{"id":49097,"date":"2024-03-21T19:22:35","date_gmt":"2024-03-21T11:22:35","guid":{"rendered":"https:\/\/swarma.org\/?p=49097"},"modified":"2024-03-21T19:22:35","modified_gmt":"2024-03-21T11:22:35","slug":"%e7%83%ad%e5%8a%9b%e5%ad%a6%e4%b8%8e%e9%87%8f%e5%ad%90%e5%8a%9b%e5%ad%a6%e5%9c%a821%e4%b8%96%e7%ba%aa%e9%87%8d%e6%96%b0%e7%9b%b8%e9%81%87","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=49097","title":{"rendered":"\u70ed\u529b\u5b66\u4e0e\u91cf\u5b50\u529b\u5b66\u572821\u4e16\u7eaa\u91cd\u65b0\u76f8\u9047"},"content":{"rendered":"
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\u5728Jarzynski\u7b49\u5f0f\u88ab\u63d0\u51fa\u6765\u4ee5\u524d\uff0c\u4eba\u4eec\u66f4\u591a\u7684\u662f\u91c7\u7528\u8def\u5f84\u79ef\u5206\u5bf9\u81ea\u7531\u80fd\u7684\u5904\u7406\u65b9\u5f0f\uff0c\u4e5f\u5c31\u662f\u5c06\u6e29\u5ea6\u770b\u4f5c\u865a\u65f6\u95f4\uff0c\u5e76\u5c06\u5176\u4f5c\u4e3a\u6f14\u5316\u7684\u53e6\u4e00\u4e2a\u7ef4\u5ea6\u3002\u8fd9\u8ddf\u7ecf\u5178\u70ed\u529b\u5b66\u7684\u5b9a\u4e49\u5e76\u4e0d\u81ea\u6d3d\uff0c\u56e0\u4e3a\u7b49\u6e29\u2014\u7edd\u70ed\u8fc7\u7a0b\u5728\u5361\u8bfa\u70ed\u673a\u4e2d\u88ab\u8ba4\u4e3a\u662f\u53ef\u9006\u7684\uff0c\u5b83\u65e0\u6cd5\u7528\u6765\u5b9a\u4e49\u65f6\u95f4\u4e4b\u77e2\u3002\u5982\u4eca\u6211\u4eec\u5728\u91cf\u5b50\u6da8\u843d\u7406\u8bba\u7684\u6846\u67b6\u4e0b\uff0c\u5229\u7528\u4e0d\u540c\u80fd\u7ea7\u72b6\u6001\u4e4b\u95f4\u76f8\u5e72\u6027\u7684\u53d8\u5316\uff0c\u53ef\u4ee5\u5c06\u6e29\u5ea6\u4e4b\u77e2\u5b9a\u4e49\u4e3a\u91cf\u5b50\u7cfb\u7edf\u7684\u56fa\u6709\u6f14\u5316\u65b9\u5411\uff0c\u4ece\u800c\u4e3a\u70ed\u7684\u91cf\u5b50\u5316\u63d0\u4f9b\u65b0\u7684\u8be0\u91ca\uff0c\u8fd9\u6b63\u662f\u4e0b\u9762\u8981\u8c08\u7684\u91cf\u5b50\u8d44\u6e90\u8bba\u7684\u4e3b\u8981\u7814\u7a76\u601d\u60f3\u3002<\/span><\/section>\n

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2002\u5e74\u53d1\u8868\u5728Science<\/em>\u6742\u5fd7\u4e0a\u7684\u4e00\u4e2a\u5de5\u4f5c\u9a8c\u8bc1\u4e86Jarzynski\u7b49\u5f0f[3]\u3002\u4ed6\u4eec\u5229\u7528\u7eaf\u673a\u68b0\u7684\u65b9\u6cd5\u5c06\u6298\u53e0\u7684\u6838\u7cd6\u6838\u9178\u5f3a\u884c\u5c55\u5f00\uff0c\u901a\u8fc7\u6d4b\u91cf\u65bd\u52a0\u7684\u529b\u6765\u786e\u5b9a\u76f8\u5e94\u7684\u529f\uff0c\u5e76\u4e0e\u81ea\u7531\u80fd\u5bf9\u6bd4\u3002\u6b64\u540e\uff0c\u5728\u86cb\u767d\u8d28\u3001\u805a\u5408\u7269\u3001\u51b7\u539f\u5b50\u3001\u79bb\u5b50\u9631\u7b49\u8bf8\u591a\u5b9e\u9a8c\u4f53\u7cfb\u4e2d\uff0c\u5747\u4ee5\u4e0d\u540c\u5f62\u5f0f\u9a8c\u8bc1\u4e86\u8fd9\u4e00\u7b49\u5f0f\u7684\u5408\u7406\u6027\u3002\u7b14\u8005\u8ba4\u4e3a\uff0cJarzynski\u7b49\u5f0f\u662f\u91cf\u5b50\u70ed\u529b\u5b66\u4e00\u4e2a\u5f88\u597d\u7684\u5207\u5165\u70b9\uff0c\u672a\u6765\u6211\u4eec\u4e0d\u59a8\u7528DNA\u6216\u5176\u4ed6\u66f4\u5177\u6807\u5fd7\u6027\u7684\u751f\u7269\u5927\u5206\u5b50\u4f5c\u4e3a\u6d4b\u91cf\u81ea\u7531\u80fd\u7684\u201c\u6807\u51c6\u5668\u201d\uff0c\u5e76\u636e\u6b64\u5b9a\u4e49\u66f4\u52a0\u5fae\u89c2\u7684\u6e29\u5ea6\uff0c\u4f5c\u4e3a\u57fa\u672c\u7269\u7406\u91cf\u4f7f\u7528<\/strong>\u3002<\/span><\/section>\n

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\u81ea\u4f3d\u5229\u7565\u53d1\u660e\u6e29\u5ea6\u8ba1\u81f3\u4eca\uff0c\u4eba\u7c7b\u5bf9\u4e8e\u6e29\u5ea6\u7684\u7814\u7a76\u5df2\u6709\u56db\u767e\u591a\u5e74\uff0c\u65e9\u4e8e\u7535\u3001\u78c1\u3001\u5149\u7b49\u5176\u4ed6\u5b66\u79d1\u3002\u4ece\u70ed\u7535\u5076\u5230\u7ea2\u5916\u7ebf\uff0c\u4eba\u7c7b\u7684\u6d4b\u6e29\u624b\u6bb5\u65e5\u76ca\u4e30\u5bcc\uff0c\u7136\u800c\u6a2a\u5411\u5bf9\u6bd4\u5176\u4ed6\u51e0\u95e8\u5b66\u79d1\uff0c\u7535\u5df2\u80fd\u591f\u5c0f\u5230\u76ae\u5b89\uff0c\u78c1\u5df2\u80fd\u591f\u5f31\u5230\u9ad8\u65af\uff0c\u5149\u5df2\u80fd\u591f\u77ed\u5230\u963f\u79d2\uff0c\u800c\u5373\u4f7f\u76ee\u524d\u6700\u5148\u8fdb\u7684\u6d4b\u6e29\u63a7\u6e29\u8bbe\u5907\uff0c\u5176\u6e29\u5ea6\u4ecd\u5728\u5c0f\u6570\u70b9\u540e\u7b2c\u4e00\u4f4d\u6765\u56de\u8df3\u52a8\uff0c\u548c\u56db\u767e\u5e74\u524d\u51e0\u65e0\u8fdb\u6b65\u3002\u53d1\u5c55\u65b0\u7684\u5fae\u89c2\u6d4b\u6e29\u65b9\u6848\uff0c\u6211\u4eec\u9700\u8981\u5168\u65b0\u7684\u7406\u8bba\u6846\u67b6\u3002<\/span><\/section>\n

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3. \u91cf\u5b50\u6df7\u6c8c<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u91cf\u5b50\u70ed\u529b\u5b66\u6700\u6838\u5fc3\u7684\u7406\u8bba\u4f53\u7cfb\u662f\u5728\u91cf\u5b50\u6df7\u6c8c\u7406\u8bba\u7684\u57fa\u7840\u4e0a\u5efa\u7acb\u8d77\u6765\u7684\uff0c\u76ee\u524d\u5e38\u89c1\u7684\u6587\u732e\u4e2d\uff0c\u5173\u4e8e\u91cf\u5b50\u6df7\u6c8c\u7684\u540d\u79f0\u901a\u5e38\u8868\u8ff0\u4e3aquantum chaos[4]\u3002Berry\u5f53\u5e74\u66fe\u4f7f\u7528quantum chaology\uff0c\u7528\u4ee5\u533a\u5206\u5168\u91cf\u5b50\u7cfb\u7edf\u7684\u6df7\u6c8c\u6548\u5e94\uff0c\u8fd9\u4e2a\u8bcd\u5076\u5c14\u4f1a\u51fa\u73b0\u5728\u6587\u732e\u4e2d\uff0c\u4f46\u672a\u5e7f\u4e3a\u63a5\u53d7\u3002\u6211\u4eec\u73b0\u5728\u901a\u5e38\u7814\u7a76\u7684\u91cf\u5b50\u6df7\u6c8c\uff0c\u662f\u6307\u5c06\u91cf\u5b50\u7cfb\u7edf\u7ecf\u5178\u5316\u6216\u534a\u7ecf\u5178\u5316\u540e\u7684\u6df7\u6c8c\uff0c\u540e\u8005\u662f\u6307\u5c06\u539f\u5b50\u6838\u90e8\u5206\u7ecf\u5178\u5316\uff0c\u518d\u4e0e\u7ecf\u5178\u6df7\u6c8c\u76f8\u6bd4\u8f83\u3002\u5168\u91cf\u5b50\u7cfb\u7edf\u7684\u6df7\u6c8c\u7814\u7a76\u76ee\u524d\u672a\u6709\u91cd\u5927\u8fdb\u5c55\u3002<\/span><\/section>\n

<\/section>\n
\u5728\u7ecf\u5178\u529b\u5b66\u4e2d\uff0c\u4e0e\u6df7\u6c8c\u76f8\u5bf9\u5e94\u7684\u6982\u5ff5\u662f\u53ef\u79ef\u3002\u5f53\u4e00\u4e2a\u8fd0\u52a8\u7cfb\u7edf\u7684\u81ea\u7531\u5ea6\u4e0e\u5b88\u6052\u91cf <\/span>(\u8fd0\u52a8\u79ef\u5206) <\/span>\u7684\u6570\u91cf\u4e00\u81f4\u65f6\uff0c\u5176\u8fd0\u52a8\u65b9\u7a0b\u662f\u53ef\u79ef\u7684<\/span> (\u53ef\u89e3\u7684) <\/span>\u3002\u76f8\u53cd\uff0c\u82e5\u627e\u4e0d\u51fa\u8db3\u591f\u6570\u91cf\u7684\u5b88\u6052\u91cf\uff0c\u5219\u8be5\u7cfb\u7edf\u662f\u6df7\u6c8c\u7684\u3002\u4e00\u822c\u5730\u8bb2\uff0c\u7531\u4e8e\u80fd\u91cf\u5b88\u6052\u603b\u662f\u5148\u9a8c\u6210\u7acb\uff0c\u6545\u800c\u4e00\u7ef4\u7ecf\u5178\u4f53\u7cfb\u603b\u662f\u53ef\u79ef\u7684\u3002\u82e5\u518d\u52a0\u4e0a\u89d2\u52a8\u91cf\u5b88\u6052\uff0c\u5219\u4e8c\u7ef4\u4f53\u7cfb\u4e5f\u53ef\u79ef\uff0c\u6bd4\u5982\u5f00\u666e\u52d2\u884c\u661f\u6a21\u578b\u3002\u4f46\u82e5\u4e8c\u7ef4\u4f53\u7cfb\u6709\u7279\u6b8a\u7684\u8fb9\u754c\uff0c\u6bd4\u5982\u56fe1\u6240\u793a\u7684\u662f\u6df7\u6c8c\u7406\u8bba\u4e2d\u7ecf\u5e38\u4f5c\u4e3a\u51fa\u53d1\u70b9\u7684L. A. Bunimovich\u4f53\u80b2\u573a<\/span> (stadium)<\/span> \u6a21\u578b[5]\uff0c\u5176\u5f62\u72b6\u5982\u4e00\u4e2a\u7530\u5f84\u8fd0\u52a8\u573a\uff0c\u8fd9\u79cd\u60c5\u51b5\u4e0b\u65e0\u6cd5\u627e\u5230\u7b2c\u4e8c\u4e2a\u5b88\u6052\u91cf\uff0c\u5219\u4f1a\u51fa\u73b0\u6df7\u6c8c\u3002\u9664\u6b64\u4ee5\u5916\uff0c\u975e\u5fae\u6270\u4e09\u4f53\u7cfb\u7edf\u4e5f\u56e0\u627e\u4e0d\u5230\u8db3\u591f\u7684\u5b88\u6052\u91cf\u800c\u6210\u4e3a\u6df7\u6c8c\uff0c\u6bd4\u5982\u6c34\u5206\u5b50\u7684\u4e09\u4e2a\u539f\u5b50\u3001\u8d28\u5b50\u7684\u4e09\u4e2a\u5938\u514b\u7b49\uff0c\u8fd9\u662f\u6d41\u4f53\u529b\u5b66\u3001\u6838\u7269\u7406\u4e2d\u65f6\u5e38\u53d1\u751f\u6df7\u6c8c\u73b0\u8c61\u7684\u539f\u56e0\u3002\u81f3\u4e8e\u4e09\u7ef4\uff0c\u4e0d\u53ef\u79ef\u7684\u60c5\u51b5\u66f4\u4e3a\u5e38\u89c1\uff0c\u6240\u4ee5\u7edd\u5927\u591a\u6570\u81ea\u7136\u7cfb\u7edf\u90fd\u662f\u6df7\u6c8c\u7684\uff0c\u53ef\u79ef\u7cfb\u7edf\u53ea\u662f\u5c11\u6570\u3002<\/span><\/section>\n

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\u56fe1 \u4f53\u80b2\u573a\u6a21\u578b<\/span><\/section>\n

<\/section>\n
\u5c06\u8fd9\u4e9b\u7ecf\u5178\u6df7\u6c8c\u7684\u6982\u5ff5\u5411\u91cf\u5b50\u63a8\u5e7f\u7684\u7814\u7a76\u65e9\u5728van Vleck\u65f6\u5c31\u6709\u4e86\uff0c\u4f46\u771f\u6b63\u7684\u8fdb\u5c55\u53d1\u751f\u4e8e1950\u5e74\u4ee3\u540e\u3002Wigner\u7b49\u4eba\u9996\u5148\u7528\u968f\u673a\u77e9\u9635\u7406\u8bba\u6765\u5904\u7406\u91cf\u5b50\u6df7\u6c8c\uff0c\u7136\u540e\u662fGutzwiller\u7b49\u4eba\u63d0\u51fa\u8ff9\u516c\u5f0f<\/span> (trace formula)<\/span>\uff0c\u8de8\u51fa\u4e86\u7ecf\u5178\u6df7\u6c8c\u91cf\u5b50\u5316\u7684\u5173\u952e\u4e00\u6b65\u30021980\u5e74\u4ee3\u4ee5\u540e\uff0c\u968f\u7740\u539f\u5b50\u5206\u5b50\u5149\u5b66\u7684\u53d1\u5c55\uff0c\u5c24\u5176\u662f\u5bf9\u7535\u78c1\u573a\u4e2d\u6c22\u539f\u5b50\u52a8\u529b\u5b66\u884c\u4e3a\u7684\u7814\u7a76\uff0c\u63ed\u793a\u51fa\u91cf\u5b50\u6df7\u6c8c\u5df2\u7ecf\u662f\u65e0\u6cd5\u56de\u907f\u7684\u95ee\u9898\uff0c\u968f\u673a\u77e9\u9635\u4e0e\u8ff9\u516c\u5f0f\u8fd9\u4e24\u5957\u7406\u8bba\u5747\u5f97\u4ee5\u8fc5\u901f\u53d1\u5c55\uff0c\u5f62\u6210\u8f83\u4e3a\u5b8c\u6574\u7684\u7406\u8bba\u4f53\u7cfb\u3002<\/span><\/section>\n

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\u5173\u4e8e\u6df7\u6c8c\u7684\u5b9a\u4e49\uff0c\u4e00\u822c\u5e94\u6ee1\u8db3\u5982\u4e0b\u4e09\u4e2a\u6761\u4ef6\uff1a<\/span><\/p>\n

(1)\u6709\u754c\u6027<\/span> (boundedness)<\/span>\uff1a\u5176\u8fd0\u52a8\u8303\u56f4\u5b58\u5728\u4e00\u4e2a\u786e\u5b9a\u7684\u8fb9\u754c\uff1b<\/span><\/p>\n

(2)\u56de\u5f52\u6027<\/span> (recurrence)<\/span>\uff1a\u65e0\u8bba\u4ece\u54ea\u4e2a\u8d77\u70b9\u51fa\u53d1\uff0c\u603b\u80fd\u4e0d\u65ad\u56de\u5230\u8be5\u8d77\u70b9\uff1b<\/span><\/p>\n

(3)\u6307\u6570\u654f\u611f\u6027<\/span> (exponential sensitivity)<\/span>\uff1a\u4e24\u6761\u8d77\u70b9\u4efb\u610f\u63a5\u8fd1\u7684\u8f68\u8ff9\u603b\u662f\u4ee5\u6307\u6570\u5f62\u5f0f\u5206\u79bb\u3002<\/span><\/section>\n

<\/section>\n
\u7b2c\u4e00\u6761\u63d0\u793a\u4e86\u8981\u5f62\u6210\u6df7\u6c8c\u5fc5\u987b\u6709\u786e\u5b9a\u7684\u52bf\u573a\u6216\u76f8\u4e92\u4f5c\u7528\u6765\u7ea6\u675f\u7cfb\u7edf\u7684\u8fd0\u52a8\uff0c\u6392\u9664\u4e86\u5b8c\u5168\u81ea\u7531\u7684\u7cfb\u7edf\u4e2d\u5b58\u5728\u6df7\u6c8c\u7684\u53ef\u80fd\u3002\u7b2c\u4e8c\u6761\u63d0\u793a\u4e86\u4e0d\u5b58\u5728\u4e0d\u7a33\u5b9a\u7684\u521d\u59cb\u72b6\u6001\uff0c\u6bd4\u5982\u4ece\u9ad8\u7a7a\u629b\u4e0b\u4e00\u4e2a\u7269\u4f53\uff0c\u4ece\u5730\u9762\u53cd\u5f39\u540e\u65e0\u6cd5\u56de\u5230\u539f\u4f4d\uff0c\u5219\u4e0d\u662f\u6df7\u6c8c\u7684\u3002\u4e00\u822c\u4eba\u66f4\u719f\u6089\u7684\u201c\u8774\u8776\u6548\u5e94\u201d\u5219\u662f\u6307\u7b2c\u4e09\u6761\u3002\u5728\u7ecf\u5178\u6df7\u6c8c\u4e2d\uff0c\u4e00\u822c\u5b9a\u4e49<\/span>\uff0c\u5176\u4e2d<\/span>\u03b4<\/em>(<\/span>t<\/em>)\u662f\u4e24\u6761\u8d77\u70b9\u76f8\u4e92\u63a5\u8fd1\u7684\u8fd0\u52a8\u8f68\u8ff9\u4e4b\u5dee\uff0c<\/span>\u03be<\/em>\u662fLiapunov\u6307\u6570\uff0c\u5b83\u4e3a\u6b63\u65f6\u5c31\u662f\u6df7\u6c8c\u7684\u3002\u7531\u4e8e\u8fd0\u52a8\u8f68\u8ff9\u6709\u754c\uff0c\u6240\u4ee5<\/span>\u03b4<\/em>(<\/span>t<\/em>)\u968f\u7740\u65f6\u95f4\u6f14\u5316\u5e76\u4e0d\u4f1a\u65e0\u9650\u589e\u52a0\uff0c\u800c\u662f\u4f1a\u9010\u6e10\u8d8b\u4e8e\u9971\u548c\uff0c\u6240\u4ee5\u4e3a\u4e86\u771f\u5b9e\u53cd\u6620\u6307\u6570\u654f\u611f\u6027\uff0c\u5728\u5b9e\u9645\u8ba1\u7b97\u65f6\u5f80\u5f80\u8981\u6620\u5c04\u5230\u6b63\u5207\u7a7a\u95f4\uff0c\u4e5f\u5c31\u662f\u8fd0\u52a8\u8f68\u8ff9\u7684\u5bfc\u6570\u6240\u5f20\u6210\u7684\u7a7a\u95f4\u3002<\/span><\/span><\/section>\n

<\/section>\n
\u503c\u5f97\u4e00\u63d0\u7684\u662f\uff0cLiapunov\u6307\u6570\u662f\u7ecf\u5178\u6df7\u6c8c\u7406\u8bba\u7684\u6982\u5ff5\u3002\u5728\u91cf\u5b50\u529b\u5b66\u7684\u6846\u67b6\u4e0b\uff0c\u5982\u679c\u6ce2\u51fd\u6570\u4e25\u683c\u6309\u859b\u5b9a\u8c14\u65b9\u7a0b\u6f14\u5316\uff0c\u5373\u4f7f\u5728\u6b63\u5207\u7a7a\u95f4\u4e2d\u4e5f\u5f88\u96be\u770b\u5230\u03b4<\/em>(t<\/em>)\u968fe\u6307\u6570\u53d1\u6563\u7684\u884c\u4e3a\u3002\u6309\u7167Ehrenfest\u5bf9\u6b64\u7684\u89e3\u91ca\uff0c\u9700\u8981\u5b9a\u4e49\u4e00\u4e2a\u5207\u65ad\u65f6\u95f4<\/span> (break time)<\/span>\uff0c\u5728\u8fd9\u4e2a\u65f6\u95f4\u5185\uff0c\u91cf\u5b50\u4f53\u7cfb\u7684\u6f14\u5316\u5e94\u5f53\u4e0e\u7ecf\u5178\u6df7\u6c8c\u5bf9\u5e94\uff0c\u53cd\u4e4b\u5219\u4e0d\u5b58\u5728\u6df7\u6c8c\u7684\u73b0\u8c61\u3002\u6700\u521d\uff0c\u5207\u65ad\u65f6\u95f4\u88ab\u8ba4\u4e3a\u5c31\u662f\u666e\u6717\u514b\u65f6\u95f4\uff0c\u4f46\u968f\u7740\u7406\u89e3\u7684\u6df1\u5165\uff0c\u8fd9\u4e00\u5b9a\u4e49\u8d8a\u6765\u8d8a\u4e0d\u88ab\u8ba4\u53ef\u3002<\/span><\/section>\n

<\/section>\n
\u7b2c\u4e8c\u79cd\u5e38\u7528\u7684\u9274\u522b\u6df7\u6c8c\u7684\u6307\u6807\u662f\u63cf\u8ff0\u56de\u5f52\u6027\u7684\u5e9e\u52a0\u83b1\u6620\u5c04\u3002\u4ece\u9ad8\u7ef4\u7684\u7a7a\u95f4\u5207\u51fa\u4e00\u4e2a\u4efb\u610f\u7684\u5e73\u9762\uff0c\u8fd0\u52a8\u8f68\u8ff9\u6bcf\u7a7f\u8fc7\u8be5\u5e73\u9762\u4e00\u6b21\uff0c\u5c31\u5728\u8fd9\u4e2a\u5e73\u9762\u4e0a\u6253\u4e00\u4e2a\u70b9\u3002\u8db3\u591f\u957f\u65f6\u95f4\u540e\uff0c\u89c4\u5219\u7684\u4e24\u4f53\u7cfb\u7edf\u53ea\u4f1a\u51fa\u73b0\u6781\u5c11\u6570\u7684\u70b9\uff0c\u5fae\u6270\u7684\u4e09\u4f53\u7cfb\u7edf\u4f1a\u51fa\u73b0\u4e00\u4e9b\u6709\u89c4\u5f8b\u7684\u66f2\u7ebf\uff0c\u6df7\u6c8c\u7cfb\u7edf\u5219\u4f1a\u904d\u5386\u6574\u4e2a\u5e73\u9762\uff0c\u8fd9\u6b63\u662f\u7528\u6765\u7406\u89e3\u5404\u6001\u5386\u7ecf\u7684\u5e38\u7528\u56fe\u50cf\u3002<\/span><\/section>\n

<\/section>\n
\u76ee\u524d\u9488\u5bf9\u91cf\u5b50\u6df7\u6c8c\u7684\u7814\u7a76\u4e2d\uff0c\u4f7f\u7528\u6700\u591a\u7684\u6307\u6807\u662f\u80fd\u7ea7\u5206\u5e03\u3002\u7531\u4e8e\u53ef\u79ef\u6027\u7684\u5dee\u5f02\uff0c\u6df7\u6c8c\u7cfb\u7edf\u7684\u80fd\u7ea7\u662f\u4e92\u65a5\u7684<\/span> (level repulsion)<\/span>\uff0c\u800c\u53ef\u79ef\u7cfb\u7edf\u5219\u662f\u805a\u7c07\u7684<\/span> (level clustering)<\/span>\u3002\u524d\u8005\u7684\u80fd\u7ea7\u95f4\u8ddd\u8868\u73b0\u4e3a\u9ad8\u65af\u5206\u5e03\uff0c\u540e\u8005\u8868\u73b0\u4e3a\u6cca\u677e\u5206\u5e03\uff0c\u8fd9\u662f\u7528\u6765\u5206\u8fa8\u91cf\u5b50\u70ed\u5316\u6001\u4e0e\u5c40\u57df\u6001\u7684\u91cd\u8981\u6307\u6807\u3002\u80fd\u7ea7\u4e92\u65a5\u6b63\u662f\u81ea\u7136\u754c\u53bb\u7b80\u5e76\u503e\u5411\u7684\u4f53\u73b0\uff0c\u56e0\u6b64\u7edd\u5927\u591a\u6570\u81ea\u7136\u7cfb\u7edf\u503e\u5411\u4e8e\u6df7\u6c8c\u4e0e\u70ed\u5316\uff0c\u8fd9\u662f\u6211\u4eec\u5c06\u70ed\u529b\u5b66\u91cf\u5b50\u5316\u7684\u7406\u8bba\u57fa\u7840\u3002<\/span><\/section>\n

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4. \u91cf\u5b50\u70ed\u5316\u7406\u8bba<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


<\/p>\n

2008\u5e74\uff0cM. Rigol\u7b49\u4eba\u5728Nature<\/em>\u6742\u5fd7\u4e0a\u53d1\u8868\u6587\u7ae0[6]\uff0c\u7ffb\u5f00\u4e86\u91cf\u5b50\u70ed\u5316\u9886\u57df\u5168\u65b0\u7684\u4e00\u9875\uff0c\u8fd9\u5957\u5168\u65b0\u7684\u7406\u8bba\u73b0\u5728\u4e00\u822c\u88ab\u79f0\u4e3a<\/span>\u672c\u5f81\u6001\u70ed\u5316\u5047\u8bf4<\/span> <\/span><\/strong>(eigenstate thermalization hypothesis\uff0cETH) <\/span>\u3002<\/span><\/section>\n

<\/section>\n
\u91cf\u5b50\u70ed\u5316\u7406\u8bba\u7684\u51fa\u53d1\u70b9\uff0c\u662f\u4e3a\u91cf\u5b50\u591a\u4f53\u7cfb\u7edf\u5efa\u7acb\u4e00\u4e2a\u65b0\u7684\u5409\u5e03\u65af\u7cfb\u7efc\uff0c\u901a\u5e38\u53eb\u505a\u5e7f\u4e49\u5409\u5e03\u65af\u7cfb\u7efc<\/span> (generalized Gibbs ensemble\uff0cGGE)<\/span>\u3002\u5b83\u7684\u6838\u5fc3\u601d\u60f3\u4e0d\u518d\u662f\u50cf\u4f20\u7edf\u91cf\u5b50\u7edf\u8ba1\u90a3\u6837\u4ee5\u67d0\u4e9b\u5fae\u89c2\u7c92\u5b50\u4f5c\u4e3a\u7cfb\u7edf\uff0c\u800c\u662f\u4ee5\u76f8\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u5c40\u57df\u7a7a\u95f4\u8303\u56f4\u4f5c\u4e3a\u7cfb\u7edf\uff0c\u8fd9\u662f\u6700\u6838\u5fc3\u7684\u89c6\u89d2\u8f6c\u53d8\u3002\u5728\u8fd9\u4e2a\u65b0\u89c6\u89d2\u4e0b\uff0c\u80fd\u91cf\u72b6\u6001\u7684\u4e0d\u53ef\u533a\u5206\u6027\u53ef\u4ee5\u7528\u6765\u53d6\u4ee3\u5fae\u89c2\u7c92\u5b50\u7684\u4e0d\u53ef\u533a\u5206\u6027\uff0c\u4ece\u800c\u53ef\u4ee5\u5728\u5fae\u89c2\u72b6\u6001\u7684\u5c42\u9762\u91cd\u65b0\u5b9a\u4e49\u70ed\u5316\u3002<\/span><\/section>\n

<\/section>\n
<\/section>\n
\u56fe2 \u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u7cfb\u7edf<\/span><\/section>\n

<\/span><\/section>\n
\u5728\u7ecf\u5178\u7edf\u8ba1\u7684\u56fe\u50cf\u4e2d\uff0c\u5982\u56fe2\u6240\u793a\uff0c\u8981\u60f3\u4ece\u6574\u4e2a\u5b87\u5b99\u7684\u76f8\u7a7a\u95f4\u91cc\u5206\u79bb\u51fa\u4e00\u4e2a\u6211\u4eec\u611f\u5174\u8da3\u7684\u7cfb\u7edf\uff0c\u9700\u8981\u628a\u8fd9\u4e2a\u7cfb\u7edf\u7684\u5168\u90e8\u81ea\u7531\u5ea6\u62ff\u51fa\u6765\uff0c\u5c31\u50cf\u5e9e\u52a0\u83b1\u6620\u5c04\uff0c\u5728\u4e00\u4e2a\u4e09\u7ef4xyz<\/em>\u7684\u7a7a\u95f4\u4e2d\u628a\u4e00\u6574\u4e2axy<\/em>\u622a\u9762\u5168\u90e8\u62bd\u51fa\u6765\uff0c\u6784\u6210\u4e00\u4e2a\u7cfb\u7edf\u3002\u6211\u4eec\u4e0d\u80fd\u53ea\u622a\u53d6\u8fd9\u4e2a\u7a7a\u95f4\u5185\u7684\u4e00\u4e2a\u5c40\u57df\u8303\u56f4\uff0c\u6bd4\u5982\u4e00\u4e2a\u5c0f\u65b9\u5757\uff0c\u56e0\u4e3a\u5b83\u5e76\u4e0d\u5305\u542b\u5b8c\u5907\u7684\u81ea\u7531\u5ea6\u3002\u7136\u800c\u5728\u91cf\u5b50\u70ed\u5316\u7406\u8bba\u4e2d\uff0c\u4f8b\u5982\u4e00\u7ef4x<\/em>\u65b9\u5411\u7684\u94fe\uff0c\u6211\u4eec\u53ef\u4ee5\u53ea\u62bd\u53d6\u5176\u4e2d\u82e5\u5e72\u4e2a\u683c\u70b9\u4f5c\u4e3a\u7cfb\u7edf\uff0c\u4e0d\u7528\u628a\u6574\u4e2a\u4e00\u7ef4\u94fe<\/span> (x<\/em>\u65b9\u5411\u81ea\u7531\u5ea6) <\/span>\u5168\u90e8\u62ff\u51fa\u6765\u3002<\/span><\/section>\n

<\/section>\n
\u5f53\u6211\u4eec\u628a\u76f8\u7a7a\u95f4\u4e2d\u67d0\u4e2a\u5c40\u57df\u8303\u56f4<\/span> (\u800c\u4e0d\u662f\u67d0\u4e2a\u7c92\u5b50) <\/span>\u4f5c\u4e3a\u7cfb\u7edf\uff0c\u5269\u4e0b\u7684\u8303\u56f4\u4f5c\u4e3a\u73af\u5883\uff0c\u73af\u5883\u901a\u8fc7\u4e0e\u7cfb\u7edf\u7684\u8026\u5408\u7834\u574f\u7cfb\u7edf\u7684\u67d0\u4e9b\u5bf9\u79f0\u6027\uff0c\u4f7f\u5f97\u7cfb\u7edf\u53ef\u80fd\u5230\u8fbe\u7684\u76f8\u7a7a\u95f4 <\/span>(\u81ea\u7531\u5ea6) <\/span>\u5f97\u4ee5\u6269\u5927\uff0c\u8fd9\u4e9b\u65b0\u81ea\u7531\u5ea6\u6b63\u662f\u7531\u73af\u5883\u63d0\u4f9b\u6216\u8005\u6620\u5c04\u5230\u7cfb\u7edf\u4e0a\u7684\u3002\u53cd\u6620\u5728\u91cf\u5b50\u6d4b\u91cf\u8bba\u4e2d\uff0c\u5c31\u662f\u73af\u5883\u626e\u6f14\u4e00\u4e2a\u5b8f\u89c2\u6d4b\u91cf\u8005\u7684\u89d2\u8272\uff0c\u901a\u8fc7\u6d4b\u91cf\u6253\u5f00\u7cfb\u7edf\u7684\u65b0\u81ea\u7531\u5ea6\uff0c\u7528\u6570\u5b66\u8bed\u8a00\u6765\u8bb2\u5c31\u662f\u73af\u5883\u7684\u67d0\u4e9b\u7b97\u7b26\u4e0e\u7cfb\u7edf\u7684\u54c8\u5bc6\u987f\u91cf\u4e0d\u5bf9\u6613\uff0c\u4ece\u800c\u4e0d\u80fd\u4e3a\u7cfb\u7edf\u627e\u5230\u8db3\u591f\u591a\u7684\u5c40\u57df\u8fd0\u52a8\u79ef\u5206\u3002<\/span><\/section>\n

<\/section>\n
\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u5c31\u6709\u4e86ETH\u7684\u57fa\u672c\u8bba\u8ff0[7]\u3002ETH\u4e00\u822c\u5206\u4e3a\u4e24\u90e8\u5206\u5185\u5bb9\uff0c\u4e00\u662f\u5bf9\u89d2\u70ed\u5316\u5047\u8bf4\uff0c\u4e8c\u662f\u975e\u5bf9\u89d2\u70ed\u5316\u5047\u8bf4\u3002\u8003\u8651\u4e00\u7cfb\u5217\u7b97\u7b26<\/span>\uff0c\u7b2c\u4e00\u6761\u662f\u6307\uff0c\u5b83\u5728\u5fae\u6b63\u5219\u7cfb\u7efc\u4e2d\u7684\u5e73\u5747\u503c\uff0c\u7b49\u4e8e\u5176\u5728\u54c8\u5bc6\u987f\u91cf\u4e0d\u540c\u672c\u5f81\u6001\u4e0a\u5e73\u5747\u503c\u7684\u7b49\u6743\u91cd\u6c42\u548c\uff0c\u5373<\/span>\uff0c\u5176\u4e2d\u03b5i <\/sub><\/em>\u7684\u53d6\u503c\u8303\u56f4\u662f\u7ed9\u5b9a\u7684\u80fd\u91cf\u8303\u56f4[E<\/em>, E<\/em>+\u03b4<\/em>]\uff0cD<\/em>\u4ee3\u8868\u76f8\u5e94\u80fd\u91cf\u8303\u56f4\u5185\u91cf\u5b50\u6001\u7684\u4e2a\u6570\u3002\u7b2c\u4e8c\u6761\u662f\u6307\uff0c<\/span>\u7684\u975e\u5bf9\u89d2\u5143<\/span>\u968f\u7740\u03b5i <\/sub><\/em>\u548c\u03b5j <\/sub><\/em>\u7684\u80fd\u91cf\u5dee\u968f\u673a\u53d8\u5316\u5e76\u5feb\u901f\u8870\u51cf\u81f30\u3002<\/span><\/section>\n

<\/section>\n
\u9700\u8981\u6307\u51fa\uff0c\u65e0\u8bba\u9488\u5bf9\u54ea\u4e00\u6761\u6211\u4eec\u90fd\u5f88\u5bb9\u6613\u627e\u51fa\u53cd\u4f8b\u3002\u6bd4\u5982\u53ea\u8981\u4ee4<\/span>\u662f\u54c8\u5bc6\u987f\u91cf\u7684\u67d0\u4e2a\u7279\u5b9a\u6cdb\u51fd\uff0c\u5c31\u81ea\u52a8\u4e0d\u6ee1\u8db3\u7b2c\u4e00\u6761\u3002\u6216\u8005\u4ee4<\/span>\u662f\u67d0\u4e2a\u7b97\u7b26\u7684\u5e73\u65b9\uff0c\u5c31\u4e00\u5b9a\u4e0d\u6ee1\u8db3\u7b2c\u4e8c\u6761\u3002\u6240\u4ee5\u5728\u5b9e\u9645\u64cd\u4f5c\u65f6\uff0c<\/span>\u7684\u9009\u53d6\u5e76\u4e0d\u4efb\u610f\uff0c\u800c\u662f\u8981\u9009\u62e9\u81ea\u7531\u5ea6\u8f83\u5c0f\u7684\u5c40\u57df\u7b97\u7b26\uff0c\u4e00\u822c\u662f\u67d0\u4e2a\u5bf9\u79f0\u6027\u4e0d\u53ef\u7ea6\u7684\u4ea7\u751f\u5b50\uff0c\u4ece\u800c\u5c3d\u91cf\u907f\u514d\u4e0a\u8ff0\u95ee\u9898\u3002<\/span><\/section>\n

<\/section>\n
\u7531\u4e8e\u4e0d\u518d\u5c06\u5355\u4e2a\u7c92\u5b50\u5f53\u4f5c\u7cfb\u7edf\uff0c\u800c\u662f\u5c06\u5c40\u57df\u7684\u7a7a\u95f4\u5f53\u4f5c\u7cfb\u7edf\uff0c\u6240\u4ee5\u8bb8\u591a\u7ecf\u5178\u70ed\u7edf\u7684\u89c2\u5ff5\u90fd\u8981\u6709\u6240\u8f6c\u53d8\u3002\u6bd4\u5982\uff0c\u7ecf\u5178\u70ed\u529b\u5b66\u901a\u5e38\u8ba4\u4e3a\u7a7a\u95f4\u52bf\u80fd\u7684\u65e0\u5e8f\u5ea6\u8d8a\u9ad8\u8d8a\u5bb9\u6613\u70ed\u5316\uff0c\u7ecf\u5178\u6df7\u6c8c\u7406\u8bba\u4e5f\u8fd9\u6837\u8ba4\u4e3a\u3002\u91cf\u5b50\u70ed\u5316\u7406\u8bba\u5219\u76f8\u53cd\uff0c\u7a7a\u95f4\u8d8a\u65e0\u5e8f\u8d8a\u5bb9\u6613\u5c40\u57df\u5316\uff0c\u4ece\u800c\u96be\u4ee5\u70ed\u5316\u3002\u56e0\u6b64\uff0c\u6211\u4eec\u4e0d\u80fd\u518d\u50cf\u7ecf\u5178\u6df7\u6c8c\u90a3\u6837\u4ee5\u5168\u5c40\u7684\u5b88\u6052\u91cf\uff0c\u6bd4\u5982\u80fd\u91cf\u3001\u52a8\u91cf\u3001\u89d2\u52a8\u91cf\u7b49\u6765\u4f5c\u4e3a\u5224\u65ad\u662f\u5426\u53ef\u79ef\u7684\u6807\u51c6\u3002\u5728\u91cf\u5b50\u70ed\u5316\u7406\u8bba\u4e2d\uff0c\u5373\u4fbf\u6211\u4eec\u80fd\u627e\u5230\u8db3\u591f\u591a\u7684\u5168\u5c40\u8fd0\u52a8\u79ef\u5206\uff0c\u5bf9\u5e94\u4e8e\u7ecf\u5178\u53ef\u79ef\u7684\u60c5\u51b5\u4e0b\uff0c\u7cfb\u7edf\u4ecd\u7136\u6709\u53ef\u80fd\u662f\u70ed\u5316\u7684\u3002\u6211\u4eec\u8981\u5bfb\u627e\u7684\u662f\u5c40\u57df\u8fd0\u52a8\u79ef\u5206<\/span> (local integral of motion)<\/span>\uff0c\u5b83\u4eec\u7684\u6570\u91cf\u4e0e\u5c40\u57df\u72b6\u6001\u6570\u7684\u5173\u7cfb\uff0c\u51b3\u5b9a\u4e86\u4e00\u4e2a\u7cfb\u7edf\u662f\u70ed\u5316\u7684\uff0c\u8fd8\u662f\u5c40\u57df\u5316\u7684\u3002<\/span><\/section>\n

<\/section>\n
\u4e0d\u540c\u5c40\u57df\u8fd0\u52a8\u79ef\u5206\u4e4b\u95f4\u7406\u5e94\u4e92\u76f8\u5bf9\u6613\uff0c\u6bd4\u5982\u4e0d\u540c\u683c\u70b9\u7684\u81ea\u65cb\u7b97\u7b26\u603b\u662f\u5bf9\u6613\u7684\uff0c\u6240\u4ee5\u6574\u4e2a\u54c8\u5bc6\u987f\u91cf\u672a\u5fc5\u4f1a\u5b58\u5728\u7b80\u5e76\u6027\u3002\u6309\u7167\u91cf\u5b50\u6df7\u6c8c\u7406\u8bba\uff0c\u8fd9\u5e94\u8be5\u662f\u70ed\u5316\u7684\u60c5\u51b5\u3002\u7684\u786e\u5982\u6b64\uff0c\u5373\u4f7f\u5b58\u5728\u5c40\u57df\u8fd0\u52a8\u79ef\u5206\uff0c\u73af\u5883\u5bf9\u7cfb\u7edf\u5bf9\u79f0\u6027\u7684\u7834\u574f\u4f5c\u7528\u4ecd\u975e\u5e38\u666e\u9002\uff0c\u8fd9\u4e5f\u662f\u70ed\u5316\u53d1\u751f\u4e8e\u7edd\u5927\u591a\u6570\u7cfb\u7edf\u7684\u539f\u56e0\u3002\u7b80\u5e76\u6027\u7684\u4fdd\u62a4\u9700\u8981\u5728\u5c40\u57df\u8fd0\u52a8\u79ef\u5206\u7684\u57fa\u7840\u4e0a\uff0c\u8fdb\u4e00\u6b65\u5f15\u5165\u5bf9\u79f0\u6027\u3001\u62d3\u6251\u3001\u591a\u4f53\u76f8\u4e92\u4f5c\u7528\u7b49\u5176\u4ed6\u56e0\u7d20\u3002<\/span><\/section>\n

<\/section>\n
ETH\u548c\u7ecf\u5178\u7edf\u8ba1\u4e2d\u7684\u5404\u6001\u5386\u7ecf\u5047\u8bf4\u7a76\u7adf\u6709\u4ec0\u4e48\u4e0d\u540c\uff1f\u7b14\u8005\u8ba4\u4e3a\uff0cETH\u6700\u5927\u7684\u4f18\u70b9\u5e76\u4e0d\u5728\u4e8e\u5b83\u63cf\u8ff0\u4e86\u201c\u7edd\u5927\u591a\u6570\u201d\u7cfb\u7edf\u7684\u884c\u4e3a\uff0c\u800c\u662f\u5b83\u7ed9\u51fa\u4e86\u4e0d\u6ee1\u8db3\u5404\u6001\u5386\u7ecf\u7684\u660e\u786e\u6761\u4ef6\u3002\u5404\u6001\u5386\u7ecf\u867d\u7136\u662f\u7ecf\u5178\u7edf\u8ba1\u7684\u57fa\u672c\u5047\u5b9a\uff0c\u4f46\u5b83\u4e0d\u540c\u4e8e\u5176\u4ed6\u7269\u7406\u7406\u8bba\uff0c\u5176\u9884\u6d4b\u6027\u5dee\uff0c\u53c8\u96be\u4ee5\u8bc1\u4f2a\uff0c\u603b\u662f\u4f1a\u4ea7\u751f\u5404\u79cd\u4f3c\u662f\u800c\u975e\u7684\u7ed3\u679c\u3002\u800c\u5728ETH\u7684\u5b9a\u4e49\u4e2d\uff0c\u5bf9\u4e8e\u5148\u9a8c\u6210\u7acb\u7684\u5404\u6001\u5386\u7ecf\u5047\u8bf4\uff0c\u6211\u4eec\u6709\u4e86\u53ef\u4ee5\u5b9a\u91cf\u8bc1\u4f2a\u5b83\u7684\u65b9\u6848\uff0c\u8fd9\u662f\u4e86\u4e0d\u8d77\u7684\u8fdb\u6b65\u3002<\/span><\/section>\n

<\/section>\n

<\/section>\n

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<\/svg><\/section>\n<\/section>\n<\/section>\n
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5. \u5c40\u57df\u5316<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n

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


<\/p>\n

\u63d0\u5230\u5c40\u57df\u5316\u4e00\u8bcd\uff0c\u5f88\u5bb9\u6613\u60f3\u5230\u7684\u662f\u5b89\u5fb7\u68ee\u5c40\u57df\u5316\u3002\u7136\u800c\uff0c\u8d6b\u8d6b\u6709\u540d\u7684\u5c40\u57df\u5316\u5728\u5f88\u957f\u65f6\u95f4\u5185\u5176\u5b9e\u90fd\u672a\u6210\u4e3a\u663e\u5b66\uff0c\u56fd\u5185\u8bb8\u591a\u201c\u56fa\u4f53\u7269\u7406\u201d\u8bfe\u7a0b\u4e2d\uff0c\u201c\u5c40\u57df\u5316\u201d\u4e09\u4e2a\u5b57\u57fa\u672c\u662f\u4e00\u7b14\u5e26\u8fc7\u3002\u96f6\u661f\u7684\u7814\u7a76\u4ee5\u5bfc\u7535\u673a\u7406\u4e3a\u4e3b\uff0c\u6709\u4e0d\u5c11\u4eba\u8fdb\u5165\u8be5\u9886\u57df\u662f\u57fa\u4e8e\u5b89\u5fb7\u68ee\u3001\u83ab\u7279\u7b49\u4eba\u7684\u540d\u58f0\u3002\u57fa\u4e8e\u5386\u53f2\u4f20\u7edf\uff0c\u56fa\u4f53\u7269\u7406\u4e2d\u7814\u7a76\u66f4\u591a\u7684\u662f\u6676\u4f53\u7269\u7406\uff0c\u7528\u80fd\u5e26\u548c\u80fd\u9699\u6765\u533a\u5206\u91d1\u5c5e\u3001\u534a\u5bfc\u4f53\u548c\u7edd\u7f18\u4f53\u662f\u7269\u7406\u5b66\u5bb6\u66f4\u4e60\u60ef\u7684\u601d\u8003\u65b9\u5f0f\uff0c\u505a\u7b2c\u4e00\u6027\u539f\u7406\u8ba1\u7b97\u65f6\uff0c\u6676\u80de\u603b\u662f\u5c3d\u53ef\u80fd\u53d6\u5c0f\u4ee5\u51cf\u8f7b\u8ba1\u7b97\u91cf\u3002\u5982\u56fe3\u6240\u793a\uff0c\u5c40\u57df\u5316\u7684\u7814\u7a76\u9700\u8981\u5728\u683c\u5b50\u6a21\u578b\u4e2d\u5f15\u5165\u65e0\u5e8f\uff0c\u7834\u574f\u5e73\u79fb\u5bf9\u79f0\u6027\uff0c\u8fd9\u4e0e\u6676\u4f53\u7684\u8ba1\u7b97\u5e76\u4e0d\u5b8c\u5168\u76f8\u5bb9\u3002\u7531\u6b64\uff0c\u5c40\u57df\u5316\u5728\u5f88\u957f\u65f6\u95f4\u5185\u90fd\u50cf\u662f\u5316\u5b66\u8bed\u8a00\u3002\u5316\u5b66\u5bb6\u4e0d\u6267\u7740\u4e8e\u6676\u4f53\uff0c\u66f4\u5173\u6ce8\u65e0\u5e8f\u6240\u5e26\u6765\u7684\u8f7d\u6d41\u5b50\u5c40\u57df\u5316\uff0c\u5e76\u53d1\u5c55\u51fa\u8bf8\u5982\u6781\u5316\u5b50\u8fc1\u79fb\u4e4b\u7c7b\u7684\u5bfc\u7535\u673a\u7406\u3002\u5229\u7528Marcus\u7406\u8bba\u3001\u52bf\u80fd\u9762\u8dc3\u8fc1\u7b49\u534a\u7ecf\u9a8c\u7406\u8bba\uff0c\u5316\u5b66\u5bb6\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u80fd\u5904\u7406\u597d\u5bfc\u7535\u7684\u91cf\u5b50\u6027\u95ee\u9898\u3002<\/span><\/section>\n

<\/section>\n
<\/section>\n
\u56fe3 \u70ed\u5316\u4e0e\u5c40\u57df\u5316<\/span><\/section>\n

<\/section>\n
\u5982\u4eca\uff0c\u5c40\u57df\u5316\u88ab\u63d0\u5347\u5230\u7269\u8d28\u79d1\u5b66\u6700\u672c\u539f\u7684\u7a0b\u5ea6\u6765\u7814\u7a76\uff0c\u8131\u79bb\u4e86\u91d1\u5c5e\u2014\u7edd\u7f18\u4f53\u8f6c\u53d8\u7b49\u5177\u4f53\u95ee\u9898\u7684\u675f\u7f1a\uff0c\u662f\u7269\u8d28\u79d1\u5b66\u5bb6\u4eec\u5bf9\u91cf\u5b50\u70ed\u5316\u7406\u8bba\u7684\u56de\u5e94\u3002\u7814\u7a76\u5c40\u57df\u5316\u7684\u6838\u5fc3\u6b63\u662f\u5bfb\u627e\u91cf\u5b50\u8d44\u6e90\uff0c\u662f\u627e\u5230\u63a8\u52a8\u4eba\u7c7b\u8fdb\u6b65\u7684\u65b0\u6750\u6599\u3002\u5982\u679c\u4e07\u7269\u90fd\u4f1a\u88ab\u70ed\u5316\uff0c\u7269\u8d28\u79d1\u5b66\u5bb6\u4eec\u4e5f\u8981\u81f4\u529b\u4e8e\u627e\u51fa\u90a3\u4e07\u5206\u4e4b\u4e00\u4e0d\u4f1a\u88ab\u70ed\u5316\u7684\u91cf\u5b50\u7269\u8d28\u3002<\/span><\/section>\n

<\/section>\n
\u80fd\u5e26\u7684\u51fa\u73b0\u662f\u4e0d\u540c\u539f\u5b50\u4e0a\u539f\u672c\u7b80\u5e76\u7684\u5c40\u57df\u8f68\u9053\u5728\u7535\u5b50\u52a8\u80fd\u7684\u4f5c\u7528\u4e0b\u53d1\u751f\u4e86\u53bb\u7b80\u5e76\u6548\u5e94\uff0c\u4e5f\u5c31\u662f\u53d1\u751f\u4e86\u70ed\u5316\uff0c\u4ece\u800c\u5f62\u6210\u80fd\u7ea7\u4e92\u65a5\u3002\u5316\u5b66\u4e0a\uff0c\u8fd9\u662f\u6210\u952e\u548c\u53cd\u952e\u8f68\u9053\u5f62\u6210\u7684\u539f\u56e0\u3002\u5373\u4f7f\u6211\u4eec\u5c06\u4efb\u610f\u6742\u8d28\u653e\u8fdb\u4f53\u6750\u6599\u4e2d\uff0c\u8be5\u6742\u8d28\u7684\u80fd\u7ea7\u51fa\u73b0\u5728\u80fd\u5e26\u91cc\u9762\uff0c\u6742\u8d28\u8f68\u9053\u4ecd\u7136\u4f1a\u4e0e\u6bcd\u4f53\u6750\u6599\u4e2d\u7684\u539f\u5b50\u8f68\u9053\u6742\u5316\uff0c\u4f7f\u6211\u4eec\u770b\u4e0d\u6e05\u6742\u8d28\u548c\u6bcd\u4f53\u7684\u533a\u522b\u3002\u8981\u60f3\u7834\u574f\u70ed\u5316\uff0c\u6216\u5f62\u6210\u5c40\u57df\u5316\uff0c\u5fc5\u987b\u8981\u6709\u4e00\u4e9b\u975e\u51e1\u7684\u7269\u7406\u56e0\u7d20\u51fa\u73b0\u3002\u603b\u7ed3\u8d77\u6765\uff0c\u53ef\u5f52\u7ed3\u4e3a\u5982\u4e0b\u51e0\u79cd\u60c5\u51b5\u3002<\/span><\/section>\n

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\u7b2c\u4e00\u79cd\u60c5\u51b5\u662f\u6d3e\u5c14\u65af\u4e0d\u7a33\u5b9a\u6027\uff0c\u901a\u8fc7\u5728\u4e00\u7ef4\u4f53\u7cfb\u4e2d\u5f15\u5165\u6676\u683c\u539f\u5b50\u5fae\u5c0f\u632f\u52a8\uff0c\u5728\u539f\u672c\u7684\u80fd\u5e26\u4e2d\u5288\u88c2\u51fa\u65b0\u7684\u80fd\u9699\uff0c\u5e76\u5728\u80fd\u9699\u5185\u90e8\u5f62\u6210\u9699\u95f4\u6001\uff0c\u4f8b\u5982\u5b64\u5b50\u3001\u6781\u5316\u5b50\u7b49\u3002\u4e00\u822c\u8ba4\u4e3a\uff0c\u4e00\u7ef4\u4f53\u7cfb\u4e2d\u5373\u4f7f\u518d\u5f31\u7684\u65e0\u5e8f\u4e5f\u4f1a\u5bfc\u81f4\u5c40\u57df\u5316\uff0c\u8fd9\u5c31\u662f\u201c\u4e00\u7ef4\u4f53\u7cfb\u65e0\u91d1\u5c5e\u201d\u5b9a\u5f8b\u3002\u8fd9\u4e0e\u6df7\u6c8c\u7406\u8bba\u81ea\u6d3d\uff0c\u56e0\u4e3a\u7ef4\u5ea6\u8d8a\u4f4e\u8d8a\u96be\u4ee5\u70ed\u5316\uff0c\u5373\u4f7f\u662f\u54c8\u4f2f\u5fb7\u6a21\u578b\u8fd9\u6837\u5e73\u79fb\u7b80\u5e76\u7684\u5c40\u57df\u8f68\u9053\u5728\u7535\u5b50\u52a8\u80fd\u7684\u4f5c\u7528\u4e0b\u53d1\u751f\u4e86\u53bb\u7b80\u5e76\u6548\u5e94\uff0c\u4e5f\u5c31\u662f\u53d1\u751f\u4e86\u70ed\u5316\uff0c\u4ece\u800c\u5f62\u6210\u80fd\u7ea7\u4e92\u65a5\u3002\u5316\u5b66\u4e0a\uff0c\u8fd9\u662f\u6210\u952e\u548c\u53cd\u952e\u8f68\u9053\u5f62\u6210\u7684\u539f\u56e0\u3002\u5373\u4f7f\u6211\u4eec\u5c06\u4efb\u610f\u6742\u8d28\u653e\u8fdb\u4f53\u6750\u6599\u4e2d\uff0c\u8be5\u6742\u8d28\u7684\u80fd\u7ea7\u51fa\u73b0\u5728\u80fd\u5e26\u91cc\u9762\uff0c\u6742\u8d28\u8f68\u9053\u4ecd\u7136\u4f1a\u4e0e\u6bcd\u4f53\u6750\u6599\u4e2d\u7684\u539f\u5b50\u8f68\u9053\u6742\u5316\uff0c\u4f7f\u6211\u4eec\u770b\u4e0d\u6e05\u6742\u8d28\u548c\u6bcd\u4f53\u7684\u533a\u522b\u3002\u8981\u60f3\u7834\u574f\u70ed\u5316\uff0c\u6216\u5f62\u6210\u5c40\u57df\u5316\uff0c\u5fc5\u987b\u8981\u6709\u4e00\u4e9b\u975e\u51e1\u7684\u7269\u7406\u56e0\u7d20\u51fa\u73b0\u3002\u603b\u7ed3\u8d77\u6765\uff0c\u53ef\u5f52\u7ed3\u4e3a\u5982\u4e0b\u51e0\u79cd\u60c5\u51b5\u3002\u4e0d\u53d8\u7684\u7cfb\u7edf\uff0c\u4e5f\u53ea\u80fd\u662f\u5f31\u70ed\u5316\u3002<\/span><\/section>\n

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\u7b2c\u4e8c\u79cd\u60c5\u51b5\u662f\u5728\u4e09\u7ef4\u4f53\u7cfb\u4e2d\uff0c\u6742\u8d28\u80fd\u7ea7\u51fa\u73b0\u5728\u80fd\u5e26\u5916\u9762\u7684\u60c5\u51b5\u3002\u4ee5\u6807\u51c6\u7684\u7d27\u675f\u7f1a\u6a21\u578b\u4e3a\u4f8b\uff0c\u8003\u8651\u6bcf\u4e2a\u683c\u70b9\u7684\u5728\u4f4d\u80fd\u5177\u6709\u65e0\u5e8f\u6027\uff0c\u5176\u53d8\u5316\u7684\u4e0a\u4e0b\u9650\u4e3a<\/span>\uff0c\u82e5\u7d27\u675f\u7f1a\u6a21\u578b\u7684\u5e26\u5bbd\u662fB<\/em>\uff0c\u5f53W<\/em>>B<\/em>\u65f6\uff0c\u5c31\u4f1a\u6709\u65e0\u5e8f\u7684\u80fd\u7ea7\u8dd1\u5230\u80fd\u5e26\u5916\u9762\u5f62\u6210\u5b64\u7acb\u7684\u5c40\u57df\u80fd\u7ea7\u3002<\/span>\u662f\u4e00\u4e2a\u4e34\u754c\u6307\u6807\uff0c\u5b83\u57281\u4ee5\u4e0b\u662f\u5c40\u57df\u76f8\uff0c\u57281\u4ee5\u4e0a\u662f\u70ed\u5316\u76f8\u3002<\/span><\/section>\n

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\u7b2c\u4e09\u79cd\u60c5\u51b5\u662f\u83ab\u7279\u7684\u8fc1\u79fb\u7387\u8fb9<\/span> (mobility edge) <\/span>\u548c\u53d8\u7a0b\u8dc3\u8fc1<\/span> (variablerange hopping) <\/span>\u6a21\u578b\u3002\u5728\u65e0\u5e8f\u5206\u5e03\u7684\u5728\u4f4d\u80fd\u4e2d\uff0c\u603b\u6709\u4e00\u4e9b\u80fd\u7ea7\u6781\u4e3a\u63a5\u8fd1\uff0c\u4f46\u7a7a\u95f4\u8ddd\u79bb\u5f88\u8fdc\u3002\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u7535\u5b50\u4e0d\u80fd\u50cf\u5728\u901a\u5e38\u7684\u80fd\u5e26\u4e2d\u90a3\u6837\u6b63\u5e38\u6269\u6563\uff0c\u5b83\u4eec\u4f1a\u5f62\u6210\u6df1\u5165\u5e26\u9699\u7684\u8fc1\u79fb\u7387\u8fb9\u3002\u4e3a\u4e86\u523b\u753b\u53d8\u7a0b\u8dc3\u8fc1\u8fc7\u7a0b\uff0c\u83ab\u7279\u7ed9\u51fa\u4e86\u4e00\u4e2a\u552f\u8c61\u7684\u8dc3\u8fc1\u901f\u7387\u516c\u5f0f\uff0c\u5373<\/span>\uff0c\u5176\u4e2d<\/span>r <\/em>\u548c\u0394<\/span>\u03b5 <\/em>\u5206\u522b\u662f\u8dc3\u8fc1\u521d\u672b\u6001\u95f4\u7684\u7a7a\u95f4\u8ddd\u79bb\u548c\u80fd\u91cf\u5dee\uff0c<\/span>\u03b1<\/em>\u662f\u523b\u753b\u8ddd\u79bb\u65e0\u5e8f\u5ea6\u7684\u53c2\u6570\u3002\u5982\u679c\u6211\u4eec\u8fdb\u4e00\u6b65\u5047\u5b9a\u65e0\u5e8f\u80fd\u7ea7\u7684\u80fd\u91cf\u5dee\u4e0e\u4f53\u79ef\u6210\u53cd\u6bd4\uff0c\u5373\u0394<\/span>\u03b5<\/em>=<\/span>cr<\/em>-3<\/sup>\uff0c<\/span>c<\/em>\u662f\u6bd4\u4f8b\u7cfb\u6570\uff0c\u5219\u6700\u5927\u7684\u8dc3\u8fc1\u6982\u7387\u4e3a<\/span><\/span><\/section>\n

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\u8fd9\u5c31\u662f\u8457\u540d\u7684\u7535\u5bfc\u7387<\/span>\u5f8b\uff0c\u4e0e\u5b9e\u9a8c\u5b9a\u6027\u543b\u5408\u3002<\/span><\/section>\n

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\u4e0a\u8ff0\u5c40\u57df\u5316\u672c\u8d28\u4e0a\u90fd\u662f\u5355\u7535\u5b50\u56fe\u50cf\uff0c\u800c\u5f3a\u5173\u8054\u4f53\u7cfb\u4e2d\u7531\u4e8e\u591a\u4f53\u76f8\u4e92\u4f5c\u7528\u7684\u5b58\u5728\uff0c\u4e00\u4e9b\u7b80\u5e76\u6027\u65e0\u6cd5\u88ab\u53bb\u9664\uff0c\u80fd\u7ea7\u65e0\u6cd5\u4e92\u65a5\uff0c\u4e0d\u518d\u662f\u4e25\u683c\u610f\u4e49\u4e0a\u7684\u91cf\u5b50\u70ed\u5316\u6001\uff0c\u4e5f\u65e0\u6cd5\u5199\u6210\u4efb\u4f55\u5e7f\u4e49\u5409\u5e03\u65af\u7cfb\u7efc\u5f62\u5f0f\u7684\u5c40\u57df\u5316\uff0c\u8fd9\u5c31\u662f\u6240\u8c13\u7684\u591a\u4f53\u5c40\u57df\u5316<\/span> (many-body localization\uff0cMBL)<\/span>\u3002\u8fd9\u4e2a\u8bcd\u6700\u65e9\u51fa\u73b0\u4e8e2006\u5e74D. M. Basko\u7b49\u4eba\u53d1\u8868\u5728Annals of Physics<\/em>\u4e0a\u7684\u6587<\/span>\u7ae0[8]\u3002\u4e0d<\/span>\u8fc7\u65e9\u671f\u5de5\u4f5c\u4ecd\u4ee5\u5b89\u5fb7\u68ee\u5c40\u57df\u5316\u7684\u6846\u67b6\u4e3a\u4e3b\uff0c\u53ea\u662f\u4f20\u7edf\u6a21\u578b\u7684\u7b80\u5355\u63a8\u5e7f\u3002\u771f\u6b63\u4ea7\u751f\u5f71\u54cd\u529b\u662f\u5728\u91cf\u5b50\u70ed\u5316\u7406\u8bba\u6210\u540d\u4ee5\u540e\uff0c\u91cf\u5b50\u7edf\u8ba1\u548c\u51dd\u805a\u6001\u7406\u8bba\u5f00\u59cb\u6df1\u5ea6\u878d\u5408\uff0c\u591a\u4f53\u5c40\u57df\u5316\u4e0e\u91cf\u5b50\u70ed\u5316\u6210\u4e3a\u76f8\u4e92\u5bf9\u5e94\u7684\u540d\u8bcd\uff0c\u5e76\u5e7f\u6cdb\u201c\u51fa\u5708\u201d\u3002<\/span><\/section>\n

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\u65e9\u671f\u7684\u591a\u4f53\u5c40\u57df\u5316\u7814\u7a76\u6cbf\u88ad\u70ed\u5316\u7406\u8bba\u7684\u4e60\u60ef\uff0c\u4e3b\u8981\u63a2\u8ba8\u80fd\u7ea7\u5206\u5e03\u3002\u901a\u8fc7\u5efa\u7acb\u4e00\u4e2a\u591a\u4f53\u76f8\u4e92\u4f5c\u7528\u6a21\u578b\uff0c\u52a0\u4e0a\u65e0\u5e8f\u52bf\uff0c\u8ba1\u7b97\u5176\u672c\u5f81\u80fd\u7ea7\u5206\u5e03\u662f\u4e92\u65a5\u7684\u8fd8\u662f\u805a\u7c07\u7684\uff0c\u82e5\u4e3a\u524d\u8005\u5219\u662f\u70ed\u5316\uff0c\u82e5\u4e3a\u540e\u8005\u5219\u662f\u591a\u4f53\u5c40\u57df\u5316\u3002\u8fd9\u6837\u505a\u7684\u6700\u5927\u95ee\u9898\uff0c\u662f\u96be\u4ee5\u4e0e\u70ed\u5316\u4e2d\u7684\u9884\u70ed\u5316\u3001\u5c40\u57df\u5316\u4e2d\u7684\u5b89\u5fb7\u68ee\u5c40\u57df\u5316\u76f8\u533a\u5206\u3002\u968f\u540e\u5c31\u51fa\u73b0\u4e86\u7b2c\u4e8c\u7c7b\u7814\u7a76\u65b9\u6848\uff0c\u5373\u91cf\u5b50\u6dec\u706b\u52a8\u529b\u5b66\uff0c\u6dec\u706b\u4f1a\u5bfc\u81f4\u6709\u9650\u5c3a\u5bf8\u7684\u5c40\u57df\u5b64\u5b50\u51fa\u73b0\uff0c\u8fd9\u662f\u7814\u7a76\u5c40\u57df\u5316\u975e\u5e38\u597d\u7684\u51fa\u53d1\u70b9\u3002\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u4e00\u4e2a\u5b8c\u5168\u8d85\u8d8a\u9884\u671f\u7684\u73b0\u8c61\u88ab\u53d1\u73b0\uff0c\u90a3\u5c31\u662f\u7ea0\u7f20\u71b5\u7684\u5bf9\u6570\u4f20\u64ad\u3002<\/span><\/section>\n

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\u5728\u5b89\u5fb7\u68ee\u5c40\u57df\u5316\u4e2d\uff0c\u5c40\u57df\u6001\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u662fe\u6307\u6570\u8870\u51cf\u7684\uff0c\u5373\u4e92\u76f8\u4e4b\u95f4\u5b8c\u5168\u9694\u7edd\uff0c\u4e0d\u4f1a\u53d1\u751f\u4efb\u4f55\u4fe1\u606f\u4f20\u64ad\u3002\u4f46\u5728\u591a\u4f53\u5c40\u57df\u5316\u4e2d\uff0cJ. H. Bardarson\u7b49\u4eba\u7684\u6570\u503c\u8ba1\u7b97\u7ed3\u679c\u8868\u660e[9]\uff0c\u7ea0\u7f20\u71b5\u4f1a\u5728\u5f88\u957f\u65f6\u95f4\u5185\u4ee5\u5bf9\u6570\u5f62\u5f0f\u7f13\u6162\u589e\u957f\u3002\u8fd9\u4e00\u7ed3\u679c\u5728\u8bb8\u591a\u8ba1\u7b97\u4e2d\u5f97\u4ee5\u8bc1\u5b9e\uff0c\u88ab\u786e\u8ba4\u4e3a\u591a\u4f53\u5c40\u57df\u5316\u6700\u5173\u952e\u7684\u52a8\u529b\u5b66\u7279\u5f81\uff0c\u5b83\u53cd\u6620\u4e86\u5c40\u57df\u6001\u4e4b\u95f4\u5b58\u5728\u7740\u7b49\u6548\u957f\u7a0b\u76f8\u4e92\u4f5c\u7528\u3002\u8fd9\u662f\u4e00\u4e2a\u4ee4\u4eba\u632f\u594b\u7684\u7ed3\u679c\uff0c\u610f\u5473\u7740\u91cf\u5b50\u8ba1\u7b97\u53ef\u4ee5\u5728\u4e0d\u6539\u53d8\u5c40\u57df\u6001\u5e03\u5c45\u6570\uff0c\u4e5f\u5c31\u662f\u80fd\u91cf\u7684\u60c5\u51b5\u4e0b\uff0c\u4f20\u64ad\u91cf\u5b50\u4fe1\u606f\u3002<\/span><\/section>\n

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\u4e8e\u662f\uff0c\u5728\u591a\u4f53\u5c40\u57df\u5316\u5e94\u7528\u5230\u91cf\u5b50\u8ba1\u7b97\u7684\u63a2\u8ba8\u4e2d\uff0c\u6709\u4e86\u5c40\u57df\u6bd4\u7279<\/span> (l-bit) <\/span>\u7684\u6982\u5ff5\u3002\u6240\u8c13\u5c40\u57df\u6bd4\u7279\uff0c\u5176\u5b9e\u5c31\u662f\u5c40\u57df\u8fd0\u52a8\u79ef\u5206\uff0c\u5b83\u4eec\u662f\u80fd\u591f\u957f\u65f6\u95f4\u4fdd\u6301\u4e0d\u53d8\u7684\u5c40\u57df\u5b88\u6052\u91cf\u3002\u4ee5\u7ecf\u5178\u7684\u4f0a\u8f9b\u6a21\u578b\u4e3a\u4f8b\uff0c\u5b83\u7684<\/span>\u5c31\u662f\u5c40\u57df\u8fd0\u52a8\u79ef\u5206\uff0c\u521d\u59cb\u72b6\u6001\u4e00\u65e6\u786e\u5b9a\u4e3a\u5b83\u7684\u672c\u5f81\u6001\uff0c\u5c31\u65e0\u6cd5\u88ab\u6539\u53d8\u3002\u4e00\u822c\u7684\uff0c\u5047\u8bbe\u67d0\u4e2a\u591a\u4f53\u5c40\u57df\u5316\u7cfb\u7edf\u7684\u5c40\u57df\u6bd4\u7279\u4e3a<\/span>\uff0c\u5b83\u7684\u54c8\u5bc6\u987f\u91cf\u603b\u53ef\u4ee5\u5199\u4e3a\u5982\u4e0b\u5f62\u5f0f\uff1a<\/span><\/section>\n

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6. \u91cf\u5b50\u70ed\u673a<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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\u7531\u4e8e\u5bf9\u70ed\u7684\u5fae\u89c2\u8ba4\u8bc6\u4ecd\u4e0d\u5145\u5206\uff0c\u5373\u4f7f\u5728\u4e09\u80fd\u7ea7\u7cfb\u7edf\u8fd9\u6837\u6709\u7740\u660e\u786e\u672c\u5f81\u80fd\u8c31\u7684\u7cfb\u7edf\u4e2d\uff0c\u5bf9\u5916\u505a\u529f\u8fc7\u7a0b\u7684\u6a21\u62df\u4ecd\u5b58\u5728\u76f8\u5f53\u5927\u7684\u6280\u672f\u96be\u5ea6\u3002\u91cf\u5b50\u52a8\u529b\u5b66\u65e0\u6cd5\u6a21\u62df\u6574\u4e2a\u5de5\u4f5c\u5faa\u73af\uff0c\u751a\u81f3\u5355\u6b21\u70ed\u529f\u8f6c\u6362\u90fd\u96be\u4ee5\u6a21\u62df\uff0c\u6240\u4ee5\u5e38\u89c1\u505a\u6cd5\u662f\u901a\u8fc7\u5916\u52a0\u542b\u65f6\u7684\u9a71\u52a8\u573a\uff0c\u5c06\u80fd\u591f\u5bf9\u5916\u505a\u529f\u7684\u6d3b\u6027\u6001<\/span> (active state) <\/span>\u548c\u4e0d\u80fd\u5bf9\u5916\u505a\u529f\u7684\u88ab\u52a8\u6001<\/span> (passive state)<\/span> \u533a\u5206\u5f00\u6765\uff0c\u76f8\u5f53\u4e8e\u529f\u88ab\u4e09\u80fd\u7ea7\u7cfb\u7edf\u8fd9\u6837\u7684\u5de5\u8d28\u50a8\u5b58\u8d77\u6765\uff0c\u5de5\u8d28\u626e\u6f14\u4e86\u7535\u6c60 <\/span>(battery) <\/span>\u6216\u98de\u8f6e<\/span> (flywheel) <\/span>\u7684\u89d2\u8272\u3002\u5728\u91cf\u5b50\u70ed\u673a\u4e2d\uff0c\u8fd9\u79cd\u7cfb\u7edf\u5de5\u8d28\u7684\u4f5c\u7528\u79f0\u4e3a\u529f\u8d2e\u85cf\u5ba4<\/span> (work repository)<\/span> \uff0c\u5176\u4e2d\u53ef\u4ee5\u88ab\u63d0\u53d6\u51fa\u6765\u7684\u6700\u5927\u529f\u88ab\u79f0\u4e3aergotropy\uff0c\u8be5\u8bcd\u5c1a\u65e0\u7edf\u4e00\u4e2d\u6587\u8bd1\u540d\u3002<\/span><\/section>\n

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\u5c06\u7ecf\u5178\u70ed\u673a\u53cd\u5411\u64cd\u4f5c\uff0c\u5c31\u662f\u4e00\u53f0\u5438\u6536\u5f0f\u5236\u51b7\u673a<\/span> (absorption refrigerator)<\/span>\u3002\u7136\u800c\uff0c\u91cf\u5b50\u5236\u51b7\u673a\u5e76\u4e0d\u80fd\u7b80\u5355\u5730\u5c06\u91cf\u5b50\u70ed\u673a\u53cd\u5411\uff0c\u8fd9\u6d89\u53ca\u81ea\u53d1\u5bf9\u79f0\u6027\u7834\u7f3a\u548c\u4fe1\u606f\u64e6\u9664\u7684\u590d\u6742\u95ee\u9898\u3002\u76ee\u524d\uff0c\u7814\u7a76\u8005\u5df2\u7ecf\u8bbe\u8ba1\u51fa\u4e86\u5404\u79cd\u6709\u8da3\u7684\u91cf\u5b50\u5236\u51b7\u673a\uff0c\u6bd4\u5982\u7ed9\u4e00\u4e2a\u56db\u80fd\u7ea7\u7cfb\u7edf\u63a5\u4e0a\u4e09\u4e2a\u5e93\uff0c\u5176\u4e2d\u4e24\u4e2a\u626e\u6f14\u4f4e\u6e29\u70ed\u6e90\uff0c\u53e6\u4e00\u4e2a\u626e\u6f14\u9ad8\u6e29\u70ed\u6e90\uff0c\u7c7b\u4f3c\u4e8e\u91cf\u5b50\u5149\u5b66\u4e2d\u7684\u53cc\u5149\u5b50\u5438\u6536\u3002\u5177\u4f53\u5185\u5bb9\u4e0d\u518d\u8d58\u8ff0\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u82e5\u8bf4\u7814\u7a76\u5c40\u57df\u5316\u662f\u81f4\u529b\u4e8e\u7834\u574f\u7a7a\u95f4\u5e73\u79fb\u4e0d\u53d8\u6027\uff0c\u7814\u7a76\u65f6\u95f4\u6676\u4f53\u5c31\u662f\u7834\u574f\u70ed\u529b\u5b66\u7b2c\u4e00\u5b9a\u5f8b\uff0c\u90a3\u4e48\u8ba8\u8bba\u91cf\u5b50\u70ed\u673a\u7684\u51fa\u53d1\u70b9\u5c31\u662f\u81f4\u529b\u4e8e\u7834\u574f\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\uff0c\u4e5f\u5c31\u662f\u71b5\u589e\u539f\u7406\u3002\u5728\u7ecf\u5178\u70ed\u673a\u4e2d\uff0c\u71b5\u7684\u4f5c\u7528\u6c38\u8fdc\u662f\u8d1f\u9762\u7684\uff0c\u62e5\u6709\u6700\u9ad8\u6548\u7387\u7684\u7406\u60f3\u70ed\u673a\u5fc5\u987b\u4fdd\u6301\u5168\u8fc7\u7a0b\u53ef\u9006\uff0c\u71b5\u4fdd\u6301\u4e0d\u53d8\u3002\u91cf\u5b50\u70ed\u673a\u7684\u672c\u8d28\u5c31\u662f\u8981\u63a2\u8ba8\u5c06\u71b5\u4f5c\u4e3a\u6b63\u9762\u8d44\u6e90\u52a0\u4ee5\u5229\u7528\u3002\u8981\u4e48\u662f\u76f4\u63a5\u4e0e\u80fd\u91cf\u6216\u529f\u76f8\u4e92\u8f6c\u6362\uff0c\u8981\u4e48\u662f\u4ee5\u91cf\u5b50\u76f8\u5e72\u6027\u4f5c\u4e3a\u50ac\u5316\u5242<\/span> (catalyst)<\/span>\uff0c\u95f4\u63a5\u4fc3\u8fdb\u6709\u7528\u529f\u6216ergotropy\u7684\u589e\u52a0\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u8fd9\u6b63\u662f\u7ecf\u5178\u70ed\u529b\u5b66\u4e2d\u7684\u9ea6\u514b\u65af\u97e6\u5996\u3002\u5e38\u89c1\u7684\u5b9e\u73b0\u9ea6\u514b\u65af\u97e6\u5996\u7684\u88c5\u7f6e\u5305\u62ec\u8d39\u66fc\u68d8\u8f6e\u3001Lochmidt\u56de\u6ce2\u7b49\u3002\u5728\u6240\u6709\u53ef\u80fd\u7684\u9009\u9879\u4e2d\uff0c20\u4e16\u7eaa20\u5e74\u4ee3\u51fa\u73b0\u7684Szil\u00e1rd\u70ed\u673a\u6700\u5177\u542f\u53d1\u6027\u3002\u6240\u8c13Szil\u00e1rd\u70ed\u673a\uff0c\u662f\u6307\u5f53\u4e00\u4e2a\u76d2\u5b50\u91cc\u53ea\u6709\u4e00\u4e2a\u5206\u5b50\u65f6\uff0c\u82e5\u5206\u5b50\u5728\u76d2\u5b50\u5de6\u8fb9\uff0c\u8ba9\u53f3\u8fb9\u5bf9\u5916\u505a\u529f\uff0c\u5f53\u5206\u5b50\u5728\u53f3\u8fb9\u65f6\uff0c\u8ba9\u5de6\u8fb9\u5bf9\u5916\u505a\u529f\u3002\u7531\u4e8e\u603b\u662f\u771f\u7a7a\u7684\u4e00\u8fb9\u5728\u505a\u529f\uff0c\u80fd\u91cf\u635f\u8017\u53ef\u5ffd\u7565\uff0c\u5c31\u76f8\u5f53\u4e8e\u4ece\u5355\u4e00\u7684\u7b49\u6e29\u73af\u5883\u4e2d\u63d0\u53d6\u4e86\u6709\u7528\u529f\uff0c\u7c97\u770b\u4e0a\u53bb\u7684\u786e\u8fdd\u80cc\u7b2c\u4e8c\u5b9a\u5f8b\u3002<\/span><\/section>\n

<\/span><\/section>\n
2010\u5e74\uff0cS. Toyabe\u7b49\u4eba\u53d1\u8868\u5728Nature Physics<\/em>\u4e0a\u7684\u4e00\u7bc7\u6587\u7ae0\u636e\u6b64\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u6709\u8da3\u7684\u5b9e\u9a8c\u88c5<\/span>\u7f6e[12]\u3002\u4ed6<\/span>\u4eec\u5c06\u4e24\u4e2a\u76f4\u5f84\u4e3a287 nm\u7684\u805a\u82ef\u4e59\u70ef\u5851\u6599\u9897\u7c92\u5438\u9644\u5728\u6d82\u62b9\u4e86\u4eb2\u548c\u5242\u7684\u73bb\u7483\u886c\u5e95\u4e0a\uff0c\u4e24\u4e2a\u9897\u7c92\u7ed3\u5408\u5f62\u6210\u7c7b\u4e8c\u805a\u4f53\u7ed3\u6784\uff0c\u5177\u6709\u9762\u5185\u65cb\u8f6c\u81ea\u7531\u5ea6\u3002\u4e4b\u540e\u5c06\u5b83\u4eec\u653e\u7f6e\u5728\u4e00\u4e2a\u7cbe\u5de7\u8bbe\u8ba1\u7684\u56db\u6781\u7535\u573a\u5185\uff0c\u901a\u8fc7\u5411\u56db\u4e2a\u7535\u6781\u52a0\u5165\u692d\u5706\u65cb\u8f6c\u7684\u4ea4\u53d8\u7535\u573a\uff0c\u53ef\u4ee5\u8ba9\u8fd9\u4e2a\u4e8c\u805a\u4f53\u65cb\u8f6c\u8d77\u6765\u3002\u4e8c\u805a\u4f53\u5f88\u5c0f\uff0c\u5b83\u7684\u65cb\u8f6c\u5177\u6709\u968f\u673a\u6027\u3002\u4e00\u76f4\u7531\u663e\u5fae\u955c\u5728\u5b9e\u65f6\u89c2\u5bdf\u6574\u4e2a\u7cfb\u7edf\uff0c\u5f53\u67d0\u65f6\u523b\u4e8c\u805a\u4f53\u6240\u5904\u7684\u65cb\u8f6c\u89d2\u5ea6\u6b63\u597d\u5904\u4e8e\u7535\u52bf\u7684\u6ce2\u5cf0\u5904\uff0c\u5c31\u4f1a\u5f00\u542f\u4e00\u4e2a\u53cd\u9988\u7535\u573a\uff0c\u8ba9\u8f90\u89d2\u53cd\u5411\uff0c\u4e8c\u805a\u4f53\u4f1a\u56e0\u80fd\u91cf\u964d\u4f4e\u800c\u6389\u5230\u6ce2\u8c37\u4e2d\u3002\u5982\u6b64\u53cd\u590d\u64cd\u4f5c\uff0c\u4e8c\u805a\u4f53\u7684\u65cb\u8f6c\u5c31\u4f1a\u5448\u73b0\u51fa\u5355\u5411\u6f14\u5316\u7684\u7279\u5f81\u3002<\/span><\/section>\n

<\/section>\n
\u8fd9\u4e2a\u88c5\u7f6e\u770b\u4e0a\u53bb\u5e76\u6ca1\u6709\u5bf9\u5206\u5b50\u505a\u529f\uff0c\u4e0e\u9ea6\u514b\u65af\u97e6\u5996\u7684\u8bbe\u60f3\u76f8\u4e00\u81f4\u3002\u4f46\u4ed4\u7ec6\u5206\u6790\u4f1a\u53d1\u73b0\uff0c\u8981\u5b9e\u73b0\u4e0a\u8ff0\u64cd\u63a7\u9700\u8981\u5bf9\u7eb3\u7c73\u9897\u7c92\u7684\u5fae\u89c2\u8fd0\u52a8\u5b9e\u65f6\u4e86\u89e3\u3002\u65e0\u8bba\u662f\u663e\u5fae\u955c\u3001\u56fe\u50cf\u8bc6\u522b\uff0c\u8fd8\u662f\u53cd\u9988\u7535\u573a\u7684\u5f15\u5165\uff0c\u90fd\u9700\u8981\u5de8\u5927\u7684\u80fd\u91cf\u6d88\u8017\uff0c\u5176\u4f5c\u7528\u4e0d\u662f\u8ba9\u7eb3\u7c73\u9897\u7c92\u8fd0\u52a8\uff0c\u800c\u4ec5\u662f\u77e5\u9053\u5b83\u7684\u5b9e\u65f6\u8fd0\u52a8\u4fe1\u606f\u3002\u4e8b\u5b9e\u4e0a\u65e9\u5728Szil\u00e1rd\u70ed\u673a\u7684\u8ba8\u8bba\u4e2d\u4eba\u4eec\u5c31\u5df2\u7ecf\u660e\u767d\u4e86\u8fd9\u4e00\u70b9\uff0c\u4fe1\u606f\u7684\u83b7\u53d6\u672c\u8eab\u662f\u9700\u8981\u80fd\u91cf\u7684\uff0c\u8fd9\u6b63\u662fLandauer\u90a3\u53e5\u540d\u8a00\u8981\u8868\u8fbe\u7684\u542b\u4e49\u3002<\/span><\/section>\n

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7. \u91cf\u5b50\u8d44\u6e90\u8bba<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

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


<\/p>\n

\u7269\u7406\u5b9a\u5f8b\u7684\u672c\u8d28\u5c31\u662f\u9650\u5236\u548c\u7ea6\u675f<\/span> (constraint)<\/span>\uff0c\u6bd4\u5982\u8fd0\u52a8\u901f\u5ea6\u4e0d\u80fd\u8d85\u8fc7\u771f\u7a7a\u5149\u901f\uff0c\u80fd\u91cf\u4e0d\u80fd\u4ece\u65e0\u5230\u6709\u7b49\u3002\u6240\u8c13\u7684\u8d44\u6e90\u8bba\uff0c\u5c31\u662f\u7814\u7a76\u5982\u4f55\u5bf9\u8fd9\u4e9b\u5ba2\u89c2\u9650\u5236\u52a0\u4ee5\u5229\u7528\u3002\u91cf\u5b50\u529b\u5b66\u66f4\u52a0\u6ce8\u91cd\u5bf9\u79f0\u6027\u548c\u5b88\u6052\u5f8b\uff0c\u6240\u4ee5\u5728\u5c06\u70ed\u529b\u5b66\u91cf\u5b50\u5316\u7684\u8fc7\u7a0b\u4e2d\uff0c\u8d44\u6e90\u8bba\u4e5f\u5e94\u5f53\u88ab\u91cf\u5b50\u5316[13]\u3002<\/span><\/section>\n

<\/section>\n
\u8d44\u6e90\u8bba\u6700\u65e9\u662f2000\u5e74\u7531D. Janzing\u7b49\u4eba\u5f15\u5165\u5230\u7269\u7406\u5b66\u4e2d[14]\uff0c\u5176\u51fa\u53d1\u70b9\u662f\u5728\u5f53\u65f6\u5982\u706b\u5982\u837c\u7684\u51b7\u539f\u5b50\u6280\u672f\u3002\u4eba\u4eec\u9189\u5fc3\u4e8e\u8ba9\u539f\u5b50\u7684\u6e29\u5ea6\u8d8a\u6765\u8d8a\u4f4e\uff0c\u4f46\u5374\u5ffd\u89c6\u5176\u4ee3\u4ef7\u3002\u76f8\u6bd4\u4e8e\u5355\u4e2a\u539f\u5b50\uff0c\u8ba9\u5b83\u51b7\u5374\u7684\u6fc0\u5149\u5668\u548c\u5176\u4ed6\u88c5\u7f6e\u6781\u5176\u5e9e\u5927\uff0c\u6240\u6d88\u8017\u7684\u80fd\u6e90\u96be\u4ee5\u8ba1\u6570\u3002\u5982\u679c\u4ee5\u51b7\u539f\u5b50\u5b9e\u73b0\u7684\u91cf\u5b50\u8ba1\u7b97\u673a\u5f53\u4f5c\u4e00\u53f0\u91cf\u5b50\u70ed\u673a\uff0c\u90a3\u4e48\u5176\u6548\u7387\u5fc5\u7136\u6781\u4f4e\u3002\u6211\u4eec\u7a76\u7adf\u80fd\u4ee5\u591a\u5c0f\u7684\u4ee3\u4ef7\u6765\u51b7\u5374\u539f\u5b50\u5462\uff1f\u5bfb\u627e\u8fd9\u4e2a\u6781\u9650\u662f\u91cf\u5b50\u8d44\u6e90\u8bba\u7684\u51fa\u53d1\u70b9\u3002<\/span><\/section>\n

<\/section>\n
\u91cf\u5b50\u8d44\u6e90\u8bba\u4e4b\u6240\u4ee5\u4e0d\u6cbf\u7528\u91cf\u5b50\u4fe1\u606f\u8bba\u7684\u540d\u79f0\uff0c\u4e3b\u8981\u662f\u4e3a\u4e86\u63a2\u8ba8\u4fe1\u606f\u4e0e\u80fd\u91cf\u4e4b\u95f4\u7684\u8f6c\u6362\uff0c\u7279\u522b\u662f\u5982\u4f55\u5c06\u91cf\u5b50\u201c\u76f8\u5e72\u6027\u201d\u4f5c\u4e3a\u8d44\u6e90\u6765\u4f7f\u7528\uff0c\u800c\u4e0d\u662f\u76f4\u63a5\u8017\u6563\u6389\uff0c\u672a\u6765\u53ef\u80fd\u7684\u5de5\u4e1a\u9769\u547d\u6781\u6709\u53ef\u80fd\u53d1\u751f\u5728\u5bf9\u76f8\u5e72\u6027\u8fd9\u79cd\u65b0\u80fd\u91cf\u5f62\u5f0f\u7684\u4f7f\u7528\u4e0a\u3002\u4f20\u7edf\u70ed\u529b\u5b66\u4ee5\u71b5\u6216\u81ea\u7531\u80fd\u4f5c\u4e3a\u57fa\u7840\u7269\u7406\u91cf\uff0c\u5b83\u4eec\u7684\u5355\u5411\u6f14\u5316\u5b9a\u4e49\u4e86\u70ed\u529b\u5b66\u8fc7\u7a0b\u7684\u4e0d\u53ef\u9006\u6027\u3002\u91cf\u5b50\u8d44\u6e90\u8bba\u5219\u8981\u63a2\u8ba8\uff0c\u4e00\u4e2a\u91cf\u5b50\u7cfb\u7edf\u4f1a\u81ea\u53d1\u9009\u62e9\u600e\u6837\u7684\u6f14\u5316\u65b9\u5411\uff0c\u6211\u4eec\u9700\u8981\u4e3a\u6b64\u5b9a\u4e49\u4e00\u7ec4<\/span> (\u4e0d\u518d\u662f\u4e00\u4e2a) <\/span>\u65b0\u7684\u7269\u7406\u91cf\u5bf9\u5176\u6f14\u5316\u52a0\u4ee5\u9650\u5236\u3002<\/span><\/section>\n

<\/section>\n
\u7528\u5230\u7684\u6570\u5b66\u5de5\u5177\u5c31\u662f\u7ebf\u6027\u4ee3\u6570\u4e2d\u7684\u5b8c\u5168\u6b63\u5b9a\u4fdd\u8ff9\u6620\u5c04<\/span> (completely positive trace-preserving map)<\/span>\u3002\u6240\u8c13\u5b8c\u5168\u6b63\u5b9a\uff0c\u662f\u6307\u8be5\u6620\u5c04\u4f5c\u7528\u5230\u67d0\u7b97\u7b26\u4e0a\uff0c\u4f5c\u7528\u524d\u540e\u8be5\u7b97\u7b26\u5747\u662f\u534a\u6b63\u5b9a\u7684\uff0c\u534a\u6b63\u5b9a\u7684\u610f\u601d\u5c31\u662f\u5b83\u4f5c\u7528\u5230\u4efb\u610f\u6001\u77e2\u91cf\u4e0a\u6240\u5f97\u7684\u5185\u79ef\u4e3a\u975e\u8d1f\u3002\u5047\u8bbe\u67d0\u4e2a\u7cfb\u7edfS\u7684\u72b6\u6001\u7528\u5bc6\u5ea6\u77e9\u9635\u03c1<\/em><\/strong>\u8868\u793a\uff0c\u5f15\u5165\u4e00\u4e2a\u5904\u4e8e\u70ed\u5e73\u8861\u72b6\u6001\u03b3<\/strong><\/em><\/span>\u7684\u73af\u5883R\uff0c\u4f7f\u4e4b\u4e0e\u03c1<\/strong><\/em><\/span>\u76f4\u79ef\u5e76\u5171\u540c\u6f14\u5316\uff0c\u518d\u5c06\u73af\u5883\u90e8\u5206\u6c42\u8ff9\uff0c\u5373\u5b9a\u4e49\u5982\u4e0b\u8d85\u7b97\u7b26\uff1a<\/span><\/section>\n

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

<\/section>\n
\u5176\u4e2d<\/span>\u662f\u5e7a\u6b63\u64cd\u4f5c\uff0c\u4e14\u521d\u672b\u65f6\u523b\u6ee1\u8db3<\/span>\u3002\u8fd9\u4e2a\u8d85\u7b97\u7b26\u79f0\u4e3a\u70ed\u64cd\u4f5c <\/span>(thermal operation)<\/span>\uff0c\u5b83\u53ea\u5305\u542b\u91cf\u5b50\u529b\u5b66\u4e2d\u5b9a\u4e49\u6700\u826f\u597d\u7684\u5e7a\u6b63\u53d8\u6362\u548c\u6c42\u8ff9\u64cd\u4f5c\uff0c\u53ef\u4ee5\u5728\u5b9e\u9645\u7269\u7406\u4f53\u7cfb\u4e2d\u5b9e\u73b0\u3002\u70ed\u64cd\u4f5c\u662f\u5b8c\u5168\u6b63\u5b9a\u4fdd\u8ff9\u6620\u5c04\uff0c\u5b83\u6ee1\u8db3\u65f6\u95f4\u5e73\u79fb\u4e0d\u53d8\u6027\u5e76\u4fdd\u6301\u70ed\u5e73\u8861\u72b6\u6001\u4e0d\u53d8\uff0c\u8fd9\u6b63\u662f\u70ed\u529b\u5b66\u7b2c\u4e00\u548c\u7b2c\u4e8c\u5b9a\u5f8b\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u53ea\u8981\u6570\u5b66\u4e0a\u5b58\u5728\u8fd9\u6837\u7684\u4e0d\u7b49\u5f0f<\/span>\uff0c\u5176\u4e2df<\/em>\u662f\u4efb\u610f\u53ef\u80fd\u7684\u51fd\u6570\uff0c\u5219\u70ed\u64cd\u4f5c\u5c31\u662f\u4e00\u4e2a\u5355\u5411\u64cd\u4f5c\uff0c\u5b83\u5728\u91cf\u5b50\u70ed\u529b\u5b66\u7684\u6846\u67b6\u4e0b\u91cd\u65b0\u5b9a\u4e49\u81ea\u7136\u6f14\u5316\u65b9\u5411\u3002\u5728\u91cf\u5b50\u8d44\u6e90\u8bba\u4e2d\u7528\u5f97\u6700\u4e3a\u5e7f\u6cdb\u7684\u51fd\u6570\u662f\u8ff9\u8303\u6570\u548c\u76f8\u5bf9\u71b5\u3002\u8ff9\u8303\u6570\u662f\u6307<\/span>\uff0c\u5b83\u662f\u4e00\u4e2a\u5728\u5b8c\u5168\u6b63\u5b9a\u4fdd\u8ff9\u6620\u5c04\u4e0b\u5355\u8c03\u4e0b\u964d\u7684\u51fd\u6570\u3002\u76f8\u5bf9\u71b5\u5219\u662f\u6307<\/span>\uff0c\u4e5f\u53eb\u91cf\u5b50R\u00e9nyi\u76f8\u5bf9\u71b5\uff0c\u5176\u4e2d\u03b1<\/em>\u4ee3\u8868\u71b5\u7684\u9636\u6570\uff0c\u5f530\u2264\u03b1<\/em>\u22642\u65f6\uff0c\u5b83\u662f\u5355\u8c03\u4e0b\u964d\u7684\u3002\u4e0e\u6807\u51c6\u7684R\u00e9nyi\u71b5\u4e00\u6837\uff0c\u5f53\u03b1<\/em>\u21921\u65f6\u5c31\u662f\u51af\u00b7\u8bfa\u4f0a\u66fc\u76f8\u5bf9\u71b5<\/span>\uff0c\u5b83\u53cd\u6620\u4e24\u4e2a\u5bc6\u5ea6\u77e9\u9635\u4e4b\u95f4\u7684\u5dee\u5f02\u3002<\/span><\/section>\n

<\/section>\n
\u8981\u8bc1\u660e\u4e0a\u8ff0\u4e24\u4e2a\u51fd\u6570\u7684\u5355\u8c03\u6027\uff0c\u5173\u952e\u662f\u5bf9\u70ed\u64cd\u4f5c\u505aKraus\u5206\u89e3\uff0c\u4e5f\u5c31\u662f\uff1a<\/span><\/section>\n

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

<\/span><\/section>\n
\u5176\u4e2d\u662f\u73af\u5883\u90e8\u5206\u968f\u65f6\u95f4\u6f14\u5316\u540e\u518d\u88ab\u6c42\u8ff9\u6240\u4ea7\u751f\u7684\u5bf9\u7cfb\u7edf\u7684\u64cd\u4f5c\uff0c\u79f0\u4e3aKraus\u7b97\u7b26\u3002\u4e0d\u5931\u4e00\u822c\u6027\uff0c\u603b\u53ef\u4ee5\u5206\u4e3a\u4e24\u90e8\u5206\uff0c\u5373<\/span>\uff0c\u5176\u4e2d<\/span>\u662f\u6295\u5f71\u7b97\u7b26\uff0c\u6539\u53d8\u7cfb\u7edf\u5728\u4e0d\u540c\u80fd\u91cf\u672c\u5f81\u6001\u4e0a\u7684\u5206\u5e03\uff0c<\/span>\u79f0\u4e3a\u6ed1\u79fb\u7b97\u7b26\uff0c\u76f8\u5f53\u4e8e\u628a\u7cfb\u7edf\u7684\u6240\u6709\u72b6\u6001\u5411\u67d0\u4e2a\u80fd\u91cf\u65b9\u5411\u79fb\u52a8\u3002\u5f88\u663e\u7136\uff0c\u6ed1\u79fb\u7b97\u7b26\u7531\u73af\u5883\u7684\u67d0\u4e2a\u80fd\u91cf\u72b6\u6001\u63d0\u4f9b\u6216\u662f\u5438\u6536\u4e86\u7cfb\u7edf\u7684\u80fd\u91cf\u6240\u5bfc\u81f4\uff0c<\/span>\u548c\u8054\u5408\u4f5c\u7528\u53ef\u4ee5\u4fdd\u6301\u73af\u5883\u7684\u72b6\u6001\u4e0d\u53d8\uff0c\u6240\u4ee5\u5728\u8fd9\u4e2a\u64cd\u4f5c\u4e0b\u73af\u5883\u662f\u4e00\u4e2a\u50ac\u5316\u5242\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u53ef\u4ee5\u5b9a\u4e49\u5e7f\u4e49\u4e0a\u7684\u91cf\u5b50\u81ea\u7531\u80fd\uff0c\u5373<\/span><\/section>\n

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

<\/section>\n
\u5176\u4e2d\uff0c\u03c1<\/em><\/strong>T<\/sub><\/em>\u662f\u70ed\u5e73\u8861\u5206\u5e03\u3002\u7b2c\u4e8c\u9879\u5c31\u662f\u7ecf\u5178\u81ea\u7531\u80fd\uff0c\u7b2c\u4e00\u9879\u5219\u662f\u7531\u91cf\u5b50\u76f8\u5e72\u6027\u7684\u53d8\u5316\u5bfc\u81f4\u71b5\u53d8\u6240\u5f15\u8d77\u7684\u81ea\u7531\u80fd\u53d8\u5316\u3002\u8fd9\u91cc\u7684\u03b1<\/em>\u6709\u5f88\u591a\u53d6\u503c\uff0c\u6240\u4ee5\u53ef\u4ee5\u6709\u5f88\u591a\u4e2a\u4e0d\u540c\u7684\u81ea\u7531\u80fd\uff0c\u5b83\u4eec\u5171\u540c\u5f62\u6210\u5bf9\u91cf\u5b50\u4f53\u7cfb\u6f14\u5316\u65b9\u5411\u7684\u9650\u5236\u3002\u5982\u4f55\u5c06\u8fd9\u4e00\u90e8\u5206\u81ea\u7531\u80fd\u52a0\u4ee5\u5229\u7528\uff0c\u662f\u91cf\u5b50\u8d44\u6e90\u8bba\u7684\u91cd\u8981\u7814\u7a76\u8bfe\u9898\u3002<\/span><\/section>\n

<\/span><\/section>\n
\u5176\u4e2d\u6700\u503c\u5f97\u5173\u6ce8\u7684\u83ab\u8fc7\u4e8e\u975e\u5bf9\u79f0\u6027<\/span> (asymmetry)<\/span> \u7406\u8bba\u3002\u6240\u8c13\u975e\u5bf9\u79f0\u6027\uff0c\u5c31\u662f\u6307\u03c1<\/em><\/strong>\u5f53\u4e2d\u5305\u542b\u4e86<\/span>\u8fd9\u6837\u7684\u5728\u67d0\u4e2a\u5bf9\u79f0\u8868\u8c61\u4e0b\u7684\u975e\u5bf9\u89d2\u5143\uff0c\u4e5f\u5c31\u662f\u53e0\u52a0\u6001\u3002\u6700\u5e38\u89c1\u7684\u5f53\u7136\u5c31\u662f\u65f6\u95f4\u5e73\u79fb\u4e0d\u53d8\u6027\u6240\u5bf9\u5e94\u7684\u80fd\u91cf\u8868\u8c61\uff0c\u5bf9\u89d2\u5143\u5728\u65f6\u95f4\u6f14\u5316\u7b97\u7b26\u4f5c\u7528\u4e0b\u5b8c\u5168\u4fdd\u6301\u4e0d\u53d8\uff0c\u6240\u4ee5\u53eb\u5bf9\u79f0\u6001\uff0c\u5bf9\u79f0\u6001\u53ef\u4ee5\u662f\u7eaf\u6001\u4e5f\u53ef\u4ee5\u662f\u6df7\u6001\u3002\u800c\u975e\u5bf9\u89d2\u5143\u5728\u65f6\u95f4\u6f14\u5316\u65f6\u4f1a\u589e\u52a0\u4e00\u4e2a\u76f8\u4f4d\uff0c\u6240\u4ee5\u662f\u7834\u574f\u5e73\u79fb\u4e0d\u53d8\u6027\u7684\u975e\u5bf9\u79f0\u6001\u3002\u6839\u636e\u70ed\u64cd\u4f5c\u7684\u5355\u8c03\u6027\u53ef\u4ee5\u53d1\u73b0\uff0c\u6700\u5747\u5300\u7684\u53e0\u52a0\u6001\u901a\u5e38\u53ea\u80fd\u4f5c\u4e3a\u70ed\u64cd\u4f5c\u7684\u521d\u6001\uff0c\u800c\u5f88\u96be\u4f5c\u4e3a\u672b\u6001\u3002\u8fd9\u79cd\u96be\u4ee5\u88ab\u70ed\u64cd\u4f5c\u81ea\u7136\u6f14\u5316\u800c\u5236\u5907\u5f97\u5230\u7684\u975e\u5bf9\u79f0\u6001\uff0c\u5c31\u662f\u201c\u6602\u8d35\u7684\u201d\u8d44\u6e90\uff0c\u4e0e\u4e4b\u76f8\u53cd\uff0c\u4e0d\u5747\u5300\u7684\u53e0\u52a0\u6001\u5219\u662f\u201c\u5ec9\u4ef7\u7684\u201d\uff0c\u80fd\u91cf\u672c\u5f81\u6001\u5219\u662f\u201c\u514d\u8d39\u7684\u201d\u3002\u975e\u5bf9\u79f0\u6027\u7406\u8bba\uff0c\u53ef\u4ee5\u5e2e\u52a9\u6211\u4eec\u56de\u7b54\u4e00\u4e2a\u57fa\u7840\u4f46\u60ac\u800c\u672a\u51b3\u7684\u91cf\u5b50\u529b\u5b66\u95ee\u9898\uff1a\u80fd\u91cf\u672c\u5f81\u6001\u7684\u7ebf\u6027\u53e0\u52a0\u6001\u7a76\u7adf\u662f\u5982\u4f55\u4ea7\u751f\uff0c\u53c8\u5e94\u5982\u4f55\u88ab\u5229\u7528\u3002\u6b64\u5916\uff0c\u5728\u975e\u5bf9\u79f0\u6027\u7406\u8bba\u7684\u5e2e\u52a9\u4e0b\uff0c\u6211\u4eec\u8fd8\u53ef\u4ee5\u5c06\u7ea0\u7f20\u7684\u63d0\u7eaf\u4e0e\u5f62\u6210\u8fc7\u7a0b\u7ec4\u6210\u4e00\u4e2a\u91cf\u5b50\u70ed\u673a\u7684\u5faa\u73af\uff0c\u4ece\u800c\u7814\u7a76\u5982\u4f55\u5c06\u91cf\u5b50\u76f8\u5e72\u6027\u4f5c\u4e3a\u8d44\u6e90\u52a0\u4ee5\u5faa\u73af\u5229\u7528\u3002<\/span><\/section>\n

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<\/svg><\/section>\n<\/section>\n<\/section>\n
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8. \u901a\u5411\u4e07\u7269\u7406\u8bba\u4e4b\u8def<\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

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


<\/p>\n

\u7269\u8d28\u79d1\u5b66\u7684\u53d1\u5c55\u5386\u53f2\u4e0a\uff0c\u65e0\u6570\u4eba\u8ffd\u5bfb\u7740\u4e07\u7269\u7406\u8bba<\/span> (theory of everything) <\/span>\u7684\u5149\u8292\uff1a\u901a\u8fc7\u4e00\u7ec4\u65b9\u7a0b\u63cf\u8ff0\u6240\u6709\u5df2\u53d1\u73b0\u7684\u73b0\u8c61[15]\u3002\u66fe\u7ecf\uff0c\u91d1\u5179\u5821\u2014\u6717\u9053\u7406\u8bba\u88ab\u8ba4\u4e3a\u6700\u63a5\u8fd1\u8fd9\u4e00\u76ee\u6807\u3002\u5b83\u4ee5\u81ea\u7531\u80fd\u4f5c\u4e3a\u5224\u636e\uff0c\u901a\u8fc7\u81ea\u53d1\u5bf9\u79f0\u6027\u7834\u7f3a\u8fbe\u5230\u6700\u7ec8\u7269\u6001\uff0c\u4e0d\u4ec5\u88ab\u6210\u529f\u8fd0\u7528\u4e8e\u5e38\u89c4\u8d85\u5bfc\uff0c\u8fd8\u88ab\u5e7f\u6cdb\u8fd0\u7528\u5230\u5404\u79cd\u5176\u4ed6\u7269\u6001\u3002\u7136\u800c\u968f\u7740\u9ad8\u6e29\u8d85\u5bfc\u3001\u5206\u6570\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u7b49\u65b0\u5947\u51dd\u805a\u6001\u7269\u76f8\u7684\u53d1\u73b0\uff0c\u8fd9\u5957\u7406\u8bba\u4f53\u7cfb\u4e0d\u518d\u666e\u9002\u6210\u7acb[16]\u3002\u91cf\u5b50\u6db2\u4f53\u3001\u5f3a\u5173\u8054\u3001\u62d3\u6251\u5e8f\u3001\u91cf\u5b50\u70ed\u5316\u7b49\u4e00\u7cfb\u5217\u65b0\u7406\u8bba\u4e0d\u65ad\u88ab\u63d0\u51fa\u4ee5\u89e3\u91ca\u8fd9\u4e9b\u65b0\u5947\u7269\u6027\u3002<\/span><\/section>\n

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\u91cf\u5b50\u4fe1\u606f\u7684\u53d1\u5c55\u5bf9\u4e07\u7269\u7406\u8bba\u7684\u63a2\u7d22\u5f62\u6210\u4e86\u4e00\u6761\u5168\u65b0\u8d5b\u9053\u3002\u8fc7\u53bb\uff0c\u4eba\u4eec\u65e0\u8bba\u7814\u5236\u51fa\u591a\u4e48\u5148\u8fdb\u7684\u8868\u5f81\u4eea\u5668\uff0c\u5bf9\u4e8e\u7269\u8d28\u5185\u90e8\u5fae\u89c2\u5c42\u9762\u53d1\u751f\u7684\u7269\u7406\u4ecd\u7136\u9700\u8981\u5927\u80c6\u5047\u8bbe\u3001\u5c0f\u5fc3\u6c42\u8bc1\u3002\u91cf\u5b50\u6a21\u62df\u5219\u53ef\u4ee5\u5148\u7406\u8bba\u540e\u5b9e\u9a8c\uff0c\u901a\u8fc7\u4e8b\u5148\u8bbe\u8ba1\u6765\u5b9e\u73b0\u65b0\u5947\u7269\u76f8\uff0c\u8fd9\u662f\u4e00\u6761\u524d\u6240\u672a\u6709\u7684\u7814\u7a76\u65b0\u601d\u8def\uff0c\u6b63\u5982Nature Physics<\/em>\u7684\u4e00\u7bc7\u65b0\u95fb\u6807\u9898\u8bb2\u7684\uff1a\u201cMeasurements make the phase\u201d[17]\u3002<\/span><\/section>\n

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\u5f53\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\u521a\u88ab\u63d0\u51fa\u65f6\uff0c\u71b5\u88ab\u8ba4\u4e3a\u662f\u4eba\u7c7b\u5bf9\u5b87\u5b99\u65e0\u77e5\u7684\u7a0b\u5ea6\uff0c\u540e\u6765\u4e0e\u4fe1\u606f\u8bba\u76f8\u7ed3\u5408\uff0c\u71b5\u4e5f\u56e0\u6b64\u88ab\u8d4b\u4e88\u4e86\u4fe1\u606f\u91cf\u7684\u7269\u7406\u5185\u6db5\u3002\u4ece\u8fd9\u4e2a\u610f\u4e49\u4e0a\u8bb2\uff0c\u53ea\u8981\u8fd8\u5b58\u5728\u71b5\u8fd9\u4e2a\u7269\u7406\u91cf\uff0c\u4e07\u7269\u7406\u8bba\u4f3c\u4e4e\u5c31\u4e0d\u5e94\u8be5\u5b58\u5728\u3002\u4f46\u662f\u73b0\u5728\uff0c\u7ea0\u7f20\u71b5\u4f5c\u4e3a\u4e00\u4e2a\u53ef\u89c2\u6d4b\u91cf\u5df2\u7ecf\u6e17\u900f\u5230\u7269\u8d28\u79d1\u5b66\u7814\u7a76\u7684\u65b9\u65b9\u9762\u9762\uff0c\u57fa\u4e8e\u7ea0\u7f20\u7684\u7406\u8bba\u6781\u6709\u53ef\u80fd\u5728\u672a\u6765\u626e\u6f14\u4e07\u7269\u7406\u8bba\u7684\u89d2\u8272\u3002\u5728\u90a3\u4e4b\u524d\uff0c\u5173\u4e8e\u70ed\u7684\u5b9a\u4e49\u662f\u5426\u8fd8\u5e94\u5f53\u4e0e\u71b5\u6302\u94a9\uff0c\u9700\u8981\u66f4\u52a0\u4ed4\u7ec6\u7814\u7a76\u3002<\/span><\/section>\n

<\/section>\n
\u4e0d\u4ec5\u662f\u70ed\uff0c\u7c92\u5b50\u6570\u662f\u5426\u4e00\u4e2a\u591a\u4f59\u7684\u6982\u5ff5\uff1f\u5316\u5b66\u52bf\u4e0e\u6e29\u5ea6\u662f\u5426\u540c\u4e00\u4e2a\u7269\u7406\u91cf\uff1f\u8fd9\u4e00\u7c7b\u95ee\u9898\u8fd1\u5e74\u6765\u4e5f\u88ab\u5e7f\u6cdb\u63a2\u8ba8[18]\u3002\u968f\u7740\u62d3\u6251\u5f26\u7b49\u56fe\u50cf\u9010\u6e10\u5c06\u57fa\u672c\u7c92\u5b50\u56ca\u62ec\u8fdb\u7ea0\u7f20\u7684\u7406\u8bba\u4f53\u7cfb\u4e2d\uff0c\u8fd9\u6837\u7684\u63a2\u8ba8\u4f1a\u66f4\u52a0\u6df1\u5165\uff0c\u5e76\u9010\u6e10\u5efa\u7acb\u8d77\u771f\u6b63\u5177\u6709\u91cf\u5b50\u5316\u7279\u5f81\u7684\u70ed\u529b\u5b66\u7406\u8bba\uff0c\u90a3\u4e5f\u5c06\u662f\u66f4\u5177\u9769\u547d\u6027\u7684\u4e07\u7269\u7406\u8bba\u3002<\/span><\/section>\n

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

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[1] Crooks G E. Phys. Rev. E\uff0c1999\uff0c60\uff1a2721<\/span><\/section>\n
[2] Jarzynski C. Phys. Rev. E\uff0c1997\uff0c58\uff1a5018<\/span><\/section>\n
[3] Liphardt J\uff0cDumont S\uff0cSmith S B et al. Science\uff0c2002\uff0c296\uff1a1832<\/span><\/section>\n
[4] Haake F. Quantum Signatures of Chaos. 2nd edition\uff0cSpringer Series in Synergetics. Berlin\uff1aSpringerVerlag\uff0c2001<\/span><\/section>\n
[5] Bunimovich L A. Commun. Math. Phys.\uff0c1979\uff0c65\uff1a295<\/span><\/section>\n
[6] Rigol M\uff0cDunjko V\uff0cOlshanii M. Nature\uff0c2008\uff0c452\uff1a854<\/span><\/section>\n
[7] Nandkishore R\uff0cHuse D A. Annu. Rev.Condens. Matter Phys.\uff0c2015\uff0c6\uff1a15<\/span><\/section>\n
[8] Basko D M\uff0cAleiner I L\uff0cAltshuler B L. Annals of Physics\uff0c2006\uff0c321\uff1a1126<\/span><\/section>\n
[9] Bardarson J H\uff0cPollmann F\uff0cMoore J E. Phys. Rev. Lett.\uff0c2012\uff0c109\uff1a017202<\/span><\/section>\n
[10] Lande A. Phys. Rev.\uff0c1952\uff0c87\uff1a267<\/span><\/section>\n
[11] Kosloff R\uff0cLevy A. Annu. Rev. Phys. Chem.\uff0c2014\uff0c65\uff1a365<\/span><\/section>\n
[12] Toyabe S\uff0cSagawa T\uff0cUeda M et al. Nat. Phys.\uff0c2010\uff0c6\uff1a988<\/span><\/section>\n
[13] Goold J\uff0cHuber M\uff0cRiera A et al. J. Phys. A\uff1aMath. Theor.\uff0c2016\uff0c49\uff1a143001<\/span><\/section>\n
[14] Janzing D\uff0cWocjan P\uff0cZeier R et al. Int. J. Theor. Phys.\uff0c2000\uff0c39\uff1a2717<\/span><\/section>\n
[15] Laughlin R B\uff0cPines D. PNAS\uff0c2000\uff0c97\uff1a28<\/span><\/section>\n
[16] Wen X G. National Science Review\uff0c2016\uff0c3\uff1a68<\/span><\/section>\n
[17] Ware B\uff0cVasseur R. Nature Physics\uff0c2021\uff0c17\uff1a294<\/span><\/section>\n
[18] Khemani V\uff0cVishwanath A\uff0cHuse D A. Phys. Rev. X\uff0c2018\uff0c8\uff1a031057<\/span><\/section>\n


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


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\u52a0\u5927\u5723\u8fed\u6208\u5206\u6821\uff1a\u91cf\u5b50\u529b\u5b66<\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/section>\n
2022\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u6388\u4e88\u4e86\u5173\u4e8e\u91cf\u5b50\u4fe1\u606f\u79d1\u5b66\u7684\u57fa\u7840\u6027\u7814\u7a76\u3002\u4e00\u767e\u591a\u5e74\u524d\uff0c\u91cf\u5b50\u9769\u547d\u4e3a\u6211\u4eec\u5e26\u6765\u4e86\u6676\u4f53\u7ba1\u548c\u6fc0\u5149\uff0c\u4eca\u5929\uff0c\u64cd\u4f5c\u7ea0\u7f20\u7c92\u5b50\u7684\u6280\u672f\u6b63\u5728\u8ba9\u6211\u4eec\u8fdb\u5165\u4e00\u4e2a\u65b0\u7684\u91cf\u5b50\u4fe1\u606f\u65f6\u4ee3\u3002\u96c6\u667a\u4ff1\u4e50\u90e8\u957f\u671f\u5173\u6ce8\u91cf\u5b50\u79d1\u5b66\u53ca\u5176\u5728\u524d\u6cbf\u4ea4\u53c9\u9886\u57df\u7684\u5e94\u7528\uff0c\u5305\u62ec\u91cf\u5b50\u529b\u5b66\u4e0e\u673a\u5668\u5b66\u4e60\u3001\u91cf\u5b50\u751f\u7269\u5b66\u3001\u91cf\u5b50\u56e0\u679c\u3001\u91cf\u5b50\u91d1\u878d\u7b49\uff0c\u5e76\u6c89\u6dc0\u4e86\u4e00\u7cfb\u5217\u76f8\u5173\u4e3b\u9898\u7684\u6587\u7ae0\u548c\u5b66\u4e60\u8d44\u6599\uff0c<\/span>\u53c2\u89c1<\/span><\/span>\u201c\u7269\u7406\u4e3b\u9898\u6587\u7ae0\u5408\u96c6<\/a><\/span>\u201d\u4e0e\u201c<\/span>\u91cf\u5b50\u4e16\u754c\u5730\u56fe<\/a>\u201d<\/span>\u3002\u6b22\u8fce\u611f\u5174\u8da3\u7684\u670b\u53cb\u548c\u6211\u4eec\u4e00\u8d77\u63a2\u7d22\uff01<\/span><\/section>\n

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\u8be6\u60c5\u8bf7\u89c1\uff1a<\/span>\u5c24\u4ea6\u5e84\uff1aQuantum Mechanics | \u82f1\u6587\u7cfb\u5217\u8bfe\u7a0b<\/a><\/span><\/span><\/section>\n


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

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

1. <\/strong>\u53cd\u8f6c\u65f6\u95f4\u4e4b\u7bad\uff0c\u91cf\u5b50\u529b\u5b66\u5982\u4f55\u6311\u6218\u70ed\u529b\u5b66\u7b2c\u4e8c\u5b9a\u5f8b\uff1f<\/a><\/strong><\/span><\/strong><\/section>\n
2.<\/strong> \u56e0\u679c\u4e0d\u5bf9\u79f0\u6027\uff1a\u4ece\u70ed\u529b\u5b66\u4e4b\u7bad\u5230\u56e0\u679c\u4e4b\u7bad<\/a><\/strong><\/span><\/section>\n
3. <\/strong><\/strong>PRX \u901f\u9012\uff1a\u91cf\u5b50\u591a\u4f53\u52a8\u529b\u5b66\u7684\u7edf\u4e00\u7406\u8bba\u2014\u2014\u672c\u5f81\u7b97\u5b50\u70ed\u5316\u5b9a\u7406<\/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
<\/a><\/strong><\/strong><\/span><\/section>\n
<\/strong><\/strong>5.<\/strong> \u9f99\u5e74\u5927\u8fd0\u8d77\uff0c\u5b66\u4e60\u6b63\u5f53\u65f6\uff01\u89e3\u9501\u96c6\u667a\u5168\u7ad9\u5185\u5bb9\uff0c\u5f00\u542f\u65b0\u5e74\u5b66\u4e60\u8ba1\u5212<\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/a><\/strong><\/strong><\/strong><\/strong><\/span><\/section>\n
6. <\/strong>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/strong><\/span><\/a><\/section>\n


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

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u62a5\u540d\u8bfe\u7a0b <\/strong><\/span><\/strong><\/span><\/strong><\/section>\n

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

\u5bfc\u8bed \u56db\u5927\u529b\u5b66\u90fd\u6709\u5176\u7ecf\u5178\u4e0e\u91cf\u5b50\u76f8\u5bf9\u5e94\uff0c\u552f\u4e00\u7684\u4f8b\u5916\u662f\u7ecf\u5178\u70ed\u529b\u5b66\u3002\u7ecf\u5178\u70ed\u529b\u5b66\u662f\u5426\u6709\u5176\u5bf9\u5e94\u7684\u91cf\u5b50\u70ed\u529b\u5b66\u5462\uff1f\u4f34\u968f\u7740\u91cf\u5b50\u4fe1\u606f\u7684\u8fc5\u901f\u53d1\u5c55\uff0c\u662f\u5426\u53ef\u4ee5\u5728\u91cf\u5b50\u529b\u5b66\u6846\u67b6\u5185\u91cd\u65b0\u5b9a\u4e49\u91cf\u5b50\u70ed\u529b\u5b66\uff1f\u672c\u6587\u8ba8\u8bba\u4e86\u91cf\u5b50\u6df7\u6c8c\u3001\u91cf\u5b50\u70ed\u5316\u7406\u8bba\u3001\u5c40\u57df\u5316\u3001\u91cf\u5b50\u70ed\u673a\u3001\u91cf\u5b50\u8d44\u6e90\u8bba\u7b49\u6982\u5ff5\uff0c\u5e76\u63a2\u8ba8\u4e86\u91cf\u5b50\u4fe1\u606f\u5982\u4f55\u5e2e\u52a9\u63a2\u7d22\u4e07\u7269\u7406\u8bba\u3002 \u7814\u7a76\u9886\u57df\uff1a\u91cf\u5b50\u70ed\u529b\u5b66…<\/p>\n","protected":false},"author":0,"featured_media":49045,"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\/49097"}],"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=49097"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/49097\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/49045"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=49097"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=49097"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=49097"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=49097"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}