{"id":24618,"date":"2021-03-17T22:44:38","date_gmt":"2021-03-17T14:44:38","guid":{"rendered":"https:\/\/swarma.org\/?p=24618"},"modified":"2021-03-17T22:44:38","modified_gmt":"2021-03-17T14:44:38","slug":"%e5%80%9f%e5%8a%a9%e6%8b%93%e6%89%91%e5%ad%a6%ef%bc%8c%e8%a7%a3%e9%87%8a%e7%94%9f%e6%80%81%e7%b3%bb%e7%bb%9f%e4%b8%ad%e7%9a%84%e7%a7%8d%e7%be%a4%e5%8f%98%e5%8c%96","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=24618","title":{"rendered":"\u501f\u52a9\u62d3\u6251\u5b66\uff0c\u89e3\u91ca\u751f\u6001\u7cfb\u7edf\u4e2d\u7684\u79cd\u7fa4\u53d8\u5316"},"content":{"rendered":"
<\/p>\n

\u5bfc\u8bed<\/p>\n

\u62d3\u6251\u5b66\u5728\u8fc7\u53bb50\u5e74\u95f4\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u51dd\u805a\u6001\u7269\u7406\u7684\u7814\u7a76\u4e2d\uff0c\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u3001\u62d3\u6251\u7edd\u7f18\u4f53\u7b49\u53d1\u73b0\u4e2d\u5747\u8868\u73b0\u51fa\u62d3\u6251\u7684\u7269\u6027\u3002\u5728\u62d3\u6251\u6001\u4e2d\uff0c\u7269\u8d28\u7684\u884c\u4e3a\u4f53\u73b0\u6765\u6e90\u4e8e\u80fd\u5e26\u7684\u8fde\u901a\u6027\u800c\u4e0d\u662f\u5bf9\u79f0\u6027\uff0c\u800c\u62d3\u6251\u5b66\u63d0\u4f9b\u4e86\u7814\u7a76\u7269\u8d28\u884c\u4e3a\u7684\u65b0\u65b9\u5f0f\u3002\u8fd1\u671f\uff0c\u7814\u7a76\u4eba\u5458\u5f00\u59cb\u63a2\u7d22\u5176\u4ed6\u9886\u57df\u4e2d\u7cfb\u7edf\u7684\u62d3\u6251\u6548\u5e94\uff0c\u5fb7\u56fd\u6155\u5c3c\u9ed1\u5927\u5b66\u7684 Erwin Frey \u548c\u4ed6\u7684\u5c0f\u7ec4\u6210\u5458\u5728\u4e00\u4e2a\u751f\u6001\u6a21\u578b\u4e2d\u786e\u5b9a\u4e86\u62d3\u6251\u76f8\u7684\u5b58\u5728\u3002\u8fd9\u9879\u5de5\u4f5c\u63ed\u793a\u51fa\u62d3\u6251\u5b66\u5728\u5176\u4ed6\u52a8\u6001\u751f\u7269\u7cfb\u7edf\u4e2d\u7684\u6f5c\u529b\u3002
Heather Hill | \u4f5c\u8005\u6f58\u4f73\u680b | \u8bd1\u8005\u5218\u57f9\u6e90 | \u5ba1\u6821\u9093\u4e00\u96ea | \u7f16\u8f91<\/p>\n

\u539f\u6587\u9898\u76ee\uff1a
Topological phases emerge in an ecological model
\u539f\u6587\u5730\u5740\uff1ahttps:\/\/physicstoday.scitation.org\/doi\/full\/10.1063\/PT.3.4695<\/p>\n

\u5f53\u4e00\u5217\u6ce2\uff08\u4f8b\u5982\u7535\u5b50\u6ce2\u51fd\u6570\uff09\u7ed5\u7740\u4e00\u6761\u62d3\u6251\u975e\u5e73\u51e1\u8def\u5f84\u8fd0\u52a8\u65f6\uff0c\u5b83\u5728\u5b8c\u6210\u95ed\u73af\u540e\u5c06\u5f97\u5230\u4e00\u4e2a\u76f8\uff0c\u800c\u4e0d\u662f\u56de\u5230\u521d\u59cb\u72b6\u6001\u3002\u867d\u7136\u5728\u7ec6\u8282\u4e0a\uff0c\u5e26\u72b6\u7ed3\u6784\u7684\u62d3\u6251\u662f\u590d\u6742\u800c\u96be\u4ee5\u7406\u89e3\u7684\uff0c\u4f46\u5176\u91cd\u8981\u7279\u5f81\u662f\u5c40\u90e8\u7684\u52a8\u6001\u6fc0\u53d1\uff08dynamic excitations\uff09\u5728\u7cfb\u7edf\u8fb9\u754c\u5904\u7684\u6d8c\u73b0\u3002\u5373\u4f7f\u5728\u6709\u7f3a\u9677\u7684\u60c5\u51b5\u4e0b\uff0c\u8fd9\u79cd\u6fc0\u53d1\u4e5f\u662f\u7a33\u5b9a\u7684\uff0c\u8fd9\u5c31\u662f\u6240\u8c13\u7684\u9c81\u68d2\u6027\u3002 \u7814\u7a76\u8005\u5df2\u7ecf\u5728\u8ba8\u8bba\u9664\u4e86\u51dd\u805a\u6001\u7269\u8d28\u5916\uff0c\u5176\u4ed6\u7cfb\u7edf\u7684\u62d3\u6251\u6548\u5e94\uff0c\u5305\u62ec\u81ea\u63a8\u8fdb\u7c92\u5b50[1]\u3001\u5927\u6c14\u548c\u6d77\u6d0b\u4e2d\u7684\u6ce2[2]\u3002  <\/p>\n

1. \u526a\u5200\u77f3\u5934\u5e03\u6e38\u620f<\/p>\n

Frey\u7684\u7814\u7a76\u751fJohannes Knebel\u53d7\u5230\u673a\u68b0\u8d85\u6750\u6599\u62d3\u6251\u76f8\u7684\u542f\u53d1\uff0c\u5f00\u59cb\u63a2\u7d22\u5176\u4ed6\u53ef\u80fd\u5b58\u5728\u62d3\u6251\u6001\u7684\u7cfb\u7edf\u3002Knebel\u4e0eFrey\u7684\u53e6\u4e00\u4f4d\u5b66\u751fPhilipp Geiger\u4e00\u76f4\u5728\u7814\u7a76\u53cd\u5bf9\u79f0\u7684Lotka-Volterra\u65b9\u7a0b\uff08ALVE\uff0c\u53c8\u79f0\u6355\u98df\u8005-\u730e\u7269\u65b9\u7a0b\uff09\u3002ALVE\u662f\u7814\u7a76\u8bb8\u591a\u52a8\u6001\u7cfb\u7edf\u65f6\u4f1a\u7528\u5230\u7684\u6a21\u578b\uff0c\u4ee5\u751f\u6001\u5b66\u4e3a\u4f8b\uff0cALVE\u88ab\u7528\u4e8e\u7814\u7a76\u79cd\u7fa4\u4e2a\u4f53\u6570\u91cf\u7684\u52a8\u6001\u53d8\u5316\uff1a\u6355\u98df\u8005\u548c\u730e\u7269\u7684\u5173\u7cfb\u5982\u4f55\u5f71\u54cd\u79cd\u7fa4\u589e\u957f\u3002Frey\u5c0f\u7ec4\u8fd1\u671f\u7528\u7c92\u5b50\u66ff\u4ee3\u7269\u79cd\uff0c\u6765\u4ee5ALVE\u6765\u9884\u6d4b\u5728\u9ad8\u80fd\u91cf\u72b6\u6001\u4e0b\u73bb\u8272\u00b7\u7231\u56e0\u65af\u5766\u51dd\u805a\u7269\u7684\u5f62\u6210\u3002[4]   ALVE\u4e5f\u53ef\u4ee5\u7528\u6765\u63cf\u8ff0\u535a\u5f08\u8bba\u4e2d\u7684\u4e00\u90e8\u5206\uff1a\u77f3\u5934\u526a\u5200\u5e03\u5faa\u73af\u3002\u5c06\u77f3\u5934\u526a\u5200\u5e03\u6e38\u620f\u4e2d\u76843\u79cd\u52a8\u4f5c\u4f5c\u4e3a\u4e09\u89d2\u5f62\u76843\u4e2a\u70b9\uff0c\u901a\u8fc7\u7bad\u5934\u8868\u660e\u83b7\u80dc\u7684\u52a8\u4f5c\u3002\u5728\u77f3\u5934\u526a\u5200\u5e03\u7684\u5faa\u73af\u4e2d\uff0c\u6bcf\u4e2a\u52a8\u4f5c\u90fd\u4f1a\u4ee5\u4e00\u5b9a\u6982\u7387\u83b7\u80dc\u6216\u5931\u8d25\u3002\u5728\u79cd\u7fa4\u52a8\u529b\u5b66\u7684\u8ba1\u7b97\u4e2d\uff0c\u4e09\u89d2\u5f62\u7684\u6bcf\u4e2a\u70b9\u4ee3\u8868\u4e00\u4e2a\u7269\u79cd\uff0c\u7bad\u5934\u4ee3\u8868\u7269\u79cd\u95f4\u7269\u8d28\u6d41\u52a8\u7684\u901f\u7387\uff0c\u5373\u4e00\u79cd\u7269\u79cd\u6570\u91cf\u7684\u51cf\u5c0f\u5bfc\u81f4\u53e6\u4e00\u4e2a\u7269\u79cd\u6570\u91cf\u7684\u589e\u52a0\u3002\u6bcf\u4e00\u4e2a\u5faa\u73af\u90fd\u662f\u4e09\u4e2a\u7269\u79cd\u95f4\u7269\u8d28\u4f20\u9012\u7684\u5c40\u57df\u632f\u5b50\u3002 \u5355\u72ec\u7684\u5faa\u73af\uff0c\u4f8b\u5982\u7b2c\u4e00\u4e2a\uff08\u56fe1\u4e2d\u7070\u8272\u7a81\u51fa\u663e\u793a\u7684\u90e8\u5206\uff09\uff0c\u53ef\u4ee5\u7ec4\u6210\u4e0d\u540c\u7684\u51e0\u4f55\u56fe\u5f62\uff0c\u6bcf\u4e2a\u7269\u79cd\u5360\u636e\u4e00\u4e2a\u9876\u70b9\u3002\u7ed9\u5b9a\u4e0d\u540c\u7269\u79cd\u8d28\u91cf\u7684\u521d\u59cb\u7ec4\u6210\u540e\uff0c\u70b9\u4e4b\u95f4\u53d1\u751f\u975e\u7ebf\u6027\u76f8\u4e92\u4f5c\u7528\uff0c\u7269\u79cd\u7684\u8d28\u91cf\u7ec4\u6210\u4f1a\u53d1\u751f\u53d8\u5316\u3002\u8d28\u91cf\u4f20\u9012\u6a21\u578b\u6a21\u62df\u4e86\u7cfb\u7edf\u7684\u79cd\u7fa4\u52a8\u529b\u5b66\u3002  \u56fe1 \uff1a\u77f3\u5934\u526a\u5200\u5e03\u5faa\u73af\u4e2dS\u4e2a\u7269\u79cd\u7684\u76f8\u4e92\u4f5c\u7528 \u5f53Frey\u7684\u5c0f\u7ec4\u5f00\u59cb\u5bfb\u627e\u77f3\u5934\u526a\u5200\u5e03\u5faa\u73af\u7684\u4e8c\u7ef4\u7ed3\u6784\u4e2d\u7684\u62d3\u6251\u6027\u65f6\uff0c\u4ed6\u4eec\u89c2\u5bdf\u5230\u624b\u578b\u8fb9\u7f18\u6001\uff08chiral edge states\uff09\u7684\u5b58\u5728\uff0c\u7c7b\u4f3c\u4e8e\u4e8c\u7ef4\u51b7\u539f\u5b50\u683c\u70b9\u7684\u62d3\u6251\u6a21\u5f0f\u3002\u4f46\u662f\uff0c\u5f88\u96be\u5c06\u8fd9\u4e9b\u89c2\u5bdf\u548c\u62d3\u6251\u5b66\u4e25\u683c\u5173\u8054\u8d77\u6765\u3002\u5728\u4e86\u89e3\u62d3\u6251\u5b66\u4e2d\u7684\u57fa\u672c\u5185\u5bb9\u540e\uff0c\u7814\u7a76\u4eba\u5458\u8f6c\u5411\u4e86\u4e00\u4e2a\u66f4\u7b80\u5355\u7684\u7cfb\u7edf\uff1a\u4e00\u7ef4\u94fe\uff081D chain\uff09\u3002
 <\/p>\n

2. \u4e00\u7ef4\u94fe\u7684\u6781\u5316\u884c\u4e3a<\/p>\n

\u56fe2\u663e\u793a\u4e86\u4e00\u7ef4\u526a\u5200\u77f3\u5934\u5e03\u5faa\u73af\u7684\u4e00\u79cd\u6570\u503c\u7ed3\u679c\u3002\u521d\u59cb\u72b6\u6001\u4e0b\uff0c\u603b\u8d28\u91cf\u5747\u5300\u5206\u5e03\u5728\u6574\u4e2a\u94fe\u4e0a\uff0c\u901a\u8fc7\u5bf9\u8ba1\u7b97\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u4f7f\u5f97\u6240\u6709\u8bd5\u9a8c\u7684\u4f20\u8f93\u7387r1=1\u3002\u7136\u540e\uff0c\u7814\u7a76\u4eba\u5458\u6539\u53d8\u504f\u5ea6r=r2\/r3\u7684\u503c\u3002 \u56fe2\uff1a\u504f\u5ea6\u4e3a0.5\u65f6\u7684\u4e00\u7ef4\u77f3\u5934\u526a\u5200\u5e03\u94fe\uff0c\u8d28\u91cf\u7684\u65f6\u95f4\u5e73\u5747\u5206\u5e03\u5728\u53f3\u4fa7[3] \u5f53r<1\u65f6\uff0c\u8d28\u91cf\u7684\u65f6\u95f4\u5e73\u5747\u5206\u5e03\uff08\u7070\u8272\u5706\u5708\uff09\u5728\u53f3\u4fa7\uff0c\u800c\u5f53r>1\u65f6\uff0c\u5e73\u5747\u8d28\u91cf\u5206\u5e03\u5728\u5de6\u4fa7\u3002\u5c3d\u7ba1\u8d28\u91cf\u5e73\u5747\u503c\u662f\u7a33\u5b9a\u7684\uff0c\u4f46\u662f\u7cfb\u7edf\u5e76\u672a\u5904\u4e8e\u9759\u6b62\u72b6\u6001\uff0c\u800c\u662f\u4fdd\u6301\u52a8\u6001\u5e76\u56f4\u7ed5\u8be5\u5e73\u5747\u503c\u6ce2\u52a8\u3002\u7814\u7a76\u4eba\u5458\u79f0\u8fd9\u79cd\u884c\u4e3a\u4e3a\u8d28\u91cf\u6781\u5316\uff1a\u5e73\u5747\u8d28\u91cf\u53d8\u5f97\u5c40\u57df\u5316\uff0c\u5e76\u968f\u7740\u8ddd\u94fe\u8fb9\u7f18\u8ddd\u79bb\u7684\u589e\u5927\uff0c\u5448\u6307\u6570\u7ea7\u4e0b\u964d\u3002\u4ece\u751f\u6001\u89d2\u5ea6\u770b\uff0c\u8fd9\u4ee3\u8868\u4e00\u4e2a\u7269\u79cd\u4e3b\u5bfc\u4e86\u6816\u606f\u5730\u3002 \u504f\u659c\u5ea6\u72ec\u7acb\u5730\u51b3\u5b9a\u8d28\u91cf\u6781\u5316\u3002r1\u7684\u503c\u4ee5\u53car2\u548cr3\u7684\u7279\u6b8a\u503c\u4f1a\u6539\u53d8\u8d28\u91cf\u5206\u5e03\u7684\u6570\u503c\uff0c\u4f46\u662f\u4e0d\u80fd\u6539\u53d8\u8d28\u91cf\u5206\u5e03\u7684\u76f8\u5bf9\u5927\u5c0f\u3002\u800c\u4e14\uff0c\u6781\u5316\u72b6\u6001\u7684\u51fa\u73b0\u4e0e\u521d\u59cb\u8d28\u91cf\u5206\u5e03\u548c\u901f\u7387\u7684\u968f\u673a\u6270\u52a8\u03b5\u65e0\u5173\uff0c\u5982\u56fe3\u4e2d\u7bad\u5934\u7684\u989c\u8272\u6240\u793a\u3002\u5373\u4f7f\u5728\u94fe\u7684\u6700\u9ad8\u8282\u70b9\u4e4b\u95f4\u6dfb\u52a0\u8026\u5408\uff0c\u8d28\u91cf\u5206\u5e03\u7684\u76f8\u5bf9\u5927\u5c0f\u4e5f\u4e0d\u4f1a\u53d1\u751f\u6539\u53d8\u3002  \u56fe3\uff1a\u504f\u5ea6\u4e3a1\u65f6\uff0c\u8d28\u91cf\u5747\u5300\u5730\u5206\u5e03\u5728\u6574\u4e2a\u94fe\u6761\u4e0a[3] \u5f53r=1\u65f6\uff0c\u5de6\u53f3\u6781\u5316\u6001\u4e4b\u95f4\u4f1a\u53d1\u751f\u8dc3\u8fc1\uff0c\u6ca1\u6709\u4efb\u4f55\u4e00\u79cd\u7269\u79cd\u80fd\u4e3b\u5bfc\u6816\u606f\u5730\uff0c\u5e76\u4e14\u65f6\u95f4\u5e73\u5747\u8d28\u91cf\u5206\u5e03\u4e0d\u4f1a\u96c6\u4e2d\u5728\u94fe\u4e2d\u7684\u4e00\u4e2a\u70b9\u4e0a\u3002\u5728\u56fe3\u4e2d\uff0c\u5e73\u5747\u8d28\u91cf\u7684\u5206\u5e03\u5c06\u4fdd\u6301\u5176\u521d\u59cb\u72b6\u6001\uff0c\u5373\u8d28\u91cf\u5747\u5300\u5206\u5e03\u5728\u6574\u4e2a\u94fe\u4e0a\u3002\u5982\u679c\u8d28\u91cf\u6700\u521d\u9650\u5236\u5728\u51e0\u4e2a\u4f4d\u7f6e\u4e0a\uff0c\u5219\u5e73\u5747\u8d28\u91cf\u5728\u7a7a\u95f4\u4e2d\u6cbf\u94fe\u6761\u79fb\u52a8\u65f6\u4f1a\u4fdd\u6301\u76f8\u540c\u7684\u5f62\u72b6\u3002\u94fe\u4e0a\u4e24\u4e2a\u8fd9\u6837\u7684\u8d28\u91cf\u5305\uff0c\u5728\u76f8\u4e92\u4f5c\u7528\u540e\u4ecd\u4fdd\u6301\u5176\u5f62\u72b6\u548c\u901f\u5ea6\uff0c\u5176\u884c\u4e3a\u7c7b\u4f3c\u4e8e\u5b64\u5b50\u3002 \u6781\u5316\u72b6\u6001\u548c\u8fc7\u6e21\u6001\u7684\u7279\u5f81\u672c\u8d28\u4e0a\u662f\u62d3\u6251\u7684\uff0c\u8fd9\u4f7fFrey\u53ca\u5176\u56e2\u961f\u611f\u5230\u60ca\u8bb6\u3002\u5728\u5927\u591a\u6570\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u6a21\u578b\u4e2d\uff0c\u7cfb\u7edf\u7684\u884c\u4e3a\u8f83\u591a\u5730\u53d7\u5230\u53c2\u6570\u53d8\u5316\u7684\u5f71\u54cd\uff0c\u5e76\u4e14\u901a\u5e38\u4f1a\u8017\u6563\u6216\u53d8\u5f97\u6df7\u4e71\uff0c\u8fd9\u4e0e\u89c2\u5bdf\u5230\u7684\u884c\u4e3a\u76f8\u53cd\u3002  <\/p>\n

3. \u5982\u4f55\u7528\u62d3\u6251\u5b66\u89e3\u91ca\u7ed3\u679c\uff1f<\/p>\n

\u4e3a\u4e86\u4f7f\u7528\u62d3\u6251\u7ed3\u6784\u89e3\u91ca\u4ed6\u4eec\u7684\u89c2\u5bdf\u7ed3\u679c\u4ee5\u53ca\u5c06ALVE\u548c\u51dd\u805a\u6001\u7269\u7406\u8054\u7cfb\u8d77\u6765\uff0c\u7814\u7a76\u4eba\u5458\u8ba1\u7b97\u4e86\u4e00\u7ef4\u77f3\u5934\u526a\u5200\u5e03\u94fe\u7684\u80fd\u5e26\u7ed3\u6784\uff08energy band structure\uff09\u7684\u7b49\u6548\u503c[5]\u3002\u9996\u5148\uff0c\u4ed6\u4eec\u4ee5S-by-S\u53cd\u5bf9\u79f0\u77e9\u9635\u7684\u5f62\u5f0f\u5bf9\u76f8\u4e92\u4f5c\u7528\u8fdb\u884c\u516c\u5f0f\u5316\uff0c\u627e\u5230\u4e86\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\uff0c\u5e76\u4ece\u4e2d\u53d1\u73b0\u4e86\u80fd\u5e26\u7ed3\u6784\u3002 \u7531\u4e8e\u5176\u6c49\u5bc6\u5c14\u987f\u5bf9\u79f0\u6027\uff0c\u77f3\u5934\u526a\u5200\u5e03\u6a21\u578b\u4e0e\u4e00\u7ef4\u8d85\u5bfc\u7684Alexei Kitaev\u6a21\u578b\u6709\u5173\u3002\u6b63\u5982Alexei Kitaev\u6a21\u578b\u4e00\u6837\uff0c\u4e00\u4e2a\u4e0d\u53d8\u91cf\u8868\u5f81\u4e86\u80fd\u5e26\u7ed3\u6784\u7684\u62d3\u6251\u3002\u62d3\u6251\u4e0d\u53d8\u91cf\u7684\u4e00\u4e2a\u4f8b\u5b50\u662f\u7c7b\uff08genus\uff09\uff0c\u5b83\u6309\u7167\u8868\u9762\u4e0a\u7684\u5b54\u6570\u91cf\u5bf9\u51e0\u4f55\u56fe\u5f62\u8fdb\u884c\u5206\u7c7b\u3002\u751c\u751c\u5708\u548c\u5496\u5561\u676f\u5177\u6709\u76f8\u540c\u7684\u7c7b\uff0c\u56e0\u6b64\u53ef\u4ee5\u4ece\u4e00\u79cd\u5f62\u72b6\u5e73\u6ed1\u5730\u53d8\u5f62\u4e3a\u53e6\u4e00\u79cd\u5f62\u72b6\u3002\u4f46\u662f\uff0c\u751c\u751c\u5708\u4e0d\u80fd\u987a\u5229\u5730\u53d8\u5f62\u4e3a\u5177\u6709\u4e0d\u540c\u7c7b\u7684\u7403\u4f53\u3002r<1\u548cr>1\u8fd9\u4e24\u4e2a\u504f\u5ea6\u72b6\u6001\u7684\u62d3\u6251\u4e0d\u53d8\u91cf\u5177\u6709\u4e0d\u540c\u7684\u503c\uff0c\u56e0\u6b64\u8fd9\u4e24\u4e2a\u504f\u5ea6\u72b6\u6001\u662f\u4e0d\u540c\u7684\u62d3\u6251\u76f8\u3002\u8fd9\u4e9b\u62d3\u6251\u76f8\u4f53\u73b0\u5728\u7cfb\u7edf\u8fb9\u754c\u7684\u8d28\u91cf\u6781\u5316\u72b6\u6001\u4e2d\u3002 \u62d3\u6251\u6001\u662f\u5426\u4f1a\u51fa\u73b0\u5728\u73b0\u5b9e\u751f\u6d3b\u4e2d\u7684\u751f\u7269\u6216\u751f\u6001\u7cfb\u7edf\u4e2d\u8fd8\u6709\u5f85\u89c2\u5bdf\u3002\u6709\u5e0c\u671b\u7684\u5019\u9009\u8005\u662f\u57fa\u56e0\u8c03\u63a7\u7f51\u7edc\uff0c\u5b83\u7531\u4e00\u7cfb\u5217\u63a7\u5236\u7ec6\u80de\u5185\u57fa\u56e0\u8868\u8fbe\u7684\u5206\u5b50\u7ec4\u6210\u3002\u5982\u679c\u62d3\u6251\u6001\u5b58\u5728\uff0c\u90a3\u4e48\u8be5\u7f51\u7edc\u80fd\u591f\u5728\u8c03\u8282\u9009\u5b9a\u7684\u57fa\u56e0\u7684\u540c\u65f6\uff0c\u4e0d\u53d7\u5916\u90e8\u5e72\u6270\u548c\u566a\u58f0\u5f71\u54cd\u3002 Frey\u548c\u4ed6\u7684\u5b66\u751f\u4eec\u8ba1\u5212\u5c06\u4ed6\u4eec\u7684\u65b9\u6cd5\u5e94\u7528\u4e8e\u5176\u4ed6\u52a8\u6001\u7cfb\u7edf\uff0c\u7279\u522b\u662f\u968f\u673a\u7cfb\u7edf\u3002Frey\u8bf4\uff0c\u4ed6\u5e0c\u671b\u80fd\u591f\u5c06\u62d3\u6251\u76f8\u7684\u91cd\u8981\u60f3\u6cd5\u63d0\u4f9b\u7ed9\u5e7f\u5927\u7684\u751f\u7269\u548c\u8f6f\u51dd\u805a\u6001\u7269\u7406\u5b66\u7684\u8bfb\u8005\u3002\u4ed6\u89e3\u91ca\u8bf4\uff1a\u201c\u6211\u76f8\u4fe1\uff0c\u5c06\u7814\u7a76\u65b9\u6cd5\u4ece\u4e00\u4e2a\u7269\u7406\u5b66\u9886\u57df\u8f6c\u79fb\u5230\u53e6\u4e00\u4e2a\u9886\u57df\uff0c\u4ecd\u7136\u662f\u6700\u9f13\u821e\u4eba\u5fc3\u7684\u521b\u65b0\u4e4b\u4e00\u3002\u201d 
\u53c2\u8003\u6587\u732e\uff1a1. A. Souslov, B. C. van Zuiden, D. Bartolo, V. Vitelli, Nat. Phys. 13, 1091 (2017).2. P. Delplace, J. B. Marston, A. Venaille, Sci- ence 358, 1075 (2017).3. J. Knebel, P. M. Geiger, E. Frey, Phys. Rev. Lett. 125, 258301 (2020).4. J. Knebel, M. F. Weber, T. Kru\u0308ger, E. Frey, Nat. Commun. 6, 6977 (2015).5. A. Y. Kitaev, Phys.-Usp. 44, 131 (2001).          
\u590d\u6742\u79d1\u5b66\u6700\u65b0\u8bba\u6587


\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/p>\n


<\/div>\n

\u63a8\u8350\u9605\u8bfb
\u751f\u547d\u590d\u6742\u7cfb\u7edf\u4e3a\u4f55\u80fd\u6297\u5e72\u6270\uff1f\u8de8\u5b66\u79d1\u7814\u7a76\u63ed\u793a\u591a\u5c42\u751f\u7269\u5206\u5b50\u7f51\u7edc\u9c81\u68d2\u6027<\/a>\u5bf9\u79f0\u6027\u4e0e\u62d3\u6251\u5e8f\uff1a\u65b0\u578b\u91cf\u5b50\u8ba1\u7b97\u673a\u7684\u7269\u7406\u57fa\u7840<\/a>
Science Advances\uff1a\u5927\u57ce\u5e02\u518d\u4e5f\u4e0d\u7528\u8d76\u4eba\u4e86\uff0c\u7528\u62d3\u6251\u5b66\u5c31\u80fd\u6d88\u706d\u68da\u6237\u533a<\/a>
\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01<\/a><\/p>\n

\u70b9\u51fb\u201c\u9605\u8bfb\u539f\u6587\u201d\uff0c\u8ffd\u8e2a\u590d\u6742\u79d1\u5b66\u9876\u520a\u8bba\u6587 <\/div>\n","protected":false},"excerpt":{"rendered":"

\u5bfc\u8bed \u62d3\u6251\u5b66\u5728\u8fc7\u53bb50\u5e74\u95f4\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u51dd\u805a\u6001\u7269\u7406\u7684\u7814\u7a76\u4e2d\uff0c\u91cf\u5b50\u970d\u5c14\u6548\u5e94\u3001\u62d3\u6251\u7edd\u7f18\u4f53\u7b49\u53d1\u73b0\u4e2d\u5747\u8868\u73b0\u51fa\u62d3\u6251\u7684\u7269\u6027\u3002\u5728\u62d3\u6251\u6001\u4e2d\uff0c\u7269\u8d28\u7684\u884c\u4e3a\u4f53\u73b0\u6765\u6e90\u4e8e\u80fd\u5e26\u7684\u8fde\u901a\u6027\u800c\u4e0d\u662f\u5bf9\u79f0\u6027\uff0c\u800c\u62d3\u6251\u5b66\u63d0\u4f9b\u4e86\u7814\u7a76\u7269\u8d28\u884c\u4e3a\u7684\u65b0\u65b9\u5f0f\u3002\u8fd1\u671f\uff0c\u7814\u7a76\u4eba\u5458\u5f00\u59cb\u63a2\u7d22\u5176\u4ed6\u9886\u57df\u4e2d\u7cfb\u7edf\u7684\u62d3\u6251\u6548\u5e94\uff0c\u5fb7\u56fd\u6155\u5c3c\u9ed1\u5927\u5b66\u7684 Erwin Frey \u548c\u4ed6\u7684\u5c0f…<\/p>\n","protected":false},"author":1,"featured_media":24611,"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\/24618"}],"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"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=24618"}],"version-history":[{"count":0,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/24618\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/24611"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=24618"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=24618"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=24618"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=24618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}