reynolds, C. W. SIGGRAPH Comput. Graph. 21, 25\u201334 (1987).<\/span><\/section>\n
13. Mermin, N. D. & Wagner, H. Phys. Rev. Lett. 17, 1133\u20131136 (1966).<\/span><\/section>\n
14. Vicsek, T., Czir\u00f3k, A., Ben-Jacob, E., Cohen, I. & Shochet, O. Phys. Rev. Lett. 75, 1226\u20131229 (1995).<\/span><\/section>\n
15. Toner, J. & Tu, Y. Phys. Rev. Lett. 75, 4326\u20134329 (1995).<\/span><\/section>\n
16. Tu, Y., Toner, J. & Ulm, M. Phys. Rev. Lett. 80, 4819\u20134822 (1998).<\/span><\/section>\n
17. Toner, J. & Tu, Y. Phys. Rev. E 58, 4828\u20134858 (1998).<\/span><\/section>\n
18. Chen, L., Lee, C. F., Maitra, A. & Toner, J. Phys. Rev. Lett. 129, 188004 (2022).<\/span><\/section>\n
19. Cavagna, A. et al. Nat. Phys. 19, 1043\u20131049 (2023).<\/span><\/section>\n
20. Gazi, V. & Passino, K. IEEE T. Automat. Contr. 48, 692\u2013697 (2003).<\/span><\/section>\n
21. Helbing, D. Rev. Mod. Phys. 73, 1067\u20131141 (2001).<\/span><\/section>\n
22. Meshulam, L., Gauthier, J. L., Brody, C. D., Tank, D. W. & Bialek, W. Phys. Rev. Lett. 123, 178103 (2019).<\/span><\/section>\n
23. Morales, G. B., di Santo, S. & Mu\u00f1oz, M. A. Proc. Natl Acad. Sci. USA 120, e2208998120 (2023).<\/span><\/section>\n
24. Yu, Q., Zhang, D. & Tu, Y. Phys. Rev. Lett. 126, 080601 (2021).<\/span><\/section>\n
25. Yu, Q. & Tu, Y. Phys. Rev. E 105, 044140 (2022).<\/span><\/section>\n


<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\n
\n

\uff08\u53c2\u8003\u6587\u732e\u53ef\u4e0a\u4e0b\u6ed1\u52a8<\/strong>\u67e5\u770b\uff09<\/p>\n<\/section>\n<\/section>\n


<\/section>\n

<\/section>\n
\n
\n
\n
\n

\u751f\u547d\u590d\u6742\u6027\u7cfb\u5217\u8bfb\u4e66\u4f1a<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/p>\n

\u751f\u547d\u662f\u4ec0\u4e48\uff1f\u751f\u547d\u600e\u6837\u8d77\u6e90\uff1f\u751f\u547d\u600e\u6837\u6f14\u5316\uff1f\u8fd9\u4e9b\u662f\u5bf9\u751f\u547d\u73b0\u8c61\u7684\u672c\u8d28\u8ffd\u95ee\uff0c\u9664\u4e86\u4f20\u7edf\u7684\u751f\u7269\u5b66\u7814\u7a76\uff0c\u5982\u4eca\u6709\u5927\u91cf\u6765\u81ea\u4fe1\u606f\u3001\u7269\u7406\u3001\u8ba1\u7b97\u673a\u9886\u57df\u7684\u5de5\u5177\u65b9\u6cd5\uff0c\u6b63\u5728\u63ed\u5f00\u751f\u547d\u590d\u6742\u6027\u8c1c\u9898\u3002<\/span>\u57fa\u4e8e\u6b64\uff0c\u96c6\u667a\u4ff1\u4e50\u90e8\u7b56\u5212\u201c\u751f\u547d\u590d\u6742\u6027\u201d\u7cfb\u5217\u8bfb\u4e66\u4f1a\uff0c\u81ea2020\u5e7411\u67085\u65e5\u81f3\u4eca\uff0c\u8fd1\u767e\u540d\u5728\u4ece\u4e8b\u76f8\u5173\u95ee\u9898\u7814\u7a76\u7684\u8001\u5e08\u540c\u5b66\u6216\u611f\u5174\u8da3\u7684\u670b\u53cb\u53c2\u4e0e\u3002<\/span><\/span><\/p>\n


<\/p>\n

<\/span><\/span><\/a><\/section>\n


<\/p>\n

\u4e86\u89e3\u8bfb\u4e66\u4f1a\u5177\u4f53\u89c4\u5219\u3001\u62a5\u540d\u8bfb\u4e66\u4f1a\u8bf7\u70b9\u51fb\u4e0b\u65b9\u6587\u7ae0\uff1a<\/span><\/p>\n

\u751f\u547d\u590d\u6742\u6027\u7cfb\u5217\u8bfb\u4e66\u4f1a\uff1a\u4ece\u4fe1\u606f\u548c\u7269\u7406\u89c6\u89d2\u63a2\u7d22\u751f\u547d\u7684\u5185\u5728\u903b\u8f91<\/a><\/span><\/strong><\/span><\/p>\n


<\/span><\/section>\n

<\/section>\n
\n
\n
\n
\n

\u56e0\u679c\u6d8c\u73b0\u793e\u533a<\/strong>
<\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/section>\n
\u8de8\u5c3a\u5ea6\u3001\u8de8\u5c42\u6b21\u7684\u6d8c\u73b0\u662f\u590d\u6742\u7cfb\u7edf\u7814\u7a76\u7684\u5173\u952e\u95ee\u9898\uff0c\u751f\u547d\u8d77\u6e90\u548c\u610f\u8bc6\u8d77\u6e90\u8fd9\u4e24\u5ea7\u4ef0\u4e4b\u5f25\u9ad8\u7684\u5927\u5c71\u662f\u5176\u4ee3\u8868\u3002\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u3001\u673a\u5668\u5b66\u4e60\u91cd\u6574\u5316\u6280\u672f\u3001\u4fe1\u606f\u8bba\u6216\u4fe1\u606f\u5206\u89e3\u7b49\u8fd1\u5e74\u6765\u65b0\u5174\u7684\u7406\u8bba\u4e0e\u5de5\u5177\uff0c\u6709\u671b\u7834\u89e3\u590d\u6742\u7cfb\u7edf\u7684\u6d8c\u73b0\u89c4\u5f8b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u96c6\u667a\u4ff1\u4e50\u90e8\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u76ee\u524d\u5df2\u7ecf\u8fdb\u884c\u4e86\u4e09\u5b63\u3002\u7b2c\u4e00\u5b63\u8bfb\u4e66\u4f1a\u7cfb\u7edf\u5730\u68b3\u7406\u4e86\u56e0\u679c\u6d8c\u73b0\u7684\u6982\u5ff5\uff0c\u4ee5\u53ca\u5b83\u4e0eSloopy Model\u3001\u590d\u6742\u6027\u9608\u503c\u3001\u81ea\u6307\u7b49\u6982\u5ff5\u4e4b\u95f4\u7684\u8054\u7cfb\uff0c\u4e5f\u63a2\u8ba8\u4e86\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u5728\u590d\u6742\u7f51\u7edc\u3001\u673a\u5668\u5b66\u4e60\u4e2d\u7684\u5e94\u7528\u3002\u53c2\u770b\uff1a\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u542f\u52a8\uff1a\u8fde\u63a5\u56e0\u679c\u3001\u6d8c\u73b0\u4e0e\u81ea\u6307\u2014\u2014\u8de8\u5c3a\u5ea6\u52a8\u529b\u5b66\u4e0e\u56e0\u679c\u89c4\u5f8b\u7684\u63a2\u7d22<\/a>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u7b2c\u4e8c\u5b63\u8bfb\u4e66\u4f1a\u63a2\u8ba8\u4e86\u6d8c\u73b0\u3001\u56e0\u679c\u79d1\u5b66\u548c\u673a\u5668\u5b66\u4e60\u4e09\u5927\u4e3b\u9898\u7684\u878d\u5408\uff0c\u5305\u62ec\u4fe1\u606f\u8bba\u62d3\u5c55\u3001\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u3001\u56e0\u679c\u8868\u793a\u5b66\u4e60\u3001\u591a\u5c3a\u5ea6\u673a\u5668\u5b66\u4e60\u52a8\u529b\u5b66\u5efa\u6a21\u3002\u8bf7\u53c2\u770b\uff1a\u56e0\u679c\u3001\u6d8c\u73b0\u4e0e\u673a\u5668\u5b66\u4e60\uff1a\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u4e8c\u5b63\u542f\u52a8<\/a>\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u7b2c\u4e09\u5b63\u8bfb\u4e66\u4f1a\u8fdb\u4e00\u6b65\u56f4\u7ed5\u56e0\u679c\u6d8c\u73b0\u7684\u6838\u5fc3\u95ee\u9898\u300c\u56e0\u679c\u6d8c\u73b0\u7684\u5b9a\u4e49\u300d\u4ee5\u53ca\u300c\u56e0\u679c\u6d8c\u73b0\u7684\u8fa8\u8bc6\u300d\u8fdb\u884c\u6df1\u5165\u5b66\u4e60\u548c\u8ba8\u8bba\uff0c\u5bf9 Erik Hoel \u63d0\u51fa\u7684 Causal Emergence\uff0cCausal Geometry \u7b49\u56e0\u679c\u6d8c\u73b0\u7684\u6838\u5fc3\u7406\u8bba\u8fdb\u884c\u63a2\u8ba8\u548c\u5256\u6790\uff0c\u5e76\u8be6\u7ec6\u68b3\u7406\u5176\u4e2d\u6d89\u53ca\u5230\u7684\u65b9\u6cd5\u8bba\uff0c\u5305\u62ec\u4ece\u52a8\u529b\u5b66\u7ea6\u7b80\u3001\u9690\u7a7a\u95f4\u52a8\u529b\u5b66\u5b66\u4e60\u7b49\u5176\u4ed6\u9886\u57df\u4e2d\u5b66\u4e60\u548c\u501f\u9274\u76f8\u5173\u7684\u7814\u7a76\u601d\u8def\uff0c\u6700\u540e\u63a2\u8ba8\u56e0\u679c\u6d8c\u73b0\u7684\u5e94\u7528\uff0c\u5305\u62ec\u57fa\u4e8e\u751f\u7269\u7f51\u7edc\u3001\u8111\u7f51\u7edc\u6216\u8005\u6d8c\u73b0\u63a2\u6d4b\u7b49\u95ee\u9898\u5c55\u5f00\u6269\u5c55\uff0c\u53d1\u6398\u66f4\u591a\u7684\u5b9e\u9645\u5e94\u7528\u573a\u666f\u3002\u8bf7\u53c2\u770b\uff1a\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u4e09\u5b63\u542f\u52a8\uff1a\u6df1\u5165\u591a\u5c3a\u5ea6\u590d\u6742\u7cfb\u7edf\u6838\u5fc3\uff0c\u63a2\u7d22\u56e0\u679c\u6d8c\u73b0\u7406\u8bba\u5e94\u7528<\/a><\/span><\/section>\n

<\/strong><\/span><\/section>\n
\u6b64\u6b21\u8bfb\u4e66\u4f1a\u4e3b\u9898\u662f\u300c\u65b0\u4fe1\u606f\u8bba\uff1a\u4ece\u5206\u89e3\u5230\u6574\u5408\u300d\uff0c\u662f\u56e0\u679c\u6d8c\u73b0\u7cfb\u5217\u8bfb\u4e66\u4f1a\u7684\u7b2c\u56db\u5b63\uff0c\u5c06\u91cd\u70b9\u68b3\u7406\u4fe1\u606f\u5206\u89e3\u4e0e\u6574\u5408\u4fe1\u606f\u8bba\u7684\u76f8\u5173\u7814\u7a76\u3002\u8bf7\u53c2\u770b\uff1a\u65b0\u4fe1\u606f\u8bba\uff1a\u4ece\u5206\u89e3\u5230\u6574\u5408\uff5c\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u7b2c\u56db\u5b63\u542f\u52a8<\/a><\/strong><\/span><\/section>\n

<\/section>\n
\u56e0\u679c\u6d8c\u73b0\u793e\u533a\u805a\u96c6\u4e86600+\u6210\u5458\uff0c\u79ef\u7d2f\u4e86\u5927\u91cf\u8bba\u6587\u89e3\u8bfb\u8d44\u6599\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u62a5\u540d\uff0c\u52a0\u5165\u56e0\u679c\u6d8c\u73b0\u793e\u533a\uff0c\u89e3\u9501\u5bf9\u5e94\u5f55\u64ad\u6743\u9650\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u56e0\u679c\u6d8c\u73b0\u8bfb\u4e66\u4f1a\u56de\u653e\u89c6\u9891<\/strong><\/span><\/section>\n
\u7b2c\u4e00\u5b63\uff1ahttps:\/\/pattern.swarma.org\/study_group\/7<\/span><\/section>\n
\u7b2c\u4e8c\u5b63\uff1ahttps:\/\/pattern.swarma.org\/study_group\/16<\/span><\/section>\n
\u7b2c\u4e09\u5b63\uff1ahttps:\/\/pattern.swarma.org\/study_group\/28<\/span><\/section>\n
\u7b2c\u56db\u5b63\uff1ahttps:\/\/pattern.swarma.org\/study_group\/35<\/span><\/span><\/section>\n


<\/p>\n


<\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\n

\u63a8\u8350\u9605\u8bfb<\/span><\/strong><\/strong><\/p>\n

<\/strong><\/span><\/section>\n
1. <\/strong>Nature Physics\uff1a\u91cd\u6574\u5316\u7fa4\u2014\u2014\u7406\u89e3\u5f02\u6784\u7f51\u7edc\u7684\u663e\u5fae\u955c<\/a><\/strong><\/span><\/strong><\/section>\n
2.<\/strong> \u91cd\u6574\u5316\u7fa4\uff1a\u4ece\u5fae\u89c2\u5230\u5b8f\u89c2\uff0c\u4e0d\u540c\u5c3a\u5ea6\u7684\u73b0\u8c61\u5982\u4f55\u8054\u7cfb\u8d77\u6765\uff1f<\/a><\/strong><\/span><\/strong><\/section>\n
3.<\/strong> \u4eba\u8138\u548c\u5b87\u5b99\u662f\u5565\u5173\u7cfb\uff1f\u770b\u7269\u7406\u5b66\u5bb6\u600e\u6837\u7528\u91cd\u6574\u5316\u7fa4\u6d41\u6a21\u578b\u91cd\u65b0\u7406\u89e3\u89c6\u89c9<\/a><\/strong><\/strong><\/span><\/section>\n
4. <\/strong><\/strong><\/span>\u5f20\u6c5f\uff1a\u7b2c\u4e09\u4ee3\u4eba\u5de5\u667a\u80fd\u6280\u672f\u57fa\u7840\u2014\u2014\u4ece\u53ef\u5fae\u5206\u7f16\u7a0b\u5230\u56e0\u679c\u63a8\u7406 | \u96c6\u667a\u5b66\u56ed\u5168\u65b0\u8bfe\u7a0b<\/a><\/strong><\/strong><\/span><\/section>\n
5. \u6210\u4e3a\u96c6\u667aVIP\uff0c\u89e3\u9501\u5168\u7ad9\u8bfe\u7a0b\uff0f\u8bfb\u4e66\u4f1a<\/a><\/span><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


<\/p>\n


<\/p>\n<\/section>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfb\u4e66\u4f1a<\/span><\/strong><\/section>\n

<\/mp-style-type><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u4ece\u539f\u5b50\u5230\u751f\u547d\u5230\u6d69\u701a\u5b87\u5b99\uff0c\u7269\u7406\u7cfb\u7edf\u4e2d\u7684\u8bb8\u591a\u73b0\u8c61\u6d89\u53ca\u5230\u5e7f\u9614\u7684\u5c3a\u5ea6\u3002\u91cd\u6574\u5316\u7fa4\uff08renormalization group\uff09\u662f\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u8003\u5bdf\u7269\u7406\u7cfb\u7edf\u53d8\u5316\u7684\u6570\u5b66\u5de5\u5177\uff0c\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u7cfb\u7edf\u5728\u4e0d\u540c\u5c3a\u5ea6\u4e0b\u7684\u884c\u4e3a\u3002\u4e3a\u4e86\u7eaa\u5ff5\u7269\u7406\u5b66\u5bb6 Kenneth Wilson \u63d0\u51fa\u91cd\u6574\u5316\u7fa4\u7406\u8bba\u5927\u7ea650\u5e74\uff0c\u8fd1\u671f Nature Ph…<\/p>\n","protected":false},"author":0,"featured_media":46936,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/46948"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=46948"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/46948\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/46936"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=46948"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=46948"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=46948"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=46948"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}