{"id":29525,"date":"2017-10-17T00:00:41","date_gmt":"2017-10-16T16:00:41","guid":{"rendered":"https:\/\/case.ntu.edu.tw\/blog\/?p=29525"},"modified":"2018-07-29T12:18:23","modified_gmt":"2018-07-29T04:18:23","slug":"%e9%9d%9e%e5%8e%84%e7%b1%b3%e7%b3%bb%e7%b5%b1","status":"publish","type":"post","link":"https:\/\/case.ntu.edu.tw\/blog\/?p=29525","title":{"rendered":"\u975e\u5384\u7c73\u7cfb\u7d71"},"content":{"rendered":"

\u25a0\u5384\u7c73\u5c0d\u7a31(Hermitian)\u5b58\u5728\u65bc\u5927\u90e8\u5206\u7684\u91cf\u5b50\u7406\u8ad6\u4e4b\u4e2d\uff0c\u4f46\u5b83\u537b\u4e0d\u662f\u5fc5\u8981\u7684\u3002\u5982\u679c\u653e\u68c4\u9019\u500b\u5c0d\u7a31\u6027\uff0c\u7cfb\u7d71\u5c07\u51fa\u73fe\u5947\u5999\u7684\u7269\u7406\u73fe\u8c61\u548c\u6709\u8da3\u7684\u61c9\u7528\u3002<\/strong><\/span><\/p>\n

\"\"\u64b0\u6587\uff5c<\/strong>\u9673\u5955\u5ef7<\/p>\n

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\u901a\u5e38\uff0c\u7269\u7406\u5b78\u5bb6\u6703\u8981\u6c42\u54c8\u5bc6\u9813\u7b97\u7b26\u6eff\u8db3\u4e00\u4e9b\u57fa\u672c\u7684\u6578\u5b78\u689d\u4ef6\uff0c\u4ee5\u6eff\u8db3\u5927\u81ea\u7136\u4e2d\u5c0d\u7a31\u6027\uff0c\u4f8b\u5982\uff1b\u91cf\u5b50\u614b\u7684\u80fd\u91cf\u662f\u5be6\u6578\u3001\u7c92\u5b50\u6578\u548c\u80fd\u91cf\u5b88\u6046\u7b49\u3002\u9019\u4e9b\u57fa\u672c\u7684\u6578\u5b78\u689d\u4ef6\u88ab\u7a31\u505a\u5384\u7c73\u5c0d\u7a31\u6027(Hermitian)[\u8a3b1]\uff0c\u5e7e\u4e4e\u6240\u6709\u7684\u57fa\u790e\u91cf\u5b50\u7406\u8ad6\u90fd\u5efa\u7acb\u5728\u54c8\u5bc6\u9813\u7b97\u7b26\u662f\u5384\u7c73\u5c0d\u7a31\u7684\u524d\u63d0\u4e0b\u3002\u672c\u7bc7\u6587\u7ae0\u4ecb\u7d39\u5982\u679c\u4e0d\u8981\u6c42\u5384\u7c73\u5c0d\u7a31\uff0c\u91cf\u5b50\u7406\u8ad6\u6703\u51fa\u73fe\u7684\u5947\u7570\u73fe\u8c61\u548c\u6709\u8da3\u61c9\u7528\u3002<\/p>\n

\u25cf\u7368\u7279\u9ede(Exceptional Point, EP)<\/strong><\/span><\/p>\n

\u5728\u975e\u5384\u7c73\u7cfb\u7d71\u4e2d\uff0c\u6700\u5947\u7570\u7684\u7279\u6027\u662f\u300c\u7368\u7279\u9ede\u300d\u7684\u5b58\u5728 [\u8a3b2]\u3002\u4e00\u822c\u7684\u91cf\u5b50\u7cfb\u7d71\u4e2d\uff0c\u4e0d\u540c\u7684\u91cf\u5b50\u614b\u8655\u65bc\u76f8\u540c\u7684\u80fd\u91cf\u662f\u4e00\u4ef6\u6975\u70ba\u666e\u901a\u7684\u4e8b\u60c5\uff0c\u4f8b\u5982\uff1a\u82ef\u74b0\u7684\u5171\u632f\u7d50\u69cb\u3002\u5118\u7ba1\u80fd\u91cf\u76f8\u540c\uff0c\u82ef\u74b0\u7684\u5171\u632f\u78ba\u78ba\u5be6\u5be6\u662f\u7531\u300c\u5169\u500b\u300d\u91cf\u5b50\u614b\u7d44\u6210\u3002\u4f46\u5728\u7368\u7279\u9ede\u4e0a\uff0c\u591a\u500b\u91cf\u5b50\u614b\u9664\u4e86\u5177\u6709\u76f8\u540c\u7684\u80fd\u91cf\uff0c\u5b83\u5011\u878d\u5408\u6210\u70ba\u300c\u4e00\u500b\u300d\u91cf\u5b50\u614b\u3002<\/p>\n

\"\"
\u5716\u4e00\u3001\u96a8\u8457\u7cfb\u7d71\u74b0\u5883\u8b8a\u5316\uff0c\u91cf\u5b50\u614b\u7684\u80fd\u91cf\u4e5f\u8ddf\u8457\u6539\u8b8a\u3002\u5716\u4e2d\u7d05\u8272\u548c\u85cd\u8272\u5206\u5225\u662f\u5169\u500b\u4e0d\u540c\u7684\u91cf\u5b50\u614b\u3002(\u5de6)\u5728\u5384\u7c73\u7cfb\u7d71\u4e2d\uff0c\u80fd\u91cf\u7684\u6539\u8b8a\u975e\u5e38\u5e73\u6ed1\u3002(\u53f3)\u5728\u975e\u5384\u7c73\u7cfb\u7d71\u4e2d\u5b58\u5728\u300c\u7368\u7279\u9ede\u300d\uff0c\u5728\u9019\u500b\u9ede\u4e0a\u9762\uff0c\u7d05\u8272\u548c\u85cd\u8272\u5169\u500b\u4e0d\u540c\u7684\u91cf\u5b50\u614b\u878d\u5408\u6210\u4e00\u500b\u91cf\u5b50\u614b\u3002\u5728\u9019\u500b\u9ede\u9644\u8fd1\uff0c\u80fd\u91cf\u7684\u8b8a\u5316\u975e\u5e38\u8907\u96dc\u5287\u70c8\u3002<\/figcaption><\/figure>\n

\u5716\u4e00\u662f\u91cf\u5b50\u614b\u5728\u5384\u7c73\u7cfb\u7d71\u548c\u975e\u5384\u7c73\u7cfb\u7d71\u7684\u7d50\u69cb\uff0c\u5384\u7c73\u7cfb\u7d71\u96a8\u74b0\u5883\u8b8a\u5316\u975e\u5e38\u7684\u5e73\u6574\u7de9\u6162\u3002\u800c\u975e\u5384\u7c73\u7cfb\u7d71\uff0c\u5728\u7279\u5b9a\u7684\u7cfb\u7d71\u53c3\u6578\u4e0b(\u7da0\u8272\u7bad\u982d)\u91cf\u5b50\u614b\u7cfe\u7d50\u6210\u4e00\u5718\u3001\u4e26\u4e14\u878d\u5408\u3002\u7269\u7406\u5b78\u5bb6\u63d0\u51fa\u5f88\u591a\u7406\u8ad6\uff0c\u63cf\u8ff0\u7368\u7279\u9ede\u5728\u96fb\u5b50\u7d50\u69cb\u4e2d\u6f5b\u5728\u7684\u61c9\u7528\u3002\u4f46\u662f\u96fb\u5b50\u9019\u6a23\u7684\u8cbb\u7c73\u5b50(fermion)\u5fc5\u9808\u8981\u6eff\u8db3\u5be6\u6578\u80fd\u91cf\u548c\u7c92\u5b50\u6578\u5b88\u6046\uff0c\u96e3\u4ee5\u61c9\u7528\u5728\u975e\u5384\u7c73\u7cfb\u7d71\u4e2d\u3002\u76f8\u8f03\u4e4b\u4e0b\uff0c\u5149\u5b50\u662f\u4e00\u500b\u6ce2\u8272\u5b50(boson)\uff0c\u5b83\u80fd\u4efb\u610f\u5730\u88ab\u7522\u751f\u6216\u662f\u6d88\u6ec5\uff0c\u4e5f\u53ef\u4ee5\u6709\u865b\u6578\u80fd\u91cf [\u8a3b3]\uff0c\u662f\u5be6\u73fe\u5384\u7c73\u7cfb\u7d71\u975e\u5e38\u597d\u7684\u5019\u9078\u4eba\u3002\u4ee5\u4e0b\u4f86\u770b\u4e00\u4e9b\u300c\u7368\u7279\u9ede\u300d\u7684\u61c9\u7528\u3002<\/p>\n

\u25cf\u91cf\u5b50\u614b\u5207\u63db\u5668<\/strong><\/span><\/p>\n

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\"\"
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\"\"
\u5716\u4e09\u3001\u6750\u6599\u5167\u7279\u6027\u7684\u8b8a\u5316\u88ab\u8a2d\u8a08\u6210\u5716\u4e8c\u4e2dC, D\u7684\u8def\u5f91\u3002(A)\u7121\u8ad6\u8d77\u59cb\u72c0\u614b\u662f\u4ec0\u9ebc\uff0c\u5982\u679c\u5149\u5b50\u5411\u53f3\u50b3\u8f38\uff0c\u5b83\u6703\u843d\u65bc\u85cd\u8272\u91cf\u5b50\u614b\u3002(B)\u53cd\u4e4b\u6703\u5230\u7d05\u8272\u91cf\u5b50\u614b\u3002<\/figcaption><\/figure>\n

\u25cf\u9ad8\u654f\u5ea6\u5075\u6e2c\u5668<\/strong><\/span><\/p>\n

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\u900f\u904e\u9019\u500b\u539f\u7406\u88fd\u9020\u7684\u611f\u61c9\u5668\u975e\u5e38\u9748\u654f\u3002\u9019\u6a23\u7684\u88dd\u7f6e\u9760\u7684\u662f\u5c0d\u5e95\u5c64\u7269\u7406\u7684\u4e86\u89e3\u52a0\u4e0a\u6750\u6599\u7684\u8a2d\u8a08\uff0c\u7d50\u69cb\u76f8\u5c0d\u7c21\u55ae\u3002\u4e5f\u56e0\u70ba\u4e0d\u9808\u8981\u8907\u96dc\u7684\u6a5f\u69cb\uff0c\u5b83\u5728\u5948\u7c73\u5c3a\u5ea6\u4e0b\u7684\u96fb\u8def\u61c9\u7528\u975e\u5e38\u6709\u6f5b\u529b\u3002<\/p>\n

\"\"
\u5716\u56db\u3001(A)\u5916\u754c\u64fe\u52d5\u5c31\u50cf\u662f\u67d0\u7a2e\u53c3\u6578\u8b8a\u5316\uff0c\u7576\u53d7\u5230\u64fe\u52d5\u6642\uff0c\u91cf\u5b50\u614b\u7684\u80fd\u91cf\u6703\u7522\u751f\u8b8a\u5316\u3002\u900f\u904e\u9019\u500b\u80fd\u91cf\u8b8a\u5316\uff0c\u79d1\u5b78\u5bb6\u80fd\u53cd\u904e\u4f86\u5075\u6e2c\u5916\u754c\u64fe\u52d5\u7684\u5927\u5c0f\u3002(B)\u975e\u5384\u7c73\u7cfb\u7d71\u4e2d\u7684\u7368\u7279\u9ede\u5c0d\u5916\u754c\u58e4\u52d5\u7684\u9748\u654f\u5ea6\u6975\u9ad8\u3002\u5c0f\u5c0f\u7684\u5e72\u64fe\u5c31\u80fd\u7522\u751f\u5f88\u5927\u7684\u80fd\u91cf\u8b8a\u5316\u3002<\/figcaption><\/figure>\n

\u9644\u8a3b\uff1a<\/strong>
\n[\u8a3b1] \u5384\u7c73\u5c0d\u7a31\u6307\u7684\u662f\u5728\u5171\u8edb(conjugate)\u548c\u8f49\u7f6e(adjoint)\u904b\u7b97\u4e0b\u5b88\u6046\u3002
\n[\u8a3b2] \u82f1\u6587\u70baexceptional point\uff0c\u7b46\u8005\u8b6f\u70ba\u300c\u7368\u7279\u9ede\u300d\uff0c\u4e5f\u53ef\u4ee5\u7ffb\u8b6f\u70ba\u300c\u512a\u8d8a\u9ede\u300d\u3001\u300c\u4f8b\u5916\u9ede\u300d\u7b49\u3002
\n[\u8a3b3] \u5149\u5b50\u7406\u8ad6\u4e2d\uff0c\u5be6\u6578\u80fd\u91cf\u4ee3\u8868\u5149\u7684\u983b\u7387\uff0c\u865b\u6578\u80fd\u91cf\u4ee3\u8868\u5149\u5b50\u88ab\u5438\u6536\u6216\u8017\u6563\u7684\u901f\u7387\u3002<\/p>\n

 <\/p>\n

\u53c3\u8003\u8cc7\u6599\uff1a<\/strong><\/p>\n

    \n
  1. Hossein Hodaei et al., Enhanced sensitivity at higher-order exceptional points, Nature<\/em> 548, 187 (2017)<\/li>\n
  2. Weijian Chen et al., Exceptional points enhance sensing in an optical microcavity, Nature<\/em> 548, 192 (2017)<\/li>\n
  3. J\u00f6rg Doppler et al., Dynamically encircling an exceptional point for asymmetric mode switching, Nature<\/em> 537, 76 (2016)<\/li>\n
  4. H. Xu et al., Topological energy transfer in an optomechanical system with exceptional points, Nature<\/em> 537, 80 (2016)<\/li>\n<\/ol>\n

    --
    \n\u4f5c\u8005\uff1a\u9673\u5955\u5ef7\uff0c\u53f0\u5927\u7269\u7406\u7cfb\u5b78\u58eb\uff0c\u53f2\u4e39\u4f5b\u5927\u5b78\u61c9\u7528\u7269\u7406\u7cfb\u535a\u58eb\u73ed\u5c31\u8b80\u4e2d\u3002\u5c0d\u5404\u9818\u57df\u7684\u79d1\u5b78\u90fd\u975e\u5e38\u597d\u5947\uff0c\u6b61\u8fce\u4e92\u76f8\u4ea4\u6d41\u3002<\/strong><\/span><\/p>\n

     <\/p>\n

    \"\u52a0\u5165\u597d\u53cb\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

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