

{"id":26418,"date":"2016-12-12T00:24:39","date_gmt":"2016-12-11T16:24:39","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=26418"},"modified":"2018-08-03T15:31:03","modified_gmt":"2018-08-03T07:31:03","slug":"%e7%89%a9%e7%90%86%e5%ad%b8%e4%b8%ad%e7%9a%84%e5%b0%8d%e5%81%b6%e6%80%a7%e4%b8%8b","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=26418","title":{"rendered":"\u7269\u7406\u5b78\u4e2d\u7684\u5c0d\u5076\u6027(\u4e0b)"},"content":{"rendered":"<figure id=\"attachment_26420\" aria-describedby=\"caption-attachment-26420\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-26420\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2016\/12\/figure1-soliton.jpg\" alt=\"figure 1: \u6c34\u6ce2\u4e2d\u7684\u5b64\u6ce2\uff08photo credit: Wikipedia\uff09\" width=\"600\" height=\"285\"><figcaption id=\"caption-attachment-26420\" class=\"wp-caption-text\">figure 1: \u6c34\u6ce2\u4e2d\u7684\u5b64\u6ce2\uff08photo credit: Wikipedia\uff09<\/figcaption><\/figure>\n<p><span style=\"color: #333399;\"><strong>\u25a0\u5c0d\u5076\u6027\u4e0d\u53ea\u5b58\u5728\u5728<a style=\"color: #333399;\" href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=25562\" target=\"_blank\">\u524d\u9762\u7684<\/a>\u7c21\u55ae\u4f8b\u5b50\u4e2d\uff0c\u5176\u5be6\u6211\u5011\u4e5f\u6709\u8cbb\u7c73\u5b50\u8207\u73bb\u8272\u5b50\u3001\u73bb\u8272\u5b50\u8207\u73bb\u8272\u5b50\u3001\u4e43\u81f3\u65bc\u8cbb\u7c73\u5b50\u8207\u8cbb\u7c73\u5b50\u9593\u7684\u5c0d\u5076\u6027\u3002<\/strong><\/span><\/p>\n<p><strong>\u64b0\u6587\uff5c<\/strong>\u856d\u7dad\u7ff0<\/p>\n<p>\u5728<a href=\"http:\/\/case.ntu.edu.tw\/blog\/?p=25562\" target=\"_blank\">\u4e0a\u96c6<\/a>\u7684\u8a0e\u8ad6\u4e2d\uff0c\u6211\u5011\u7d04\u7565\u4ecb\u7d39\u4e86\u300c\u5c0d\u5076\u300d\uff08duality\uff09\u5728\u7269\u7406\u5b78\u4e2d\uff0c\u7684\u610f\u601d\uff1a\u8868\u9762\u4e0a\u770b\u8d77\u4f86\u4e0d\u540c\u7684\u5169\u500b\u7406\u8ad6\uff0c\u672c\u8cea\u4e0a\u63d0\u4f9b\u4e00\u6a23\u7684\u63cf\u8ff0\u3002\u6700\u57fa\u672c\u7684\u4f8b\u5b50\u662f\u6240\u8b02\u4f0a\u8f9b\u6a21\u578b\uff08Ising model\uff09\u5728\u539f\u6676\u683c\u8207\u5c0d\u5076\u6676\u683c\u4e0a\u7684\u5c0d\u5076\uff0c\u4ee5\u53ca\u96fb\u78c1\u5b78\u99ac\u514b\u65af\u5a01\u65b9\u7a0b\u5f0f\uff08Maxwell equations\uff09\u5728\u6c92\u6709\u96fb\u8377\u4e0b\u96fb\u5834\u78c1\u5834\u4ea4\u63db\u7684\u5c0d\u5076\u6027\u3002<\/p>\n<p>\u5728\u672c\u6587\u6211\u5011\u60f3\u8981\u4ecb\u7d39\u66f4\u591a\u7684\u300c\u5c0d\u5076\u6027\u300d\uff0c\u5305\u62ec\u5728\u4e00\u7dad\u7a7a\u9593\u7684\u73bb\u8272\u5316\uff08bosonization\uff09\u4ee5\u53ca\u4e8c\u7dad\u7a7a\u9593\u7684\u7c92\u5b50\u2500\u2500\u6f29\u6e26\u5c0d\u5076\u6027\uff08particle-vortex duality\uff09\u3002\u7136\u800c\uff0c\u5728\u9032\u5165\u4e3b\u984c\u4e4b\u524d\uff0c\u6211\u5011\u5e0c\u671b\u4ecb\u7d39\u4e00\u9ede\u57fa\u672c\u7684\u6982\u5ff5\u3002\u73fe\u4ee3\u56fa\u614b\u7269\u7406\u5c0d\u65bc\u591a\u9ad4\u554f\u984c\u7684\u63cf\u8ff0\uff0c\u5e38\u5e38\u662f\u61c9\u7528\u6240\u8b02\u7684\u300c\u5834\u8ad6\u300d\u3002\u96d6\u7136\u807d\u8d77\u4f86\u5f88\u6df1\u5967\uff0c\u4f46\u7d04\u7565\u7684\u6982\u5ff5\u5c31\u662f\u4e0d\u76f4\u63a5\u63cf\u8ff0\u4e00\u500b\u4e00\u500b\u7684\u7c92\u5b50\uff0c\u5728\u5834\u8ad6\u4e2d\uff0c\u67d0\u7a2e\u7c92\u5b50\u7684\u300c\u5834\u300d\u5c31\u50cf\u4e00\u7a2e\u6d41\u9ad4\u4e00\u6a23\uff0c\u8b80\u8005\u53ef\u4ee5\u60f3\u50cf\u4e00\u500b\u6c34\u76c6\uff0c\u7576\u6211\u5011\u6572\u6253\u9019\u500b\u6c34\u76c6\u6642\uff0c\u6fc0\u767c\u7684\u6f23\u6f2a\u5c31\u7b49\u540c\u65bc\u300c\u7c92\u5b50\u300d\u3002<!--more--><\/p>\n<p>\u65e2\u7136\u662f\u6d41\u9ad4\uff0c\u90a3\u5c0d\u65bc\u5f88\u591a\u65e5\u5e38\u5728\u6c34\u6ce2\u4e2d\u770b\u5230\u7684\u73fe\u8c61\uff0c\u6211\u5011\u90fd\u53ef\u4ee5\u554f\u554f\uff0c\u5728\u67d0\u7a2e\u7269\u8cea\u7684\u300c\u5834\u300d\u4e2d\uff0c\u6709\u6c92\u6709\u985e\u4f3c\u7684\u7269\u7406\u5143\u7d20\uff1f\u6bd4\u5982\u8aaa\u5728\u975e\u7dda\u6027\u7684\u7684\u6d41\u9ad4\u529b\u5b78\u4e2d\uff0c\u6709\u4e00\u7a2e\u89e3\u53eb\u505a\u5b64\u7acb\u6ce2\uff08solitary wave\uff09\u6216\u8005\u53eb\u5b64\u7acb\u5b50\uff08soliton\uff09\uff0c\u4e3b\u8981\u7684\u7279\u5fb5\u662f\u9019\u7a2e\u6ce2\u5728\u904b\u52d5\u7684\u904e\u7a0b\u4e2d\uff0c\u5f62\u72c0\u4e0d\u6703\u6539\u8b8a\u3002\u53e6\u5916\u5728\u81ea\u7136\u754c\u7684\u6c34\u529b\u5b78\u4e2d\uff0c\u9084\u6709\u6f29\u6e26\uff08vortex\uff09\u7684\u7d44\u614b\u3002\u90a3\u5e95\u4e0b\u7684\u554f\u984c\u5c31\u986f\u5f97\u81ea\u7136\u4e86\uff1a\u5728\u63cf\u8ff0\u7269\u8cea\u7684\u5834\u8ad6\u4e2d\uff0c\u6709\u6c92\u6709\u9019\u7a2e\u89e3\uff1f\u6709\u7684\u8a71\uff0c\u90a3\u4ed6\u5011\u5177\u5099\u751a\u9ebc\u6027\u8cea\u5462\uff1f<\/p>\n<figure id=\"attachment_26421\" aria-describedby=\"caption-attachment-26421\" style=\"width: 450px\" class=\"wp-caption alignright\"><img decoding=\"async\" class=\"wp-image-26421\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2016\/12\/figure2-vortices.jpg\" alt=\"figure 2: \u5496\u5561\u4e2d\u725b\u5976\u5f62\u6210\u7684\u6f29\u6e26 \uff08photo credit: Wikipedia, By Astrobob - Own work, CC BY-SA 4.0\uff09\" width=\"450\" height=\"254\"><figcaption id=\"caption-attachment-26421\" class=\"wp-caption-text\">figure 2: \u5496\u5561\u4e2d\u725b\u5976\u5f62\u6210\u7684\u6f29\u6e26 \uff08photo credit: Wikipedia, By Astrobob - Own work, CC BY-SA 4.0\uff09<\/figcaption><\/figure>\n<p><strong>\u53c8\uff0c\u70ba\u4ec0\u9ebc\u8a0e\u8ad6\u5c0d\u5076\u6027\u9700\u8981\u95dc\u5fc3\u9019\u7a2e\u7279\u6b8a\u7684\u89e3\u5462\uff1f<\/strong><\/p>\n<p>\u9996\u5148\u6211\u5011\u4f86\u5617\u8a66\u56de\u7b54\u6700\u5f8c\u4e00\u500b\u554f\u984c\u3002\u7d04\u7565\u800c\u8a00\uff0c\u5728\u6211\u5011\u611f\u8208\u8da3\u7684\u5c0d\u5076\u6027\u4e2d\uff0c\u6709\u4e9b\u5c07\u8cbb\u7c73\u5b50\uff08fermion\uff09\u7406\u8ad6\u5c0d\u61c9\u5230\u4e86\u73bb\u8272\u5b50\uff08bosons\uff09\u7406\u8ad6\uff0c\u6709\u4e9b\u5c07\u7121\u4ea4\u4e92\u4f5c\u7528\u7684\u7406\u8ad6\uff0c\u5c0d\u61c9\u5230\u5f37\u95dc\u806f\u7684\u7406\u8ad6\u3002\u8b93\u6211\u5011\u4ed4\u7d30\u9ede\u770b\u7b2c\u4e00\u4ef6\u4e8b\uff0c\u5728\u7121\u4ea4\u4e92\u4f5c\u7528\u7684\u60c5\u6cc1\u4e0b\uff0c\u73bb\u8272\u5b50\u5011\u539f\u5247\u4e0a\u53ef\u4ee5\u5b8c\u5168\u4e0d\u77e5\u9053\u5f7c\u6b64\uff0c\u7136\u800c\u8cbb\u7c73\u5b50\u5c31\u4e0d\u662f\u9019\u9ebc\u4e00\u56de\u4e8b\uff0c\u56e0\u70ba\u5e96\u7acb\u4e0d\u76f8\u5bb9\u539f\u7406\u7684\u95dc\u4fc2\uff08Pauli exclusion principle\uff09\u5373\u4fbf\u662f\u8868\u9762\u4e0a\u6c92\u6709\u4ea4\u4e92\u4f5c\u7528\u7684\u8cbb\u7c73\u5b50\u5011\uff0c\u9084\u662f\u5f97\u611f\u53d7\u5230\u5f7c\u6b64\u7684\u5b58\u5728\u3002\u4e5f\u5c31\u662f\u8aaa\uff0c\u5982\u679c\u4e00\u500b\u73bb\u8272\u5b50\u7cfb\u7d71\u8ddf\u8cbb\u7c73\u5b50\u7cfb\u7d71\u662f\u7b49\u50f9\u7684\uff0c\u90a3\u9ebc\u7d44\u6210\u8cbb\u7c73\u5b50\u7684\uff0c\u4e0d\u53ef\u80fd\u662f\u7c21\u55ae\u7684\u73bb\u8272\u5b50\u7d44\u614b\uff0c\u4ed6\u5fc5\u9808\u662f\u5168\u57df\u6027\u7684\uff1a\u5728\u4e00\u500b\u7cfb\u7d71\u4e2d\uff0c\u53ea\u8981\u6709\u9019\u6a23\u4e00\u500b\u7d44\u614b\u5b58\u5728\uff0c\u4f60\u4e0d\u9700\u8981\u9760\u5b83\u9760\u5f97\u5f88\u8fd1\uff0c\u4e5f\u6709\u8fa6\u6cd5\u77e5\u9053\u5b83\u7684\u5b58\u5728\u3002\u800c\u5b64\u7acb\u5b50\u8207\u6f29\u6e26\uff0c\u90fd\u5177\u5099\u9019\u7a2e\u6027\u8cea\u3002<\/p>\n<p>1975 \u5e74\uff0cS. Coleman [1]\uff0c\u6307\u51fa\u4e86\u4e00\u500b\u73bb\u8272\u5b50\u7684\u7406\u8ad6 Sine-Gordon\u6a21\u578b\u8207\u53e6\u4e00\u500b\u8cbb\u7c73\u5b50\u7684\u7406\u8ad6Thirring \u6a21\u578b\u5728 1+1 \u7dad\u6642\u7a7a\u662f\u7b49\u50f9\u7684\uff0c\u96a8\u5f8cMandelstam[2] \u66f4\u4ed4\u7d30\u5730\u7814\u7a76\u4e86\u9019\u500b\u554f\u984c\uff0c\u7d04\u7565\u800c\u8a00\uff0c\u73bb\u8272\u5b50\u5f62\u6210\u7684\u5b64\u7acb\u5b50\u8b8a\u6210\u4e86\u4e00\u500b\u8cbb\u7c73\u5b50\uff0c\u5c07\u8cbb\u7c73\u5b50\u4ee5\u73bb\u8272\u5b50\u8868\u793a\u5c31\u662f\u6240\u8b02\u7684\u73bb\u8272\u5316\uff08bosonization\uff09\u3002\u5f9e\u7406\u8ad6\u7b49\u50f9\u7684\u89c0\u9ede\u4f86\u8aaa\uff0c\u4e5f\u53ef\u4ee5\u88ab\u7576\u6210\u662f\u4e00\u7a2e\u300c\u5c0d\u5076\u300d\u3002<\/p>\n<figure id=\"attachment_26422\" aria-describedby=\"caption-attachment-26422\" style=\"width: 600px\" class=\"wp-caption aligncenter\"><img decoding=\"async\" class=\"wp-image-26422\" src=\"http:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2016\/12\/figure3-vortex-antivortex.jpg\" alt=\"figure 3: XY \u6a21\u578b\u4e2d\u7684\u6f29\u6e26\u7d44\u614b\uff0c\u53f3\u908a\u662f\u4e00\u500b\u6f29\u6e26\u3001\u5de6\u908a\u662f\u4e00\u500b\u53cd\u6f29\u6e26(\u4f5c\u8005\u81ea\u7e6a)\" width=\"600\" height=\"375\"><figcaption id=\"caption-attachment-26422\" class=\"wp-caption-text\">figure 3: XY \u6a21\u578b\u4e2d\u7684\u6f29\u6e26\u7d44\u614b\uff0c\u53f3\u908a\u662f\u4e00\u500b\u6f29\u6e26\u3001\u5de6\u908a\u662f\u4e00\u500b\u53cd\u6f29\u6e26(\u4f5c\u8005\u81ea\u7e6a)<\/figcaption><\/figure>\n<p>\u63a5\u8457\u8d70\u9032 2+1 \u7dad\u6642\u7a7a\u3002\u5148\u524d\u63d0\u904e\u4f0a\u8f9b\u6a21\u578b\u662f\u6a21\u64ec\u78c1\u6027\u7269\u8cea\u7684\u6700\u7c21\u55ae\u7248\u672c\uff0c\u4e5f\u5c31\u662f\u6709\u4e00\u500b\u6676\u683c\uff0c\u6bcf\u500b\u683c\u9ede\u4e0a\u6709\u4e00\u500b\u7bad\u982d\uff0c\u8981\u561b\u671d\u4e0a\u6216\u671d\u4e0b\u3002\u4e00\u500b\u66f4\u9032\u968e\u7684\u7248\u672c\u662f\u60f3\u50cf\u7bad\u982d\u662f\u53ef\u4ee5\u5728\u4e8c\u7dad\u5e73\u9762\u4e0a\u65cb\u8f49\u7684\u5411\u91cf\uff0c\u9019\u7a2e\u6a21\u578b\u53eb\u505a X-Y\u6a21\u578b\uff0c\u5728 2 \u7dad\u7a7a\u9593\u4e2d\uff0cX-Y \u6a21\u578b\u6709\u6240\u8b02\u7684\u6f29\u6e26\u89e3\uff0c\u6709\u8da3\u7684\u662f\uff0c\u4eba\u5011\u5f8c\u4f86\u767c\u73fe\u5b83\u8207 2+1 \u7dad\u7248\u672c\u7684\u5e0c\u683c\u65af\u6a21\u578b\uff08Higgs model\uff09\u662f\u7b49\u50f9\u7684 [3, 4]\uff0c\u4f46\u5728 X-Y \u6a21\u578b\u4e2d\u7684\u6f29\u6e26\uff0c\u5c0d\u61c9\u5230\u5e0c\u683c\u65af\u6a21\u578b\u4e2d\u7684\u7c92\u5b50\uff0c\u53cd\u4e4b\u4ea6\u7136\u3002\u9019\u500b\u5c0d\u5076\u4fbf\u662f\u8457\u540d\u7684\u73bb\u8272\u5b50\u7248\u672c\u6f29\u6e26-\u7c92\u5b50\u5c0d\u5076\u3002<\/p>\n<p>\u90a3\u8cbb\u7c73\u5b50\u7248\u672c\u7684\u5462\uff1f\u5728\u53bb\u5e74\u5e74\u521d\u81f3\u5e74\u4e2d\uff0c\u829d\u52a0\u54e5\u5927\u5b78\u7684D. T. Son [5]\u3001\u9ebb\u7701\u7406\u5de5\u5b78\u9662\u7684 T. Senthil \u8ddf C. Wang [6] \u548c\u52a0\u5dde\u5927\u5b78\u67cf\u514b\u840a\u5206\u6821\u8207\u8056\u5854\u82ad\u82ad\u62c9\u5206\u6821\u7684A. Vishwanath\u3001M. Metlitski [7] \u5206\u5225\u5f9e\u4e0d\u540c\u7684\u56fa\u614b\u7269\u7406\u7cfb\u7d71\u51fa\u767c\uff0c\u63d0\u51fa\u4e86\u8cbb\u7c73\u5b50\u7248\u672c\u7684\u6f29\u6e26-\u7c92\u5b50\u5c0d\u5076\u3002\u7d04\u7565\u800c\u8a00\uff0c\u5728\u9019\u500b\u65b0\u7684\u5c0d\u5076\u4e2d\uff0c\u4e00\u500b 2+1 \u7dad\u7684\u96fb\u5b50\u5c0d\u61c9\u5230\u6240\u8b02\u8907\u5408\u8cbb\u7c73\u5b50\u7684\u96d9\u6f29\u6e26<a href=\"#_ftn1\" name=\"_ftnref1\">[1]<\/a> \uff0c\u9019\u500b\u5c0d\u5076\u6027\u7684\u795e\u9ad3\u5728\u65bc\uff0c\u5b83\u5c07\u4e00\u500b\u7406\u8ad6\u4e2d\u7684\u96fb\u8377\uff0c\u5c0d\u61c9\u5230\u53e6\u4e00\u500b\u7406\u8ad6\u4e2d\u7684\u78c1\u5834\u3002\u4e5f\u5c31\u662f\u8aaa\uff0c\u63a7\u5236\u4e00\u8005\u7684\u78c1\u5834\uff0c\u7b49\u540c\u65bc\u63a7\u5236\u53e6\u4e00\u8005\u7684\u96fb\u8377\u5bc6\u5ea6\u3002<\/p>\n<p>\u5f9e\u8907\u5408\u8cbb\u7c73\u5b50\u9019\u500b\u540d\u7a31\uff0c\u53ef\u4ee5\u731c\u60f3\u9019\u65b0\u5c0d\u5076\u6027\u53ef\u4ee5\u61c9\u7528\u5230\u91cf\u5b50\u970d\u723e\u6548\u61c9\u4e0a\uff0c\u9019\u7684\u78ba\u662f\u7576\u521d D. T. Son \u70ba\u4e86\u89e3\u6c7a\u73fe\u6709\u7406\u8ad6\u7f3a\u9677\u800c\u63d0\u51fa\u7684\u731c\u60f3\u3002\u5728\u63a5\u4e0b\u4f86\u7684\u8a0e\u8ad6\uff0c\u6211\u5011\u5c07\u5f9e\u5c0d\u5076\u6027\u7684\u89c0\u9ede\u4f86\u91cd\u65b0\u4e86\u89e3\u970d\u723e\u6548\u61c9\u3002<\/p>\n<p>--<\/p>\n<p><a href=\"#_ftnref1\" name=\"_ftn1\">[1]<\/a> \u4e8b\u5be6\u4e0a\u6c92\u9019\u9ebc\u7c21\u55ae\uff0c\u66f4\u7cbe\u78ba\u4e00\u9ede\u7684\u8b1b\uff0c\u4e00\u500b\u96fb\u5b50\u5c0d\u61c9\u5230\u4e00\u500b\u8907\u5408\u8cbb\u7c73\u5b50\u8207\u5e36\u6709\u5169\u55ae\u4f4d\u78c1\u8377\u7684\u77ac\u5b50\uff08instanton\uff09\uff0c\u56e0\u70ba\u662f\u5169\u55ae\u4f4d\u78c1\u8377\uff0c\u6240\u4ee5\u770b\u8d77\u4f86\u5c31\u50cf\u662f\u4e00\u500b\u96d9\u6f29\u6e26\u4e00\u6a23\u3002<\/p>\n<p><strong>\u53c3\u8003\u8cc7\u6599\uff1a<\/strong><\/p>\n<ol>\n<li>Coleman, <em>Quantum sine-Gordon Equation as the Massive Thirring Model<\/em>, Phys. Rev. D <strong>11<\/strong>, 2088 (1975).<\/li>\n<li>Mandelstam, <em>Soliton Operators for the Quantized Sine-Gordon Equation<\/em>, Phys. Rev. D <strong>11<\/strong>, 3026 (1975).<\/li>\n<li>E. Peskin, <em>Madelstam \u2018t Hooft Duality in Abelian Lattice Models<\/em>, Ann. Phys. (N.Y.) <strong>113<\/strong>, 122 (1978).<\/li>\n<li>Dasgupta, and B. I. Halperin, <em>Phase Transition in a Lattice Model of Superconductivity<\/em>, Phys. Rev. Lett. <strong>47<\/strong>, 1556 (1981).<\/li>\n<li>T. Son, <em>Is the Composite Fermion a Dirac Particle?<\/em>, Phys. Rev. X<strong> 5<\/strong>, 031027 (2015).<\/li>\n<li>Wang, and T. Senthil, <em>Dual Dirac Liquid on the Surface of the Electron Topological Insulator<\/em>, Phys. Rev. X <strong>5<\/strong>, 041031 (2015).<\/li>\n<li>A. Metlitski, and A. Vishwanath, <em>Particle-Vortex Duality of 2D Dirac Fermion from Electric-Magnetic Duality of 3D Topological Insulators<\/em>, Phys. Rev. B <strong>93<\/strong>, 245151 (2016).<\/li>\n<\/ol>\n<p><span style=\"color: #333399;\"><strong>--<br \/>\n\u4f5c\u8005\uff1a\u856d\u7dad\u7ff0\uff0c\u81fa\u5927\u7269\u7406\u7cfb\u7562\u696d\u5f8c\u9003\u5230\u829d\u52a0\u54e5\uff0c\u5439\u98a8\u5439\u96ea\u4e4b\u9918\uff0c\u505a\u7814\u7a76\u8b80\u535a\u58eb\u73ed\u3002\u53ef\u60dc\u96e2\u958b\u81fa\u7063\u5f8c\u7121\u6d77\u53ef\u770b\uff0c\u53ea\u80fd\u5728\u5bc6\u897f\u6839\u6e56\u65c1\u63c0\u4e00\u65b9\u5824\u5cb8\uff0c\u507d\u88dd\u6210\u770b\u6d77\u7684\u4eba\u3002\u79d1\u6559\u4e2d\u5fc3\u7279\u7d04\u5beb\u624b\uff0c\u5f9e\u4e8b\u79d1\u666e\u6587\u7ae0\u5beb\u4f5c\u3002<\/strong><\/span><\/p>\n<p>&nbsp;<\/p>\n<p><a href=\"https:\/\/line.me\/R\/ti\/p\/%40fcx6182w\" target=\"_blank\" rel=\"noopener noreferrer\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/scdn.line-apps.com\/n\/line_add_friends\/btn\/zh-Hant.png\" alt=\"\u52a0\u5165\u597d\u53cb\" width=\"212\" height=\"36\" border=\"0\"><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u4e0a\u96c6\u7684\u8a0e\u8ad6\u4e2d\uff0c\u6211\u5011\u7d04\u7565\u4ecb\u7d39\u4e86\u300c\u5c0d\u5076\u300d\uff08duality\uff09\u5728\u7269\u7406\u5b78\u4e2d\uff0c\u7684\u610f\u601d\uff1a\u8868\u9762\u4e0a\u770b\u8d77\u4f86\u4e0d\u540c\u7684\u5169\u500b\u7406\u8ad6\uff0c\u672c\u8cea\u4e0a\u63d0\u4f9b\u4e00\u6a23\u7684\u63cf\u8ff0\u3002\u6700\u57fa\u672c\u7684\u4f8b\u5b50\u662f\u6240\u8b02\u4f0a\u8f9b\u6a21\u578b\uff08Ising model\uff09\u5728\u539f\u6676\u683c\u8207\u5c0d\u5076\u6676\u683c\u4e0a\u7684\u5c0d\u5076\uff0c\u4ee5\u53ca\u96fb\u78c1\u5b78\u99ac\u514b\u65af\u5a01\u65b9\u7a0b\u5f0f\uff08Maxwell equations\uff09\u5728\u6c92\u6709\u96fb\u8377\u4e0b\u96fb\u5834\u78c1\u5834\u4ea4\u63db\u7684\u5c0d\u5076\u6027\u3002<\/p>\n","protected":false},"author":20,"featured_media":26419,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3293,39],"tags":[3050,2866,1536,2793],"aioseo_notices":[],"jetpack_featured_media_url":"https:\/\/case.ntu.edu.tw\/blog\/wp-content\/uploads\/2016\/12\/figure1.jpg","_links":{"self":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/26418"}],"collection":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/users\/20"}],"replies":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=26418"}],"version-history":[{"count":3,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/26418\/revisions"}],"predecessor-version":[{"id":32724,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/posts\/26418\/revisions\/32724"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=\/wp\/v2\/media\/26419"}],"wp:attachment":[{"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26418"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=26418"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/case.ntu.edu.tw\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=26418"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}