{"id":1661,"date":"2016-04-20T11:35:42","date_gmt":"2016-04-20T03:35:42","guid":{"rendered":"http:\/\/systemsci.org\/jinshanw\/?p=1661"},"modified":"2017-11-03T14:23:24","modified_gmt":"2017-11-03T06:23:24","slug":"dyson%e6%96%b9%e7%a8%8b%e7%94%a8%e4%bb%a5%e7%ae%80%e5%8c%96%e6%8a%95%e5%85%a5%e4%ba%a7%e5%87%ba%e8%ae%a1%e7%ae%97","status":"publish","type":"post","link":"https:\/\/www.systemsci.org\/jinshanw\/2016\/04\/20\/dyson%e6%96%b9%e7%a8%8b%e7%94%a8%e4%bb%a5%e7%ae%80%e5%8c%96%e6%8a%95%e5%85%a5%e4%ba%a7%e5%87%ba%e8%ae%a1%e7%ae%97\/","title":{"rendered":"Dyson\u65b9\u7a0b\u7528\u4ee5\u7b80\u5316\u6295\u5165\u4ea7\u51fa\u8ba1\u7b97"},"content":{"rendered":"

\u5728\u6211\u4eec\u7684\u5c01\u95ed\u7cfb\u7edf\u6295\u5165\u4ea7\u51fa\u5206\u6790\u7684\u76ee\u6807\u5916\u754c\u65b9\u6cd5\u4e2d\uff0c\u9700\u8981\u5bf9\u4e00\u4e2a\u77e9\u9635A\u591a\u6b21\u505a\u5220\u9664\u884c\u5217\u4ee5\u540e\u6c42\u9006\uff0c(\\left(1-A^{\\left(-k\\right)}\\right)^{-1})\uff0c\u5176\u4e2d(k)\u53ef\u4ee5\u662f\u4efb\u4f55\u4e00\u4e2a\u884c\u53f7\uff08\u4e5f\u4ee3\u8868\u5217\u53f7\uff09\u3002\u5982\u679c\u80fd\u591f\u627e\u5230\u4e00\u4e2a\u6c42\u89e3\u4e00\u6b21\u77e9\u9635\u9006\u5c31\u80fd\u89e3\u51b3\u95ee\u9898\u7684\u65b9\u6cd5\u5c31\u4f1a\u4f7f\u5f97\u8ba1\u7b97\u7b80\u5355\u5f88\u591a\u3002\u4f8b\u5982\uff0c\u6c42(\\left(1-A\\right)^{-1})\uff0c\u7136\u540e\u4ece(\\left(1-A\\right)^{-1})\u8ba1\u7b97\u51fa\u6765(\\left(1-A^{\\left(-k\\right)}\\right)^{-1})\u3002\u53ef\u4ee5\u770b\u5230\uff0c\u4ece\u524d\u8005\u5230\u540e\u8005\uff0c\u4e5f\u5c31\u76f8\u5dee\u4e00\u884c\u4e00\u5217\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6211\u4eec\u8981\u4ece\u4e00\u4e2a\u77e9\u9635\u7684\u9006\u6c42\u51fa\u6765\u53e6\u5916\u4e00\u4e2a\u76f8\u5dee\u4e00\u884c\u4e00\u5217\u7684\u77e9\u9635\u7684\u9006\u3002<\/p>\n

\u8fd9\u4e2a\u95ee\u9898\uff0c\u5728\u7269\u7406\u5b66\u4e2d\uff0c\u662f\u901a\u8fc7Dyson\u65b9\u7a0b\u6765\u5b9e\u73b0\u7684\u3002\u7269\u7406\u5b66\u7684Green\u51fd\u6570\uff0c\u5927\u6982\u76f8\u5f53\u4e8e\u8ba1\u7b97\u77e9\u9635\u9006\uff0c\u4f8b\u5982(G=\\left(E-H\\right)^{-1})\u3002Dyson\u8bf4\uff0c\u5982\u679c(H=H_{0}+V)\uff0c\u800c\u4e14(G_{0}=\\left(E-H_{0}\\right)^{-1})\u5bb9\u6613\u8ba1\u7b97\u51fa\u6765\uff0c\u90a3\u4e48\uff0c\u6211\u4eec\u5c31\u53ef\u4ee5\u901a\u8fc7(G_{0})\u6765\u8ba1\u7b97(G)\uff0c\u5177\u4f53\u516c\u5f0f\u5982\u4e0b
\n[G=G_{0}+G_{0}VG]<\/p>\n

Dyson\u65b9\u7a0b\u5f88\u5bb9\u6613\u8bc1\u660e\uff0c\u5de6\u53f3\u4e24\u8fb9\u4e58\u4e0a(E-H)\u5c31\u884c\u3002Dyson\u65b9\u7a0b\u5927\u591a\u6570\u4e4b\u540e\u4e0d\u80fd\u7cbe\u786e\u6c42\u89e3\uff0c\u9700\u8981\u505a\u8fd1\u4f3c\u3002\u4f46\u662f\uff0c\u6709\u7684\u95ee\u9898\u4e2d\u53ef\u4ee5\u7cbe\u786e\u6c42\u89e3\u3002\u987a\u4fbf\uff0cDyson\u65b9\u7a0b\u7684\u7cbe\u786e\u6c42\u89e3\u7684\u4f8b\u5b50\uff0c\u6211\u662f\u4ece\u6211\u7684\u8001\u5e08Mona Berciu<\/a>\u90a3\u91cc\u5b66\u4e60\u6765\u7684\u3002\u5f53\u65f6\u662f\u51dd\u805a\u6001\u7269\u7406II\u8bfe\u7a0b\u4e2d\u7684\u4e00\u5c0f\u8282\u7684\u5185\u5bb9\u3002<\/p>\n

\u73b0\u5728\uff0c\u4e0a\u9762\u7684\u95ee\u9898\u5b8c\u5168\u5c31\u8f6c\u5316\u6210\u4e86Dyson\u65b9\u7a0b\u7684\u95ee\u9898\u3002\u95ee\u9898\u5c31\u5269\u4e0b\uff0c\u5bf9\u4e8e\u8fd9\u4e2a\u7cfb\u7edf\uff0cDyson\u65b9\u7a0b\u662f\u5426\u53ef\u4ee5\u7cbe\u786e\u6c42\u89e3\u4e8e\u662f\u6211\u4eec\u907f\u514d\u518d\u4e00\u6b21\u8ba1\u7b97\u77e9\u9635\u9006\u5462\uff1f<\/p>\n

\u7531\u4e8e(A)\u6709\u4e00\u4e2a\u6700\u5927\u672c\u5f81\u503c\u5c31\u662f1\uff0c\u56e0\u6b64\u76f4\u63a5\u6c42\u9006\u662f\u53d1\u6563\u7684(G^{full}{0} = \\left(1-A\\right)^{-1})\u3002\u90a3\u6709\u4ec0\u4e48\u529e\u6cd5\u80fd\u591f\u7528\u4e0a\u8fd9\u4e2a\u53ef\u80fd\u53d1\u6563\u7684(G^{full}<\/em>{0})\u5417\uff1f\u6ce8\u610f(G^{\\left(-k\\right)})\u53ea\u8981\u53bb\u6389\u7684\u90a3\u4e2a\u90e8\u95e8\u7684\u975e\u5bf9\u89d2\u5143\u4e0d\u5168\u4e3a\u96f6\uff0c\u662f\u6536\u655b\u7684\u3002\u4e5f\u5c31\u662f\uff0c\u53ea\u6709(G^{full}_{0})\u662f\u4e2a\u95ee\u9898\uff0c(G^{\\left(-k\\right)})\u4e0d\u662f\u95ee\u9898\u3002<\/p>\n

\u73b0\u5728\uff0c\u56de\u5230Dyson\u65b9\u7a0b\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u548c\u7269\u7406\u5b66\u7684Green\u51fd\u6570\u4e00\u6837\uff0c\u5728\u8fd9\u91cc\u53ea\u8981\u5f15\u5165\u4e00\u4e2a\u865a\u6570
\n[G^{\\eta}_{0} = \\left(1-A+i\\eta\\right)^{-1},]
\n\u7136\u540e\u8ba9\u8fd9\u4e2a\u865a\u6570\u5728\u6700\u540e\u7684\u8ba1\u7b97\u4e2d\u8d8b\u4e8e\u96f6\uff0c\u5c31\u89e3\u51b3\u4e86\u6240\u6709\u7684\u95ee\u9898\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u53d1\u73b0\uff0c\u5b8c\u5168\u5730\u628aGreen\u51fd\u6570\u548cDyson\u65b9\u7a0b\u4ece\u7269\u7406\u5b66\u7528\u5230\u4e86\u6295\u5165\u4ea7\u51fa\u3002<\/p>\n

\u4e0b\u4e00\u6b65\uff0c\u53bb\u770b\u770b\u89e3\u6790\u4e0a\u548c\u6570\u503c\u4e0a\u80fd\u4e0d\u80fd\u5b8c\u5168\u5b9e\u73b0\u8fd9\u4e2a\u5148\u641e\u4e00\u4e2a\u865a\u6570\uff0c\u6c42\u89e3Dyson\u65b9\u7a0b\uff0c\u7136\u540e\u8ba9\u8fd9\u4e2a\u865a\u6570\u8d8b\u4e8e\u96f6\u7684\u8fc7\u7a0b\u3002\u6216\u8005\u4e0d\u8ba9\u8fd9\u4e2a\u865a\u90e8\u53d6\u4e8e\u96f6\uff0c\u4fdd\u7559\u7740\uff0c\u4e00\u76f4\u5230\u6700\u540e\u7684\u8ba1\u7b97\u7ed3\u679c\u5f97\u5230\u4e4b\u540e\uff0c\u53d6\u5b9e\u90e8\uff0c\u770b\u770b\u884c\u4e0d\u884c\u3002\u5982\u679c\u53ef\u4ee5\u7684\u8bdd\uff0c\u6309\u7167\u5982\u4e0b\u6b65\u9aa4\u7684\u8ba1\u7b97\u4f1a\u7b80\u5355\u5f88\u591a\uff1a\u5f97\u5230\u5305\u542b\u865a\u90e8\u7684(G^{\\eta}_{0})\uff0c\u6c42\u89e3Dyson\u65b9\u7a0b\u5f97\u5230\u5305\u542b\u865a\u90e8\u7684(G^{\\left(-k, \\eta\\right)})\uff0c\u53d6\u8fd9\u4e2a(G^{\\left(-k, \\eta\\right)})\u7684\u5b9e\u90e8\u3002<\/p>\n

\u521d\u6b65\u7684\u7406\u8bba\u63a8\u5bfc\u548c\u6570\u503c\u5b9e\u9a8c\u8868\u660e\uff0c\u4ee5\u4e0a\u8ba1\u7b97\u8fc7\u7a0b\u7adf\u7136\u53ef\u4ee5\u3002\u5176\u8ba1\u7b97\u8fc7\u7a0b\u57fa\u672c\u4e0a\u548c\u7d27\u675f\u7f1a\u94fe\u6a21\u578b\u4e2d\u52a0\u4e0a\u4e00\u4e2a(\\delta)\u52bf\u6216\u8005\u5728\u67d0\u5904\u622a\u65ad\u4e00\u6837\u3002\u5177\u4f53\u7684\u8ba1\u7b97\u8fd9\u91cc\u5c31\u4e0d\u5199\u51fa\u6765\u4e86\uff0c\u592a\u957f\u4e86\u3002<\/p>\n

\u987a\u4fbf\u8bf4\u4e00\u4e0b\u8fd9\u4e2a\u5de5\u4f5c\u7684\u610f\u4e49\u3002\u8fd9\u91cc\u7528Dyson\u65b9\u7a0b\u907f\u514d\u4e86\u591a\u6b21\u6c42\u9006\u77e9\u9635\uff0c\u6240\u4ee5\u7eaf\u7cb9\u662f\u6280\u672f\u4e0a\u7684\u8d21\u732e\uff0c\u5bf9\u4e8e\u95ee\u9898\u672c\u8eab\u6ca1\u6709\u8d21\u732e\uff0c\u5b66\u672f\u4ef7\u503c\u6709\u9650\u3002\u4f46\u662f\uff0c\u5728\u7b2c\u4e8c\u4e2a\u65b9\u6cd5\u4e2d\uff0c\u5f15\u5165\u7684\u865a\u90e8\u53ef\u80fd\u6709\u72ec\u7acb\u7684\u610f\u4e49\uff08\u7269\u7406\u91cc\u9762\u6709\uff09\u3002\u5982\u679c\u540e\u7eed\u7684\u7814\u7a76\u53d1\u73b0\u8fd9\u4e2a\u610f\u4e49\uff0c\u90a3\u4e48\uff0c\u5c31\u4e0d\u518d\u662f\u4ec5\u4ec5\u5728\u6280\u672f\u4e0a\u7684\u4ef7\u503c\u4e86\u3002\u603b\u7ed3\uff1a\u76ee\u524d\u6ca1\u5565\u5927\u610f\u4e49\uff0c\u5c31\u662f\u633a\u597d\u73a9\uff0c\u865a\u90e8\u7684\u610f\u4e49\u8fd8\u6709\u5f85\u6316\u6398\u3002<\/p>\n

\u865a\u90e8\u7684\u610f\u4e49\u5728\u7269\u7406\u5b66\u4e2d\u4ee3\u8868\u4e86\u6001\u5bc6\u5ea6\uff08Density of states\uff09\u6216\u8005\u8bf4\u675f\u7f1a\u6001\uff08bounded states\uff09\u7684\u80fd\u91cf\u548c\u6ce2\u51fd\u6570\u3002\u5728\u6295\u5165\u4ea7\u51fa\u7814\u7a76\u4e2d\u662f\u4ec0\u4e48\u5462\uff1f\u6d77\u519b\u5144\u63a8\u8350\u7684\u5173\u4e8eMarkov\u94fefundamental matrix\u7684\u6587\u732e\u4e2d\uff0c\u63d0\u5230\u4e86(\\frac{1}{1-A}f)\u7684\u8ba1\u7b97\u7684\u95ee\u9898\u3002\u5176\u4e2d\uff0c\u4e00\u822c\u7684\u9006\u77e9\u9635(1-A)\u4e0d\u5b58\u5728\uff08\u7531\u4e8eA\u7684\u6700\u5927\u672c\u5f81\u503c\u662f(1)\uff09\uff0c\u4f46\u662f\u5bf9\u4e8e\u67d0\u4e9b\u7279\u6b8a\u7684(f)\uff0c\u8fd9\u4e2a\u5408\u8d77\u6765\u7684(\\frac{1}{1-A}f)\u4ecd\u7136\u5b58\u5728\uff08\u5b9e\u9645\u4e0a\uff0c\u5c31\u662f(f)\u521a\u597d\u6ca1\u6709\u6700\u5927\u672c\u5f81\u503c\u5bf9\u5e94\u7740\u7684\u90a3\u4e2a\u5411\u91cf\u5206\u91cf\uff09\u3002\u8fd9\u4e2a\uff08\u52a0\u4e0a\u6211\u4eec\u4e4b\u524d\u5728\u5c01\u95ed\u7cfb\u7edf\u6295\u5165\u4ea7\u51fa\u8ba8\u8bba(A^{-k})\u672c\u5f81\u503c\u7684\u95ee\u9898\uff09\u542f\u53d1\u6211\u601d\u8003\u4e00\u822c\u7684(\\frac{1}{\\omega-A^{-k}})\u7684\u95ee\u9898\u3002\u4e8e\u662f\uff0c\u6211\u53d1\u73b0\uff0c\u8fd9\u4e2a\u66f4\u4e00\u822c\u7684Green\u51fd\u6570\u7684\u865a\u90e8\uff0c\u5b9e\u9645\u4e0a\uff0c\u4ee3\u8868\u4e86(A^{-k})\u7684\u672c\u5f81\u503c\u548c\u672c\u5f81\u5411\u91cf\u3002\u4e8e\u662f\uff0c\u4e24\u4e2a\u95ee\u9898\u2014\u2014\u77e9\u9635\u6c42\u9006\u7684\u7b80\u5316\u3001\u77e9\u9635\u672c\u5f81\u503c\u548c\u672c\u5f81\u5411\u91cf\u7684\u7b80\u5316\u2014\u2014\u90fd\u53ef\u4ee5\u901a\u8fc7\u8fd9\u4e2aGreen\u51fd\u6570\u6765\u56de\u7b54\u3002\u5f53\u7136\uff0c\u7275\u6d89\u5230\u865a\u90e8\u7684poles\u7684\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u505a\u4e00\u4e2a\u56f4\u9053\u79ef\u5206\u3002<\/p>\n

\u8fd9\u4e2a\u4f8b\u5b50\u8bf4\u660e\uff1a\u5b66\u4e60\u7269\u7406\u771f\u7684\u5f88\u6709\u7528\uff0c\u5c24\u5176\u662f\u5728\u5206\u6790\u95ee\u9898\u7684\u601d\u8def\u548c\u65b9\u6cd5\u4e0a\u3002\u5f53\u7136\uff0c\u8fd9\u91cc\u4e3b\u8981\u662f\u65b9\u6cd5\u5c42\u6b21\u7684\uff0c\u4e5f\u5c31\u662f\u66f4\u504f\u5411\u6570\u5b66\u5c42\u6b21\u7684\u2014\u2014\u77e9\u9635\u9006\u7684\u5fae\u6270\u7cbe\u786e\u89e3\u3002\u53ef\u662f\uff0c\u8981\u6ce8\u610f\uff0c\u5355\u7eaf\u4ece\u6570\u5b66\u7684\u89d2\u5ea6\u6765\u8bf4\uff0cDyson\u65b9\u7a0b\u8fd9\u6837\u7684\u4e1c\u897f\u53ef\u80fd\u4e0d\u4f1a\u88ab\u53d1\u5c55\u8d77\u6765\u3002\u5176\u51fa\u73b0\u7684\u6839\u672c\u539f\u56e0\u662f\u5728\u7269\u7406\u4e2d\uff0c\u5927\u91cf\u7684\u7cfb\u7edf\u7684(H)\u5305\u542b\u4e00\u4e2a\u5bb9\u6613\u6c42\u89e3\u7684\u90e8\u5206(H_{0})\u4ee5\u53ca\u4e00\u4e2a\u4e0d\u5bb9\u6613\u6c42\u89e3\u7684\u90e8\u5206(V)\u3002\u4e8e\u662f\uff0c\u81ea\u7136\u5730\u5c31\u6709\u4eba\u6765\u89e3\u51b3\u8fd9\u4e2a\u4ece(G_{0})\u5f97\u5230(G)\u7684\u65b9\u6cd5\u3002<\/p>\n

\u56e0\u6b64\uff0c\u591a\u5b66\u70b9\u6570\u5b66\u7269\u7406\u5427\uff0c\u591a\u4ece\u5173\u5fc3\u5b9e\u9645\u7cfb\u7edf\u7684\u89d2\u5ea6\u6765\u4f53\u4f1a\u6570\u5b66\u5427\u3002\u5f53\u7136\uff0c\u591a\u4ece\u6570\u5b66\u4e4b\u7f8e\u7684\u89d2\u5ea6\u6765\u4f53\u4f1a\u6570\u5b66\u4e5f\u662f\u5e94\u8be5\u7684\u3002\u53e6\u5916\uff0c\u597d\u7684\u8001\u5e08\u7684\u597d\u7684\u8bfe\u7a0b\u4e0d\u77e5\u9053\u4ec0\u4e48\u65f6\u5019\u5c31\u542f\u53d1\u4f60\u4e86\u3002\u8981\u597d\u597d\u4e0a\u8fd9\u6837\u7684\u8bfe\uff0c\u96be\u5f97\u7684\u3002<\/p>\n

Dyson\u5927\u6982\u4f1a\u9ad8\u5174\uff08\u8fd8\u662f\u4f24\u5fc3\u554a\uff1f\uff09\u6211\u628a\u4ed6\u7684\u65b9\u7a0b\u7528\u6765\u89e3\u51b3\u6295\u5165\u4ea7\u51fa\u7ecf\u6d4e\u5206\u6790\u7684\u6280\u672f\u95ee\u9898\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

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