{"id":33974,"date":"2022-04-21T21:14:08","date_gmt":"2022-04-21T13:14:08","guid":{"rendered":"https:\/\/swarma.org\/?p=33974"},"modified":"2022-04-21T21:14:08","modified_gmt":"2022-04-21T13:14:08","slug":"%e8%b6%85%e8%b6%8a%e7%bb%b4%e5%ba%a6%ef%bc%9a%e5%9c%a8%e5%ae%9e%e9%aa%8c%e5%ae%a4%e4%b8%ad%e6%a8%a1%e6%8b%9f%e5%9b%9b%e7%bb%b4%e7%89%a9%e7%90%86%e5%ad%a6","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=33974","title":{"rendered":"\u8d85\u8d8a\u7ef4\u5ea6\uff1a\u5728\u5b9e\u9a8c\u5ba4\u4e2d\u6a21\u62df\u56db\u7ef4\u7269\u7406\u5b66"},"content":{"rendered":"
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<\/strong>\u6211\u4eec\u751f\u6d3b\u5728\u4e09\u7ef4\u7a7a\u95f4\uff0c\u53ef\u662f\u5982\u679c\u7a7a\u95f4\u7ef4\u5ea6\u7684\u6570\u91cf\u589e\u52a0\u5230\u56db\u4e2a\u751a\u81f3\u66f4\u591a\uff0c\u4f1a\u6709\u4ec0\u4e48\u4e0d\u540c\uff1f\u501f\u52a9\u6700\u65b0\u53d1\u5c55\u7684\u7406\u8bba\u548c\u5b9e\u9a8c\u6280\u672f\uff0c\u7269\u7406\u5b66\u5bb6\u5f00\u59cb\u63a2\u7d22\u66f4\u9ad8\u7ef4\u5ea6\u7684\u7269\u7406\u3002\u5b9e\u9a8c\u5ba4\u4e2d\u4e00\u79cd\u88ab\u79f0\u4e3a\u201c\u62d3\u6251\u7edd\u7f18\u4f53\u201d\u7684\u6750\u6599\uff0c\u662f\u6a21\u62df\u56db\u7ef4\u7269\u7406\u7684\u4e3b\u8981\u7075\u611f\u6765\u6e90\uff0c\u5176\u6027\u8d28\u4f1a\u968f\u7740\u7a7a\u95f4\u7ef4\u5ea6\u800c\u6539\u53d8\u3002\u501f\u52a9\u8d85\u51b7\u539f\u5b50\u3001\u5149\u5b50\u751a\u81f3\u7ecf\u5178\u7535\u8def\uff0c\u5c31\u53ef\u4ee5\u5728\u53d7\u63a7\u5b9e\u9a8c\u7cfb\u7edf\u4e2d\u63a2\u6d4b\u56db\u7ef4\u4e16\u754c\u7684\u65b0\u7269\u7406\u73b0\u8c61\u3002<\/span><\/strong><\/p>\n


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\u7814\u7a76\u9886\u57df\uff1a\u7a7a\u95f4\u7ef4\u5ea6\uff0c\u62d3\u6251\u7edd\u7f18\u4f53\uff0c\u51dd\u805a\u6001\u7269\u7406<\/strong><\/strong><\/span><\/strong><\/span><\/strong><\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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Hannah Price<\/span> <\/span>| \u4f5c\u8005<\/strong><\/span><\/strong><\/p>\n

\u6f58\u4f73\u680b<\/span> | <\/strong><\/span>\u8bd1\u8005<\/strong><\/span><\/p>\n

\u9ec4\u6cfd\u8c6a<\/span> | \u5ba1\u6821<\/strong><\/span><\/strong><\/span><\/p>\n

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\u62d3\u6251\u6982\u5ff5\u4ece\u6570\u5b66\u5230\u7269\u7406\u5b66\u7684\u8f6c\u79fb\u52a0\u6df1\u4e86\u7814\u7a76\u4eba\u5458\u5bf9\u7269\u8d28\u72b6\u6001\u7684\u7406\u89e3\uff0c\u5e76\u5bfc\u81f4\u4e86\u5927\u91cf\u5947\u5f02\u62d3\u6251\u6750\u6599\u7684\u53d1\u73b0\u3002\u5728\u6570\u5b66\u4e2d\uff0c\u62d3\u6251\u5b66\u662f\u5bf9\u4e0d\u540c\u8868\u9762\u8fdb\u884c\u5206\u7c7b\u7684\u6700\u8457\u540d\u7684\u6846\u67b6\u3002\u4f8b\u5982\uff0c\u751c\u751c\u5708\u5c5e\u4e8e\u6709\u4e00\u4e2a\u5b54\u7684\u66f2\u9762\u65cf\uff0c\u800c\u6a59\u5b50\u5c5e\u4e8e\u6ca1\u6709\u5b54\u7684\u66f2\u9762\u65cf\u3002\u5982\u679c\u6211\u4eec\u5e73\u6ed1\u5730\u538b\u6241\u4e00\u4e2a\u6a58\u5b50\uff0c\u5b83\u7684\u5f62\u72b6\u4f1a\u53d1\u751f\u53d8\u5316\u3002\u4f46\u5982\u679c\u4e0d\u6495\u5f00\u4e00\u4e2a\u65b0\u7684\u6d1e\uff0c\u5b83\u5c31\u4e0d\u53ef\u80fd\u53d8\u6210\u751c\u751c\u5708\u7684\u5f62\u72b6\uff0c\u4ece\u800c\u6539\u53d8\u62d3\u6251\u7ed3\u6784\u3002\u8fd9\u79cd\u60c5\u51b5\u7531\u4e00\u4e2a\u79f0\u4e3a\u4e8f\u683c<\/span>\uff08genus\uff09<\/span>\u7684\u6307\u6807\u6765\u91cf\u5316\u3002\u5176\u4ed6\u6570\u5b66\u95ee\u9898\u6709\u8bb8\u591a\u5176\u4ed6\u7c7b\u578b\u7684\u62d3\u6251\u6570\uff0c\u4f8b\u5982\u6240\u8c13\u7684\u9648\u6570<\/span>\uff08Chern numbers\uff09<\/span>\uff0c\u8fd9\u4e9b\u5c06\u5728\u540e\u9762\u8ba8\u8bba\u3002<\/span><\/section>\n
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\u56db\u7ef4\u62d3\u6251\u7edd\u7f18\u4f53\u7684\u6545\u4e8b\u59cb\u4e8e\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\uff0c\u8be5\u6548\u5e94\u7531\u5750\u843d\u4e8e\u5fb7\u56fd\u65af\u56fe\u52a0\u7279\u7684\u9a6c\u514b\u65af\u00b7\u666e\u6717\u514b\u56fa\u4f53\u7814\u7a76\u6240\u7684 Klaus von Klitzing \u4e8e1980\u5e74\u53d1\u73b0\u3002\u8fd9\u9879\u7814\u7a76\u4e3a\u4ed6\u8d62\u5f97\u4e861985\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u3002<\/span><\/section>\n
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\u987e\u540d\u601d\u4e49\uff0c\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94<\/strong><\/span>\uff082D quantum Hall effect\uff09<\/span>\u672c\u8d28\u4e0a\u662f\u4e00\u79cd\u4e8c\u7ef4\u73b0\u8c61\uff0c\u6700\u65e9\u5728\u9ad8\u8d28\u91cf\u534a\u5bfc\u4f53\u5f02\u8d28\u7ed3\u4e2d\u79fb\u52a8\u7684\u6709\u6548\u4e8c\u7ef4\u7535\u5b50\u6c14\u4f53\u4e2d\u88ab\u89c2\u5bdf\u5230\u3002[1] \u5728\u4ed6\u7684\u5f00\u521b\u6027\u5b9e\u9a8c\u4e2d\uff0cvon Klitzing\u5c06\u7845\u57fa\u5f02\u8d28\u7ed3\u66b4\u9732\u5728\u4f4e\u6e29\u548c\u5411\u5916\u7684\u5f3a\u78c1\u573a\u4e2d\uff0c\u7136\u540e\u8ba9\u7535\u6d41\u6d41\u8fc7\u88c5\u7f6e\uff0c\u6d4b\u91cf\u5176\u4e24\u7aef\u7684\u7535\u538b\u4ee5\u627e\u5230\u970d\u5c14\u7535\u5bfc\u3002\u4ed6\u7684\u53d1\u73b0\u4ee4\u4eba\u51fa\u4e4e\u610f\u6599\uff1a\u970d\u5c14\u7535\u5bfc\u8868\u73b0\u4e3a\u7a33\u5b9a\u7684\u5e73\u53f0\uff0c\u88ab \ud835\udc522<\/sup><\/span>\/\u210e \u7684\u6574\u6570\u500d\u7cbe\u786e\u91cf\u5b50\u5316\uff0c\u5176\u4e2d\ud835\udc52\u662f\u7535\u5b50\u7535\u8377\uff0c\u210e\u662f\u666e\u6717\u514b\u5e38\u91cf\u3002\u4e8b\u5b9e\u4e0a\uff0c\u8fd9\u79cd\u91cf\u5b50\u5316\u8db3\u591f\u7684\u9c81\u68d2\u548c\u7cbe\u786e\uff0c\u540e\u6765\u6210\u4e3a2019\u5e74\u56fd\u9645\u5355\u4f4d\u5236\u4e2d\u5bf9\u5343\u514b\u7684\u65b0\u5b9a\u4e49\u7684\u4e00\u90e8\u5206\u3002<\/span><\/section>\n
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\u56fe2. \u970d\u5c14\u7535\u5bfc\u548c\u78c1\u573a\u7684\u5173\u7cfb\u3002\u53ef\u4ee5\u770b\u5230\uff0c\u970d\u5c14\u7535\u5bfc\u8868\u73b0\u4e3a\u7a33\u5b9a\u7684\u5e73\u53f0\uff0c\u88ab \ud835\udc522<\/sup><\/span>\/\u210e \u7684\u6574\u6570\u500d\u7cbe\u786e\u91cf\u5b50\u5316\u3002| \u56fe\u7247\u6765\u6e90\uff1aKlaus von Klitzing\/1985 Nobel Lecture<\/span><\/p>\n

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1982\u5e74\uff0c\u897f\u96c5\u56fe\u534e\u76db\u987f\u5927\u5b66\u7684 David Thouless \u548c\u4ed6\u7684\u540c\u4e8b\u8bc1\u660e\uff0c\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u7684\u8d77\u6e90\u5728\u4e8e\u7535\u5b50\u80fd\u5e26\u7684\u62d3\u6251\u6027\u8d28\u3002\u8fd9\u4e00\u8ba4\u8bc6\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u662f Thouless \u83b7\u5f972016\u5e74\u8bfa\u8d1d\u5c14\u7269\u7406\u5b66\u5956\u7684\u539f\u56e0\u3002\u970d\u5c14\u7535\u5bfc\u4e2d\u7684\u6574\u6570\u4e0e\u79f0\u4e3a\u7b2c\u4e00\u9648\u6570\u7684\u4e8c\u7ef4\u62d3\u6251\u6570\u6709\u5173\uff0c\u5176\u4fdd\u8bc1\u4e86\u6750\u6599\u8fb9\u7f18\u5468\u56f4\u5b58\u5728\u62d3\u6251\u7535\u6d41[1]<\/span>\uff08\u89c1\u56fe1\uff09<\/span>\u3002\u6362\u53e5\u8bdd\u8bf4\uff0c\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u7cfb\u7edf\u662f\u73b0\u5728\u88ab\u79f0\u4e3a\u62d3\u6251\u7edd\u7f18\u4f53\u7684\u4e00\u4e2a\u4f8b\u5b50<\/strong>\uff0c\u970d\u5c14\u7535\u5bfc\u7684\u9c81\u68d2\u6027\u662f\u5176\u5173\u952e\u5b9e\u9a8c\u7279\u5f81\u4e4b\u4e00\u3002<\/span><\/span><\/section>\n

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\u5728\u53d1\u73b0\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u540e\uff0c\u7406\u8bba\u7269\u7406\u5b66\u5bb6\u63d0\u51fa\uff0c\u67d0\u4e9b\u4e09\u7ef4\u6750\u6599\u4e5f\u5177\u6709\u4ee5\u7b2c\u4e00\u9648\u6570\u4e3a\u7279\u5f81\u7684\u80fd\u5e26\uff0c\u4f46\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u9648\u6570\u662f\u4e09\u5143\u6570\u7ec4\uff1a\u5176\u4e2d\u6bcf\u4e2a\u6570\u5bf9\u5e94\u4e8e\u4e09\u7ef4\u6750\u6599\u7684\u4e09\u4e2a\u7b1b\u5361\u5c14\u5e73\u9762\u3002\u7406\u8bba\u4e0a\u7684\u4e09\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u4e8e2019\u5e74\u5728\u4e94\u78b2\u9506\u6676\u4f53\u4e2d\u901a\u8fc7\u5b9e\u9a8c\u89c2\u5bdf\u5230\u3002[2]\u4f46\u4e09\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94<\/strong>\u901a\u5e38\u88ab\u79f0\u4e3a\u5f31\u62d3\u6251\u73b0\u8c61\uff0c\u56e0\u4e3a\u5173\u952e\u7279\u6027<\/span>\uff08\u4f8b\u5982\u7b2c\u4e00\u9648\u6570\uff09<\/span>\u672c\u8d28\u4e0a\u4ecd\u7136\u662f\u4e8c\u7ef4\u6982\u5ff5\uff0c\u5373\u4f7f\u7cfb\u7edf\u662f\u4e09\u7ef4\u7684\u3002\u56e0\u6b64\uff0c\u7531\u6b64\u4ea7\u751f\u7684\u62d3\u6251\u884c\u4e3a\u6709\u65f6\u53ef\u80fd\u4e0d\u592a\u9c81\u68d2\u3002<\/span><\/section>\n
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\u7136\u800c\uff0c\u5728\u56db\u4e2a\u7a7a\u95f4\u7ef4\u5ea6\u7684\u60c5\u5f62\u4e0b\uff0c\u4e00\u79cd\u5728\u6839\u672c\u4e0a\u4e0d\u540c\u7684\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u7531\u745e\u58eb\u82cf\u9ece\u4e16\u8054\u90a6\u7406\u5de5\u5b66\u9662\u7684 J\u00fcrg Fr\u00f6hlich \u548c Bill Pedrini\uff0c\u4ee5\u53ca\u65af\u5766\u798f\u5927\u5b66\u7684\u5f20\u9996\u665f\u548c\u80e1\u6c5f\u5e73\u572821\u4e16\u7eaa\u521d\u72ec\u7acb\u63d0\u51fa\u3002[3]\u8be5\u56db\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94<\/strong>\u5177\u6709\u4e0e\u4e8c\u7ef4\u970d\u5c14\u6548\u5e94\u4e0d\u540c\u7684\u91cf\u5b50\u5316\u970d\u5c14\u7535\u5bfc\u5f62\u5f0f\uff0c\u5e76\u4e14\u4e0e\u4e00\u4e2a\u79f0\u4e3a\u7b2c\u4e8c\u9648\u6570\u7684\u56db\u7ef4\u62d3\u6251\u4e0d\u53d8\u91cf\u6709\u5173\uff0c\u8be5\u4e0d\u53d8\u91cf\u4ea7\u751f\u4e86\u4e09\u7ef4\u5bfc\u7535\u8868\u9762\u4f53\u79ef\uff0c\u5982\u56fe1\u6240\u793a\u3002<\/span><\/section>\n
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\u8fc4\u4eca\u4e3a\u6b62\uff0c\u79d1\u5b66\u5bb6\u5df2\u7ecf\u63d0\u51fa\u4e86\u5404\u79cd\u56db\u7ef4\u91cf\u5b50\u970d\u5c14\u6a21\u578b\u3002[3-5]\u6709\u4e9b\u6a21\u578b\u7c7b\u4f3c\u4e8e\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\uff0c\u63cf\u8ff0\u78c1\u573a\u4e2d\u7684\u5e26\u7535\u7c92\u5b50\u3002\u5176\u4ed6\u6a21\u578b\uff0c\u5982\u5f20\u9996\u665f\u548c\u80e1\u6c5f\u5e73\u7684\u6a21\u578b\uff0c\u5229\u7528\u6768-\u7c73\u5c14\u65af\u89c4\u8303\u573a<\/span>\uff08Yang\u2013Mills gauge field\uff09<\/span>\u7684\u7269\u7406\uff0c\u5982\u65b9\u68462\u6240\u89e3\u91ca\u7684\uff0c\u5e76\u4ece\u7c92\u5b50\u7269\u7406\u5b66\u4e2d\u6c72\u53d6\u7075\u611f\u3002[6]<\/span><\/section>\n

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\u4e00\u79cd\u8003\u8651\u62d3\u6251\u6cf5<\/span>\uff08topological pumping\uff09<\/span>\u7684\u65b9\u5f0f\u662f\uff0c\u5b83\u7528\u5916\u90e8\u63a7\u5236\u7684\u53c2\u6570\u53d6\u4ee3\u4e86\u54c8\u5bc6\u987f\u91cf\u4e2d\u7684\u4e00\u4e9b\u771f\u5b9e\u7a7a\u95f4\u7ef4\u5ea6\u3002\u4f46\u662f\u5982\u679c\u6240\u6709\u7684\u7a7a\u95f4\u7ef4\u5ea6\u90fd\u88ab\u6362\u6210\u4e86\u5916\u90e8\u63a7\u5236\u7684\u53c2\u6570\uff0c\u90a3\u4e48\u5c31\u4e0d\u9700\u8981\u771f\u5b9e\u7684\u7a7a\u95f4\u81ea\u7531\u5ea6\u6765\u6a21\u62df\u66f4\u9ad8\u7684\u7ef4\u5ea6\u4e86\u3002<\/span><\/section>\n

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2018\u5e74\uff0cSeiji Sugawa\u3001Ian Spielman \u548c\u4ed6\u4eec\u5728\u8054\u5408\u91cf\u5b50\u7814\u7a76\u6240\u548c\u9a6c\u91cc\u5170\u5927\u5b66\u7684\u540c\u4e8b\u4f7f\u7528\u4e86\u8fd9\u79cd\u7c7b\u578b\u7684\u65b9\u6cd5\u3002\u53d7\u5f20\u9996\u665f\u548c\u80e1\u6c5f\u5e73\u5173\u4e8e\u56db\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u7684\u5de5\u4f5c\u542f\u53d1\uff0c[4]\u7814\u7a76\u4eba\u5458\u5728\u4e00\u4e2a\u6709\u6548\u7684\u4e94\u7ef4\u53c2\u6570\u7a7a\u95f4\u4e2d\uff0c\u901a\u8fc7\u8026\u5408\u539f\u5b50\u91cf\u5b50\u6c14\u4f53\u7684\u56db\u4e2a\u5185\u90e8\u72b6\u6001\uff0c\u5b9e\u9a8c\u6a21\u62df\u4e86\u6240\u8c13\u7684\u6768\u6c0f\u5355\u6781\u5b50<\/span>\uff08Yang monopole\uff09<\/span>\u3002[16]\u4e0e\u4fdd\u7f57\u00b7\u72c4\u62c9\u514b<\/span>\uff08Paul Dirac\uff09<\/span>\u5047\u5b9a\u5047\u60f3\u7684\u78c1\u5355\u6781\u5b50\u662f\u78c1\u573a\u7684\u6765\u6e90\u7c7b\u4f3c\uff0c\u6768\u6c0f\u5355\u6781\u5b50\u88ab\u63d0\u8bae\u4f5c\u4e3a\u4e94\u7ef4\u7684\u6768-\u7c73\u5c14\u65af\u89c4\u8303\u573a\u7684\u6765\u6e90\u3002Sugawa\u3001Spielman\u548c\u4ed6\u4eec\u7684\u540c\u4e8b\u786e\u5b9a\u4e86\u6a21\u62df\u5355\u6781\u5b50\u7684\u6027\u8d28\uff0c\u5e76\u9a8c\u8bc1\u4e86\u5b83\u53ef\u4ee5\u88ab\u7b2c\u4e8c\u9648\u6570\u52a0\u4ee5\u533a\u5206\uff0c\u6b63\u5982\u9884\u6d4b\u7684\u90a3\u6837\u3002<\/span><\/section>\n

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\u6700\u8fd1\uff0c\u57282020\u5e74\uff0c\u7c7b\u4f3c\u7684\u5b9e\u9a8c\u65b9\u6cd5\u5df2\u7ecf\u6a21\u62df\u4e86\u6240\u8c13\u7684\u56db\u7ef4\u5f20\u91cf\u5355\u6781\u5b50<\/span>\uff08tensor monopole\uff09<\/span>\uff0c\u5b83\u88ab\u5047\u8bbe\u4e3a\u5f20\u91cf\u89c4\u8303\u573a\u7684\u6765\u6e90\uff0c\u5176\u7279\u5f81\u662f\u4e00\u79cd\u79f0\u4e3a Dixmier-Douady \u4e0d\u53d8\u91cf\u7684\u5947\u5f02\u62d3\u6251\u6570[14]\u3002<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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\u4e09\u3001\u62d3\u6251\u7269\u7406\u5b66\uff0c\u4e0d\u53ea\u662f\u7535\u5b50<\/strong><\/strong><\/p>\n<\/section>\n

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\u5411\u975e\u7535\u5b50\u5e73\u53f0\u7684\u6269\u5c55\u4e5f\u6709\u5229\u4e8e\u5bf9\u62d3\u6251\u73b0\u8c61\u7684\u7814\u7a76\u3002\u5176\u4e2d\u8bb8\u591a\u5e73\u53f0\u6bd4\u771f\u5b9e\u7684\u6750\u6599\u66f4\u5bb9\u6613\u8c03\u63a7\uff0c\u56e0\u6b64\u4f7f\u79d1\u5b66\u5bb6\u4eec\u80fd\u591f\u5728\u76ee\u524d\u56fa\u4f53\u7269\u7406\u5b66\u53ef\u7814\u7a76\u7684\u8303\u56f4\u4e4b\u5916\u8fdb\u884c\u63a2\u7d22\u3002[5]\u4f5c\u4e3a\u63a8\u52a8\u5de5\u4f5c\u7684\u4e00\u90e8\u5206\uff0c\u7814\u7a76\u4eba\u5458\u5df2\u7ecf\u53d1\u5c55\u4e86\u6a21\u62df\u989d\u5916\u7ef4\u5ea6\u7684\u5b9e\u9a8c\u6280\u5de7\uff0c\u90e8\u5206\u539f\u56e0\u662f\u4e3a\u4e86\u63a2\u6d4b\u9ad8\u7ef4\u62d3\u6251\u7edd\u7f18\u4f53\u3002\u4e09\u4e2a\u4e3b\u8981\u7684\u65b9\u6cd5\u662f\u62d3\u6251\u6cf5<\/span>\uff08topological pumping\uff09<\/span>\u3001\u8fde\u63a5<\/span>\uff08connectivity\uff09<\/span>\u548c\u4eba\u5de5\u7ef4\u5ea6<\/span>\uff08synthetic dimensions\uff09<\/span>\uff0c\u5c3d\u7ba1\u5176\u4ed6\u65b9\u6848\u4e5f\u5728\u5f00\u53d1\u4e2d\u3002<\/span><\/section>\n
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\u56db\u3001\u63a2\u6d4b\u9ad8\u7ef4\u62d3\u6251\u7edd\u7f18\u4f53\u7684\u65b9\u6cd5<\/strong><\/strong><\/p>\n<\/section>\n

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\u65b9\u6cd51\uff1a\u62d3\u6251\u6cf5<\/span><\/strong><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n


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\u6700\u65e9\u4f46\u4e5f\u8bb8\u662f\u6700\u62bd\u8c61\u7684\u6a21\u4eff\u9ad8\u7ef4\u5ea6\u7684\u6280\u5de7\u4e4b\u4e00\u662f\u62d3\u6251\u6cf5<\/span>\uff08topological pumping\uff09<\/span>\u3002\u8fd9\u4e2a\u6982\u5ff5\u7531 Thouless \u4f5c\u4e3a\u5b9e\u73b0\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u7684\u4e00\u79cd\u65b9\u6cd5\u57281981\u5e74\u9996\u6b21\u63d0\u51fa\u3002\u4ed6\u9884\u6d4b\uff0c\u7f13\u6162\u5730\u8c03\u6574\u67d0\u4e9b\u7c7b\u578b\u7684\u4e00\u7ef4\u91cf\u5b50\u7cfb\u7edf\u7684\u53c2\u6570\u53ef\u4ee5\u9c81\u68d2\u5730\u5728\u7cfb\u7edf\u4e2d\u6cf5\u9001\u7c92\u5b50\u3002[1]<\/span><\/section>\n
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\u6700\u7b80\u5355\u7684\u4f8b\u5b50\u4ece\u4e00\u79cd\u7edd\u7f18\u4f53\u5f00\u59cb\uff0c\u5176\u4e2d\u7c92\u5b50\u5360\u636e\u4e00\u7ef4\u5468\u671f\u52bf\u9631\u94fe\u7684\u6bcf\u4e2a\u6781\u5c0f\u503c\u3002\u5982\u679c\u6574\u4f53\u7535\u52bf\u7684\u7a7a\u95f4\u4f4d\u7f6e\u88ab\u7f13\u6162\u5730\u8c03\u6574\uff0c\u4f7f\u6574\u4e2a\u6676\u4f53\u6cbf\u7740\u94fe\u6ed1\u52a8\uff0c\u90a3\u4e48\u7531\u6b64\u4ea7\u751f\u7684\u6700\u5c0f\u503c\u70b9\u7684\u8fd0\u52a8\u5c31\u4f1a\u62d6\u52a8\u7c92\u5b50\u4e0e\u5176\u4e00\u8d77\u8fd0\u52a8\u3002Thouless \u4e0d\u4ec5\u8ba1\u7b97\u51fa\u8fd9\u79cd\u9c81\u68d2\u7684\u7c92\u5b50\u8f93\u8fd0\u662f\u4e00\u4e2a\u62d3\u6251\u4e0d\u53d8\u91cf\u7684\u4ea7\u7269\uff0c\u800c\u4e14\u8be5\u4e0d\u53d8\u91cf\u4e0e\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u4e2d\u7684\u4e8c\u7ef4\u62d3\u6251\u6570<\/span>\uff08\u7b2c\u4e00\u9648\u6570\uff09<\/span>\u76f8\u540c\u3002\u8fd9\u4e00\u7ed3\u679c\u8868\u660e\uff0c\u4ece\u67d0\u79cd\u610f\u4e49\u4e0a\u8bf4\uff0c\u4e00\u7ef4\u62d3\u6251\u6cf5\u662f\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u7684\u52a8\u6001\u7248\u672c<\/strong>\uff0c\u8fd9\u4e00\u70b9\u540e\u6765\u5df2\u5728\u5b9e\u9a8c\u4e2d\u5f97\u5230\u63a2\u7d22\u3002<\/span><\/section>\n
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\u4ece\u4e00\u7ef4\u5230\u4e8c\u7ef4\u4f3c\u4e4e\u4e0e\u9ad8\u7ef4\u7269\u7406\u5b66\u76f8\u53bb\u751a\u8fdc\u3002\u4f46\u57282013\u5e74\uff0c\u4ee5\u8272\u5217\u9b4f\u8328\u66fc\u79d1\u5b66\u7814\u7a76\u6240\u7684Yaacov Kraus\u3001\u82f1\u56fd\u725b\u6d25\u5927\u5b66\u7684Zohar Ringel\u548c\u82cf\u9ece\u4e16\u8054\u90a6\u7406\u5de5\u5b66\u9662\u7684Oded Zilberberg\u9884\u6d4b\uff0c\u4e8c\u7ef4\u62d3\u6251\u6cf5\u4e0e\u56db\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u7684\u56db\u7ef4\u62d3\u6251\u6570<\/span>\uff08\u7b2c\u4e8c\u9648\u6570\uff09<\/span>\u6709\u5173\u3002[4]<\/span><\/section>\n
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\u8be5\u9884\u8a00\u57282018\u5e74 Zilberberg \u9886\u5bfc\u7684\u4e24\u4e2a\u8865\u5145\u5b9e\u9a8c\u4e2d\u88ab\u8bc1\u660e\u662f\u6b63\u786e\u7684\u3002\u4e00\u4e2a\u662f\u4ed6\u4e0e\u5bbe\u5915\u6cd5\u5c3c\u4e9a\u5dde\u7acb\u5927\u5b66\u7684 Mikael Rechtsman \u56e2\u961f\u5728\u5149\u5b50\u5b66\u4f53\u7cfb\u4e2d\u8fdb\u884c\uff1b\u53e6\u4e00\u4e2a\u662f\u4e0e\u5fb7\u56fd\u9a6c\u514b\u601d\u00b7\u666e\u6717\u514b\u91cf\u5b50\u5149\u5b66\u7814\u7a76\u6240\u548c\u6155\u5c3c\u9ed1\u5927\u5b66\u7684 Immanuel Bloch \u56e2\u961f\u4ee5\u53ca\u6211\u5728\u4f2f\u660e\u7ff0\u5927\u5b66\u7684\u5408\u4f5c\u8005\u5728\u51b7\u539f\u5b50\u4f53\u7cfb\u4e2d\u5b8c\u6210\u7684[7]\u3002\u8fd9\u4e9b\u5b9e\u9a8c\u5206\u522b\u5728\u5149\u5728\u6ce2\u5bfc\u9635\u5217\u8fb9\u7f18\u7684\u4f20\u64ad\u548c\u539f\u5b50\u5728\u7cfb\u7edf\u4e2d\u7684\u51c0\u8fd0\u52a8\u4e2d\u53d1\u73b0\u4e86\u56db\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u7684\u7279\u5f81\uff0c\u540e\u6765\u53c8\u88ab\u5176\u4ed6\u8bfe\u9898\u7ec4\u63a8\u5e7f\u5230\u58f0\u5b66\u5e73\u53f0\u4e0a\u3002<\/span><\/section>\n
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\u62d3\u6251\u6cf5\u6709\u8bb8\u591a\u5185\u5728\u7684\u9650\u5236\uff0c\u56e0\u4e3a\u5b83\u672c\u8d28\u4e0a\u662f\u4e00\u79cd\u6570\u5b66\u6280\u5de7\uff0c\u57fa\u4e8e\u5de7\u5999\u7684\u65b9\u6cd5\u5207\u5272\u66f4\u9ad8\u7ef4\u6a21\u578b\u3002\u5b9e\u9645\u4e0a\uff0c\u7c92\u5b50\u53ea\u80fd\u5728\u4f4e\u7ef4\u7cfb\u7edf\u4e2d\u79fb\u52a8\uff0c\u800c\u4e0d\u5177\u6709\u8db3\u591f\u7684\u9ad8\u7ef4\u81ea\u7531\u5ea6\u3002\u901a\u8fc7\u5176\u4ed6\u7c7b\u578b\u7684\u5b9e\u9a8c\u65b9\u6848\uff0c\u53ef\u80fd\u5b9e\u73b0\u66f4\u63a5\u8fd1\u771f\u5b9e\u7684\u9ad8\u7ef4\u7cfb\u7edf\u3002<\/span><\/section>\n
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\u65b9\u6cd52\uff1a\u7535\u8def\u8fde\u63a5<\/span><\/strong><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n


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\u6a21\u62df\u66f4\u9ad8\u7a7a\u95f4\u7ef4\u5ea6\u7684\u7b2c\u4e8c\u79cd\u65b9\u6cd5\u662f\u57fa\u4e8e\u8fde\u63a5\u7684\u6982\u5ff5\uff0c\u8fd9\u53ef\u4ee5\u4ece\u79bb\u6563\u6676\u683c\u6a21\u578b\u5f00\u59cb\u7406\u89e3\u3002\u5728\u8fd9\u4e9b\u6a21\u578b\u4e2d\uff0c\u7c92\u5b50\u53ea\u80fd\u5b58\u5728\u4e8e\u4e00\u7ec4\u6676\u683c\u4f4d\u70b9\u4e0a\u3002\u8fd9\u4e9b\u683c\u70b9\u53ef\u4ee5\u8868\u793a\u4e3a\u5206\u5e03\u5728\u7a7a\u95f4\u4e2d\u7684\u4e00\u7ec4\u79bb\u6563\u7684\u70b9\uff0c\u5982\u56fe4\u6240\u793a\u3002\u6839\u636e\u6a21\u578b\u7684\u5177\u4f53\u60c5\u51b5\uff0c\u7c92\u5b50\u53ef\u4ee5\u5728\u6210\u5bf9\u7684\u683c\u70b9\u4e4b\u95f4\u8df3\u8dc3\uff0c\u5982\u865a\u7ebf\u6240\u793a\u3002\u8fd9\u79cd\u79bb\u6563\u7684\u6676\u683c\u6a21\u578b\u662f\u771f\u5b9e\u7cfb\u7edf\u7684\u5e38\u89c1\u8fd1\u4f3c\uff0c\u5305\u62ec\u7535\u5b50\u5728\u56fa\u4f53\u6750\u6599\u4e2d\u79fb\u52a8\u548c\u7535\u6d41\u5728\u7535\u8def\u4e2d\u79fb\u52a8\u3002\u5b83\u4eec\u8fd8\u53ef\u4ee5\u8bc6\u522b\u548c\u5206\u79bb\u73b0\u8c61\u7684\u57fa\u672c\u7ec4\u6210\u6210\u5206\u3002<\/span><\/section>\n
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\u56fe4. \u66f4\u9ad8\u7ef4\u7684\u683c\u5b50\u53ef\u4ee5\u5728\u4f4e\u7ef4\u7cfb\u7edf\u4e2d\u6784\u5efa\u3002\u5728\u5de6\u8fb9\uff0c\u4e00\u4e2a\u4e8c\u7ef4\u7684\u79bb\u6563\u6676\u683c\u6a21\u578b\u662f\u7531\u683c\u70b9\uff08\u5706\u5708\uff09\u4e0e\u8fde\u63a5\uff08\u7ebf\uff09\u7ec4\u6210\u7684\u3002\u5982\u679c\u4fdd\u6301\u76f8\u540c\u7684\u8fde\u63a5\uff0c\u76f8\u540c\u7684\u6676\u683c\u53ef\u4ee5\u6709\u6548\u5730\u5d4c\u5165\u5230\u4e00\u7ef4\u4e2d\u3002\u5728\u53f3\u8fb9\uff0c\u8fd9\u79cd\u5d4c\u5165\u6280\u5de7\u88ab\u7528\u6765\u5c06\u56db\u7ef4\u6676\u683c\u7f16\u7801\u5230\u8fd9\u4e2a\u4e09\u7ef4\u7535\u8def\u677f\u5806\u4e2d\u3002<\/span><\/p>\n

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\u7406\u89e3\u9ad8\u7ef4\u6a21\u62df\u7684\u5173\u952e\u5728\u4e8e\uff0c\u79bb\u6563\u683c\u70b9\u6a21\u578b\u672c\u8d28\u4e0a\u662f\u4e00\u4e2a\u7531\u8282\u70b9<\/span>\uff08\u5982\u683c\u70b9\uff09<\/span>\u548c\u8fde\u63a5<\/span>\uff08\u5982\u5141\u8bb8\u7684\u8df3\u8dc3\uff09<\/span>\u7ec4\u6210\u7684\u7f51\u7edc\u3002\u8fd9\u4e00\u89c2\u70b9\u8868\u660e\uff0c\u53ea\u8981\u6240\u6709\u8fde\u63a5\u90fd\u76f8\u540c\uff0c\u8282\u70b9\u5728\u5b9e\u7a7a\u95f4\u4e2d\u7684\u7269\u7406\u4f4d\u7f6e\u5e76\u4e0d\u91cd\u8981\u3002<\/span><\/section>\n
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\u4f8b\u5982\uff0c\u5982\u679c\u6bcf\u884c\u7684\u8282\u70b9\u90fd\u662f\u9996\u4f4d\u76f8\u8fde\u5730\u6392\u5217\uff0c\u5219\u56fe4\u4e2d\u7684\u4e8c\u7ef4\u65b9\u6676\u683c\u53ef\u4ee5\u8f6c\u5316\u4e3a\u4e00\u7ef4\u94fe\u3002\u53ea\u8981\u8282\u70b9\u4e4b\u95f4\u5b58\u5728\u76f8\u540c\u7c7b\u578b\u7684\u8fde\u63a5\uff0c\u8be5\u7cfb\u7edf\u5c31\u4f1a\u9075\u5b88\u4e0e\u4e4b\u524d\u76f8\u540c\u7684\u6570\u5b66\u65b9\u7a0b\u3002\u5728\u67d0\u79cd\u610f\u4e49\u4e0a\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u5c06\u4e8c\u7ef4\u6a21\u578b\u5d4c\u5165\u5230\u4e00\u7ef4\u7cfb\u7edf\u4e2d\u2014\u2014\u5c3d\u7ba1\u662f\u4e00\u4e2a\u5947\u602a\u7684\u4e00\u7ef4\u7cfb\u7edf\uff0c\u5176\u4e2d\u4e00\u4e9b\u77ed\u7a0b\u8fde\u63a5\u7f3a\u5931\uff0c\u800c\u5176\u4ed6\u957f\u7a0b\u8fde\u63a5\u51fa\u73b0\u3002<\/span><\/section>\n
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\u540c\u6837\u7684\u60f3\u6cd5\u4e5f\u53ef\u4ee5\u5ef6\u4f38\u5230\u66f4\u9ad8\u7ef4\u7684\u683c\u70b9\u4e0a\u2014\u2014\u4f8b\u5982\uff0c\u7528\u4e09\u7ef4\u6216\u4e8c\u7ef4\u7cfb\u7edf\u521b\u5efa\u4e00\u4e2a\u56db\u7ef4\u683c\u70b9\u6a21\u578b\u3002\u56e0\u6b64\uff0c\u5d4c\u5165\u6280\u5de7\u63d0\u4f9b\u4e86\u4e00\u4e2a\u5728\u771f\u5b9e\u7684\u7269\u7406\u7cfb\u7edf\u4e2d\u5b9e\u73b0\u56db\u7ef4\u6676\u683c\u6a21\u578b\u7684\u8bc0\u7a8d\uff0c\u4f46\u5374\u9762\u4e34\u7740\u8c03\u63a7\u8282\u70b9\u4e4b\u95f4\u590d\u6742\u8fde\u63a5\u7684\u6311\u6218\u3002<\/span><\/section>\n
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\u57282013\u5e74\u7684\u4e00\u4e2a\u65e9\u671f\u65b9\u6848\u4e2d\uff0c\u514b\u7f57\u5730\u4e9a\u8428\u683c\u52d2\u5e03\u5927\u5b66\u7684 Dario Juki\u0107 \u548c Hrvoje Buljan \u8bbe\u60f3\u7528\u5149\u5b50\u6ce2\u5bfc\u6a21\u62df\u4e00\u4e2a\u79bb\u6563\u7684\u56db\u7ef4\u6676\u683c\u3002[8]\u4ece\u90a3\u65f6\u8d77\uff0c\u7814\u7a76\u5174\u8da3\u5c31\u96c6\u4e2d\u5728\u66f4\u7075\u6d3b\u7684\u7cfb\u7edf\u4e0a\uff0c\u5982\u7535\u8def\uff0c\u4ee5\u53ca\u5982\u4f55\u5c06\u7531\u7535\u611f\u3001\u7535\u5bb9\u548c\u7535\u963b\u7ec4\u6210\u7684\u683c\u70b9\u8fde\u5728\u4e00\u8d77\uff0c\u5b9e\u73b0\u56db\u7ef4\u62d3\u6251\u6a21\u578b\u7684\u5404\u79cd\u65b9\u6848\u3002<\/span><\/section>\n
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2020\u5e74\uff0c\u6211\u548c\u65b0\u52a0\u5761\u5357\u6d0b\u7406\u5de5\u5927\u5b66\u7684 You Wang\u3001Baile Zhang\u3001Yidong Chong\u9996\u6b21\u5728\u5b9e\u9a8c\u4e2d\u5e94\u7528\u4e86\u8be5\u65b9\u6cd5\uff0c\u5982\u56fe4\u6240\u793a\u3002\u6211\u4eec\u521b\u5efa\u4e86\u4e00\u4e2a\u5c0f\u578b\u7684\u56db\u7ef4\u62d3\u6251\u6676\u683c\uff0c\u5305\u542b144\u4e2a\u5d4c\u5165\u7535\u8def\u7684\u683c\u70b9\u3002\u5728\u5b9e\u9a8c\u4e2d\uff0c\u6211\u4eec\u8bbe\u8ba1\u4e86\u4e00\u53e0\u4e09\u7ef4\u7535\u8def\u677f\uff0c\u5e76\u5c06\u5b83\u4eec\u8fde\u5728\u4e00\u8d77\uff0c\u4ee5\u5339\u914d\u56db\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u7684\u56db\u7ef4\u79bb\u6563\u6676\u683c\u6a21\u578b\u3002\u6b63\u5982\u5bf9\u56db\u7ef4\u62d3\u6251\u7edd\u7f18\u4f53\u7684\u9884\u6d4b\uff0c\u6211\u4eec\u89c2\u5bdf\u5230\u7535\u6d41\u6d41\u7ecf\u56db\u7ef4\u62d3\u6251\u7edd\u7f18\u4f53\u8868\u9762\u7684\u683c\u70b9\uff0c\u4f46\u6ca1\u6709\u6d41\u7ecf\u5757\u4f53\u5185\u90e8\u3002<\/span><\/section>\n
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\u56fe5. \u4eba\u5de5\u7ef4\u5ea6\u5c06\u539f\u5b50\u81ea\u65cb\u6001\u6216\u5176\u4ed6\u5185\u90e8\u72b6\u6001\u6216\u5185\u5728\u5c5e\u6027\u53d8\u6210\u7c7b\u4f3c\u4e8e\u7a7a\u95f4\u7ef4\u5ea6\u7684\u4e1c\u897f\u3002\u4e00\u4e2a\u4e8c\u7ef4\u79bb\u6563\u6676\u683c\u6a21\u578b\uff08\u5de6\uff09\u5305\u62ec\u4e00\u4e2a\u771f\u5b9e\u7a7a\u95f4\u7ef4\u5ea6\u548c\u4e00\u4e2a\u7531\u539f\u5b50\u81ea\u65cb\u6001\u7ec4\u6210\u7684\u4eba\u5de5\u7ef4\u5ea6\u3002\u6cbf\u7740\u771f\u5b9e\u7ef4\u5ea6\u7684\u8df3\u8dc3\uff08\u5b9e\u7ebf\uff09\u5bf9\u5e94\u4e8e\u771f\u5b9e\u7684\u539f\u5b50\u8fd0\u52a8\uff0c\u800c\u6cbf\u7740\u4eba\u5de5\u7ef4\u5ea6\u7684\u8df3\u8dc3\uff08\u865a\u7ebf\uff09\u5bf9\u5e94\u4e8e\u6fc0\u5149\u8bf1\u5bfc\u7684\u81ea\u65cb\u6001\u4e4b\u95f4\u7684\u8f6c\u6362\u3002\u56db\u7ef4\u8d85\u7acb\u65b9\u6676\u683c\u7684\u5355\u80de\uff08\u53f3\uff09\u662f\u4e00\u4e2a\u8d85\u7acb\u65b9\u4f53\u3002\u8fd9\u79cd\u5f62\u72b6\u53ef\u4ee5\u7528\u771f\u5b9e\u548c\u4eba\u5de5\u7a7a\u95f4\u7ef4\u5ea6\u7684\u9002\u5f53\u7ec4\u5408\u6765\u5236\u4f5c\u3002<\/span><\/p>\n

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\u539f\u5b50\u81ea\u65cb\u6001\u7684\u4eba\u5de5\u7ef4\u5ea6\u7684\u60f3\u6cd5\u8d77\u6e90\u4e8e2012\u5e74\u897f\u73ed\u7259\u5df4\u585e\u7f57\u90a3\u5927\u5b66\u7684 Octavi Boada \u548c Jos\u00e9 Ignacio Latorre \u4ee5\u53ca\u5df4\u585e\u7f57\u90a3\u5149\u5b50\u79d1\u5b66\u7814\u7a76\u6240\u7684 Alessio Celi \u548c Maciej Lewenstein \u7684\u5de5\u4f5c\u3002[10]\u4e09\u5e74\u540e\uff0c\u540c\u6837\u7684\u60f3\u6cd5\u88ab\u6269\u5c55\u5230\u79bb\u6563\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u6676\u683c\u6a21\u578b\uff0c\u5305\u62ec\u4e00\u4e2a\u771f\u5b9e\u7ef4\u5ea6\u548c\u4e00\u4e2a\u4eba\u5de5\u7ef4\u5ea6\uff0c\u5728\u51b7\u539f\u5b50\u5b9e\u9a8c\u4e2d\u5b9e\u73b0\uff0c\u5982\u65b9\u68463\u6240\u793a\u3002\u5728\u672a\u6765\uff0c\u8be5\u65b9\u6cd5\u53ef\u80fd\u88ab\u8fdb\u4e00\u6b65\u63a8\u52a8\uff0c\u4ee5\u5b9e\u73b0\u56db\u7ef4\u62d3\u6251\u6a21\u578b\u3002<\/span><\/section>\n

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\u65b9\u68463\uff1a\u4eba\u5de5\u7ef4\u5ea6\u4e2d\u7684\u8df3\u8dc3<\/span><\/strong><\/strong><\/section>\n

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2015\u5e74\uff0cLENS<\/span>\uff08\u6b27\u6d32\u975e\u7ebf\u6027\u5149\u8c31\u5b9e\u9a8c\u5ba4\uff09<\/span>\u548c\u4f5b\u7f57\u4f26\u8428\u5927\u5b66\u7684 Leonardo Fallani \u548c Massimo Inguscio \u8bfe\u9898\u7ec4\u4ee5\u53ca\u8054\u5408\u91cf\u5b50\u7814\u7a76\u6240\u548c\u9a6c\u91cc\u5170\u5927\u5b66\u5e15\u514b\u5206\u6821\u7684 Ian Spielman \u8bfe\u9898\u7ec4\u90fd\u5b9e\u73b0\u4e86\u4e00\u4e2a\u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u7cfb\u7edf\uff0c\u5305\u542b\u4e00\u4e2a\u771f\u5b9e\u7a7a\u95f4\u7ef4\u5ea6\u548c\u4e00\u4e2a\u4e09\u539f\u5b50\u81ea\u65cb\u6001\u7684\u4eba\u5de5\u7ef4\u5ea6\uff0c[17,18]\u4e0e\u56fe5\u76f8\u4f3c\u3002\u5982\u56fe6\u6240\u793a\uff0c\u8fd9\u4e9b\u7cfb\u7edf\u8868\u73b0\u51fa\u970d\u5c14\u7269\u7406\u7684\u5173\u952e\u7279\u5f81\uff1a\u6cbf\u7cfb\u7edf\u8fb9\u7f18\u8df3\u8dc3\u7684\u8f68\u9053\uff0c\u7c7b\u4f3c\u4e8e\u5e26\u7535\u7c92\u5b50\u5728\u78c1\u573a\u4e2d\u7684\u8f68\u9053\uff0c\u5982\u65b9\u68461\u6240\u89e3\u91ca\u7684\u90a3\u6837\u3002<\/span><\/p>\n


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\u56fe6. \u4e8c\u7ef4\u91cf\u5b50\u970d\u5c14\u7cfb\u7edf\uff0c\u5305\u542b\u4e00\u4e2a\u771f\u5b9e\u7a7a\u95f4\u7ef4\u5ea6\u548c\u4e00\u4e2a\u4e09\u539f\u5b50\u81ea\u65cb\u6001\u7684\u4eba\u5de5\u7ef4\u5ea6\u3002<\/span><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


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1.\u2002B. A. Bernevig, T. L. Hughes, Topological Insulators and Topological Superconductors, Princeton U. Press (2013).<\/span><\/section>\n
2.\u2002F. Tang et al., Nature 569, 537 (2019).<\/span><\/section>\n
3.\u2002J. Fr\u00f6hlich, B. Pedrini, in Mathematical Physics 2000, A. Fokas et al., eds., Imperial College Press (2000), p. 9; S.- C. Zhang, J. Hu, Science 294, 823 (2001); D. Karabali, V. P. Nair, Nucl. Phys. B 641, 533 (2002).<\/span><\/section>\n
4.\u2002Y. E. Kraus, Z. Ringel, O. Zilberberg, Phys. Rev. Lett. 111, 226401 (2013).<\/span><\/section>\n
5.\u2002N. R. Cooper, J. Dalibard, I. B. Spielman, Rev. Mod. Phys. 91, 015005 (2019); T. Ozawa et al., Rev. Mod. Phys. 91, 015006 (2019); T. Ozawa, H. M. Price, Nat. Rev. Phys. 1, 349 (2019).<\/span><\/section>\n
6.\u2002C.- K. Chiu et al., Rev. Mod. Phys. 88, 035005 (2016).<\/span><\/section>\n
7.\u2002O. Zilberberg et al., Nature 553, 59 (2018); M. Lohse et al., Nature 553, 55 (2018).<\/span><\/section>\n
8.\u2002D. Juki\u0107, H. Buljan, Phys. Rev. A 87, 013814 (2013).<\/span><\/section>\n
9.\u2002Y. Wang et al., Nat. Commun. 11, 2356 (2020).<\/span><\/section>\n
10.\u2002O. Boada et al., Phys. Rev. Lett. 108, 133001 (2012).<\/span><\/section>\n
11.\u2002K. Viebahn et al., Phys. Rev. Lett. 122, 110404 (2019).<\/span><\/section>\n
12.\u2002A. Dutt et al., Science 367, 59 (2019).<\/span><\/section>\n
13.\u2002E. Lustig et al., Nature 567, 356 (2019); E. Lustig et al., in Conference on Lasers and Electro- Optics, Optica (2020), paper FW3A.2.<\/span><\/section>\n
14.\u2002X. Tan et al., Phys. Rev. Lett. 126, 017702 (2021); M. Chen et al., http:\/\/arxiv.org\/abs\/2008.00596.<\/span><\/section>\n
15.\u2002R.- P. Riwar et al., Nat. Commun. 7, 11167 (2016).<\/span><\/section>\n
16.\u2002S. Sugawa et al., Science 360, 1429 (2018).<\/span><\/section>\n
17.\u2002M. Mancini et al., Science 349, 1510 (2015). 18.\u2002B. K. Stuhl et al., Science 349, 1514 (2015).<\/span><\/section>\n


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\u672c\u6587\u7ffb\u8bd1\u81ea Physics Today<\/em><\/span><\/section>\n
\u539f\u6587\u9898\u76ee\uff1a<\/span><\/section>\n
Simulating four-dimensional physics in the laboratory<\/span><\/section>\n
\u539f\u6587\u94fe\u63a5\uff1a<\/span><\/section>\n
https:\/\/physicstoday.scitation.org\/doi\/10.1063\/PT.3.4981<\/span><\/section>\n<\/section>\n<\/section>\n<\/blockquote>\n


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