{"id":32686,"date":"2022-02-25T23:20:26","date_gmt":"2022-02-25T15:20:26","guid":{"rendered":"https:\/\/swarma.org\/?p=32686"},"modified":"2022-02-25T23:20:26","modified_gmt":"2022-02-25T15:20:26","slug":"%e8%87%aa%e7%94%b1%e5%ba%a6%ef%bc%9a%e7%b3%bb%e7%bb%9f%e7%8a%b6%e6%80%81%e7%9b%b8%e7%a9%ba%e9%97%b4%e7%9a%84%e7%bb%b4%e6%95%b0-%e9%9b%86%e6%99%ba%e7%99%be%e7%a7%91","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=32686","title":{"rendered":"\u81ea\u7531\u5ea6\uff1a\u7cfb\u7edf\u72b6\u6001\u76f8\u7a7a\u95f4\u7684\u7ef4\u6570 | \u96c6\u667a\u767e\u79d1"},"content":{"rendered":"
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\u672c\u6587\u662f\u5bf9\u96c6\u667a\u767e\u79d1\u4e2d\u201c\u81ea\u7531\u5ea6<\/span>\u201d\u8bcd\u6761\u7684\u6458\u5f55\uff0c\u53c2\u8003\u8d44\u6599\u53ca\u76f8\u5173\u8bcd\u6761\u8bf7\u53c2\u9605\u767e\u79d1\u8bcd\u6761\u539f\u6587\u3002<\/span><\/section>\n

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\u5728\u7269\u7406\u548c\u5316\u5b66\u4e2d\uff0c\u81ea\u7531\u5ea6 Degree of freedom\u6307\u7684\u662f\u5f62\u5f0f\u5316\u63cf\u8ff0\u67d0\u4e00\u7269\u7406\u7cfb\u7edf\u7684\u72b6\u6001\u65f6\uff0c\u4e00\u4e2a\u72ec\u7acb\u7684\u7269\u7406\u91cf\u3002\u67d0\u4e00\u7cfb\u7edf\u6240\u6709\u72b6\u6001\u7684\u96c6\u5408\u79f0\u4e3a\u8be5\u7cfb\u7edf\u7684\u76f8\u7a7a\u95f4 Phase space\uff0c\u8be5\u7cfb\u7edf\u7684\u81ea\u7531\u5ea6\u4fbf\u662f\u76f8\u7a7a\u95f4\u7684\u7ef4\u6570\u3002<\/span>
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\u7c92\u5b50 particle \u5728\u4e09\u7ef4 three-dimensional \u7a7a\u95f4\u4e2d\u7684\u4f4d\u7f6e\u9700\u8981\u4e09\u4e2a\u4f4d\u7f6e\u5750\u6807\u6765\u6807\u8bc6\u3002\u540c\u6837\u5730\uff0c\u6211\u4eec\u4e5f\u80fd\u591f\u6839\u636e\u4e09\u4e2a\u901f\u5ea6\u5206\u91cf\u6765\u63cf\u8ff0\u7c92\u5b50\u8fd0\u52a8\u7684\u65b9\u5411\u548c\u901f\u5ea6\uff0c\u6bcf\u4e2a\u901f\u5ea6\u5206\u91cf\u90fd\u53c2\u7167\u8be5\u7a7a\u95f4\u7684\u4e09\u4e2a\u7ef4\u5ea6\u3002\u5982\u679c\u7cfb\u7edf\u7684\u65f6\u95f4\u6f14\u53d8\u662f\u786e\u5b9a\u7684\uff0c\u5176\u4e2d\u67d0\u4e00\u65f6\u523b\u7684\u72b6\u6001\u552f\u4e00\u5730\u786e\u5b9a\u5176\u8fc7\u53bb\u548c\u672a\u6765\u7684\u4f4d\u7f6e\u548c\u901f\u5ea6\u968f\u65f6\u95f4\u7684\u53d8\u5316\uff0c\u5219\u8be5\u7cfb\u7edf\u5177\u6709\u516d\u4e2a\u81ea\u7531\u5ea6\u3002\u5982\u679c\u5c06\u7c92\u5b50\u7684\u8fd0\u52a8\u9650\u5236\u5728\u66f4\u4f4e\u7684\u7ef4\u5ea6\uff0c\u4f8b\u5982\uff0c\u7c92\u5b50\u5fc5\u987b\u6cbf\u7740\u4e00\u6761\u7ebf\u6216\u5728\u56fa\u5b9a\u7684\u8868\u9762\u4e0a\u79fb\u52a8\uff0c\u90a3\u4e48\u7cfb\u7edf\u7684\u81ea\u7531\u5ea6\u5219\u5c0f\u4e8e6\u3002\u53e6\u4e00\u65b9\u9762\uff0c\u5982\u679c\u4e00\u4e2a\u7cfb\u7edf\u5e26\u6709\u53ef\u65cb\u8f6c\u6216\u632f\u52a8\u7684\u6269\u5c55\u5bf9\u8c61\uff0c\u90a3\u4e48\u5b83\u7684\u81ea\u7531\u5ea6\u5c06\u5927\u4e8e6\u3002<\/span><\/p>\n


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\u5728\u7ecf\u5178\u529b\u5b66\u4e2d\uff0c\u4efb\u4f55\u7ed9\u5b9a\u65f6\u95f4\u4e0b\u8d28\u70b9 Point particle\u7684\u72b6\u6001\uff0c\u901a\u5e38\u662f\u7528\u62c9\u683c\u6717\u65e5\u5f62\u5f0f Lagrangian formalism \u4e2d\u7684\u4f4d\u7f6e\u548c\u901f\u5ea6\u5750\u6807\u6765\u63cf\u8ff0\uff0c\u6216\u8005\u7528\u54c8\u5bc6\u987f\u5f62\u5f0f Hamiltonian formalism \u4e2d\u7684\u4f4d\u7f6e\u548c\u52a8\u91cf\u5750\u6807\u6765\u63cf\u8ff0\u3002<\/span><\/p>\n


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\u5728\u7edf\u8ba1\u529b\u5b66\u4e2d\uff0c\u81ea\u7531\u5ea6\u6307\u7684\u662f\u5728\u63cf\u8ff0\u67d0\u4e2a\u7cfb\u7edf\u7684\u5fae\u89c2\u72b6\u6001\u65f6\uff0c\u5355\u4e2a\u7684\u6807\u91cf\u6570\u3002\u67d0\u4e2a\u7cfb\u7edf\u6240\u6709\u5fae\u89c2\u72b6\u6001\u7684\u89c4\u683c\u53c2\u6570\u90fd\u662f\u8be5\u7cfb\u7edf\u76f8\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u70b9\u3002<\/span><\/p>\n


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\u5728\u5316\u5b66\u7684\u4e09\u7ef4\u7406\u60f3\u94fe Ideal chain\u6a21\u578b\u4e2d\uff0c\u9700\u8981\u4e24\u4e2a\u89d2\u5ea6\u6765\u63cf\u8ff0\u6bcf\u4e2a\u5355\u4f53 monomer \u7684\u65b9\u5411\u3002<\/span><\/p>\n

\u6307\u5b9a\u4e8c\u81ea\u7531\u5ea6\u901a\u5e38\u5f88\u6709\u7528\u3002\u56e0\u4e3a\u5b83\u4eec\u6709\u52a9\u4e8e\u5efa\u7acb\u7cfb\u7edf\u80fd\u91cf\u7684\u4e8c\u6b21\u51fd\u6570\u3002<\/span><\/p>\n


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\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u7c92\u5b50\u7684\u8fd0\u52a8\u4e0e\u5b83\u7684\u4e09\u4e2a\u81ea\u7531\u5ea6\u6709\u5173\u3002\u53cc\u539f\u5b50\u6c14\u4f53\u5206\u5b50\u5177\u67096\u4e2a\u81ea\u7531\u5ea6\u3002\u6211\u4eec\u53ef\u4ee5\u6839\u636e\u5176\u5206\u5b50\u7684\u5e73\u52a8\u3001\u8f6c\u52a8\u548c\u632f\u52a8\u6765\u5206\u89e3\u8fd96\u4e2a\u81ea\u7531\u5ea6\u3002\u6574\u4e2a\u5206\u5b50\u7684\u8d28\u5fc3\u8fd0\u52a8\u5177\u6709\u4e09\u4e2a\u81ea\u7531\u5ea6\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u5206\u5b50\u8fd8\u6709\u4e24\u4e2a\u8f6c\u52a8\u81ea\u7531\u5ea6\u548c\u4e00\u4e2a\u632f\u52a8\u81ea\u7531\u5ea6\u3002\u5176\u4e2d\uff0c\u8fd9\u4e24\u4e2a\u8f6c\u52a8\u81ea\u7531\u5ea6\uff0c\u662f\u5728\u7ed5\u5782\u76f4\u4e8e\u4e24\u4e2a\u539f\u5b50\u95f4\u76f4\u7ebf\u7684\u4e24\u4e2a\u8f74\u800c\u53d1\u751f\u7684\u3002\u4f46\u662f\uff0c\u7ed5\u539f\u5b50-\u539f\u5b50\u952e\u7684\u8f6c\u52a8\u5e76\u4e0d\u662f\u7269\u7406\u65cb\u8f6c\u3002\u56e0\u6b64\uff0c\u5728\u6b64\u79cd\u60c5\u51b5\u4e0b\uff0c\u53ef\u4ee5\u5c06\u53cc\u539f\u5b50\u5206\u5b50\u7684\u81ea\u7531\u5ea6\u5206\u89e3\u4e3a\uff1a<\/span><\/p>\n


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\u8fd9\u610f\u5473\u7740\u5f53N>2\u65f6\uff0cN\u539f\u5b50\u5206\u5b50\u5177\u67093N-6\u4e2a\u632f\u52a8\u81ea\u7531\u5ea6\u3002\u4e0d\u8fc7\u5728\u7279\u6b8a\u60c5\u51b5\u4e0b\uff0c\u4f8b\u5982\u4e00\u4e2a\u5438\u9644\u7684\u5927\u5206\u5b50\uff0c\u8f6c\u52a8\u81ea\u7531\u5ea6\u53ea\u80fd\u9650\u5236\u4e3a\u4e00\u4e2a\u3002<\/span><\/p>\n


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\u5982\u4e0a\u6240\u8ff0\uff0c\u8fd8\u53ef\u4ee5\u4f7f\u7528\u6307\u5b9a\u7ef4\u5ea6\u7a7a\u95f4\u6240\u9700\u7684\u6700\u5c11\u5750\u6807\u6570\u6765\u8ba1\u7b97\u81ea\u7531\u5ea6\u3002\u6bd4\u5982\uff1a<\/span><\/p>\n


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\u5bf9\u4e8e\u5355\u4e2a\u7c92\u5b50\uff0c\u6211\u4eec\u9700\u8981\u5728\u4e8c\u7ef4\u5e73\u9762\u4e2d\u6307\u5b9a2\u4e2a\u5750\u6807\uff0c\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u6307\u5b9a3\u4e2a\u5750\u6807\u3002\u56e0\u6b64\uff0c\u5b83\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u81ea\u7531\u5ea6\u4e3a3\u3002<\/span><\/p>\n


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\u4e09\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u75312\u4e2a\u7c92\u5b50\uff08\u4f8b\u5982\u53cc\u539f\u5b50\u5206\u5b50\uff09\u7ec4\u6210\u4e14\u5f7c\u6b64\u4e4b\u95f4\u5177\u6709\u6052\u5b9a\u8ddd\u79bb\uff08\u5047\u8bbed\uff09\u7684\u7269\u4f53\uff0c\uff08\u5982\u4e0b\u6240\u793a\uff09\uff0c\u53ef\u4ee5\u8868\u660e\u5176\u81ea\u7531\u5ea6\u4e3a5\u3002<\/span><\/p>\n


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\u5047\u8bbe\u8fd9\u4e2a\u7269\u4f53\u4e2d\u7684\u4e00\u4e2a\u7c92\u5b50\u7684\u5750\u6807\u4e3a(x1,\u2009y1,\u2009z1)\uff0c\u53e6\u4e00\u4e2a\u7c92\u5b50\u7684\u5750\u6807\u4e3a(x2,\u2009y2,\u2009z2)\uff0c\u5176\u4e2d\u2009z2\u672a\u77e5\u3002\u90a3\u4e48\u4e24\u4e2a\u5750\u6807\u4e4b\u95f4\u8ddd\u79bb\u7684\u516c\u5f0f\u53ef\u4ee5\u63cf\u8ff0\u4e3a\uff1a<\/span><\/p>\n


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\u5176\u7b49\u5f0f\u542b\u6709\u4e00\u4e2a\u672a\u77e5\u6570z2\uff0c\u4e0d\u8fc7\u6211\u4eec\u53ef\u4ee5\u5bf9\u5176\u6c42\u89e3\u3002\u56e0\u6b64\u5b9e\u9645\u4e0a\u662f\u5141\u8bb8x1, x2, y1, y2, z1, \u6216\u8005 z2\u5176\u4e2d\u4e4b\u4e00\u662f\u672a\u77e5\u7684\u3002<\/span><\/p>\n


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\u4e0e\u7ecf\u5178\u7684\u80fd\u91cf\u5747\u5206\u5b9a\u7406 Equipartition theorem\u76f8\u53cd\uff0c\u5728\u5ba4\u6e29\u4e0b\uff0c\u5206\u5b50\u7684\u632f\u52a8\u5bf9\u70ed\u5bb9\u91cf Heat capacity\u7684\u8d21\u732e\u901a\u5e38\u53ef\u5ffd\u7565\u4e0d\u8ba1\u3002\u8fd9\u662f\u56e0\u4e3a\u8fd9\u4e9b\u81ea\u7531\u5ea6\u88ab\u51bb\u7ed3\u4e86\uff0c\u56e0\u4e3a\u80fd\u91cf\u672c\u5f81\u503c\u4e4b\u95f4\u7684\u95f4\u9694\u8d85\u8fc7\u4e86\u4e0e\u73af\u5883\u6e29\u5ea6\uff08kBT\uff09\u76f8\u5bf9\u5e94\u7684\u80fd\u91cf\u3002\u5728\u4e0b\u8868\u4e2d\uff0c\u8fd9\u4e9b\u81ea\u7531\u5ea6\u5747\u88ab\u5ffd\u7565\uff0c\u56e0\u4e3a\u5b83\u4eec\u5bf9\u603b\u80fd\u91cf\u7684\u5f71\u54cd\u975e\u5e38\u5c0f\u3002\u53ea\u6709\u5e73\u79fb\u548c\u65cb\u8f6c\u81ea\u7531\u5ea6\u5bf9\u70ed\u5bb9\u6bd4 Heat capacity ratio\u6709\u4e9b\u8bb8\u8d21\u732e\uff08\u7b49\u91cf\uff09\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5728\u5ba4\u6e29\u4e0b\uff0c\u5355\u539f\u5b50\u6c14\u4f53 \u03b3=5\/3\u548c\u53cc\u539f\u5b50\u6c14\u4f53 \u03b3=7\/5\u7684\u539f\u56e0\u3002<\/span><\/p>\n


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\u4e0d\u8fc7\uff0c\u5728\u975e\u5e38\u9ad8\u7684\u6e29\u5ea6\u4e0b\uff0c\u5dee\u4e0d\u591a\u5728\u632f\u52a8\u6e29\u5ea6(\u0398vib)\u7684\u91cf\u7ea7\u4e0a\uff0c\u632f\u52a8\u8fd0\u52a8\u5c31\u4e0d\u80fd\u88ab\u5ffd\u7565\u4e86\u3002<\/span><\/p>\n


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\u632f\u52a8\u6e29\u5ea6\u5728103 K\u548c104 K\u4e4b\u95f4\u3002<\/span><\/p>\n

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<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u67d0\u4e2a\u7cfb\u7edf\u7684\u81ea\u7531\u5ea6X1,\u2009…\u2009,\u2009XN\u96c6\u5408\uff0c\u5982\u679c\u96c6\u5408\u7684\u80fd\u91cf\u53ef\u4ee5\u7528\u4ee5\u4e0b\u5f62\u5f0f\u8868\u793a\uff0c\u5219\u5b83\u4eec\u662f\u72ec\u7acb\u7684\uff1a<\/span><\/p>\n


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\u5176\u4e2dEi\u662f\u552f\u4e00\u53d8\u91cfXi\u7684\u51fd\u6570\u3002<\/span><\/p>\n


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\u4f8b\u5982\uff1a\u5982\u679cX1 \u548c X2\u662f\u4e24\u4e2a\u81ea\u7531\u5ea6\uff0c\u5e76\u4e14E\u662f\u5173\u8054\u7684\u80fd\u91cf\u3002<\/span><\/p>\n


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\u8fd9\u91cc\u7684i\u503c\u53ef\u4ee5\u53d61\u5230N\uff0c\u7b2ci\u4e2a\u81ea\u7531\u5ea6Xi\u7684\u503c\u4f9d\u636e\u6ce2\u5c14\u5179\u66fc\u5206\u5e03 Boltzmann distribution \u3002\u5176\u6982\u7387\u5bc6\u5ea6\u51fd\u6570 Probability density function\u5982\u4e0b\uff1a<\/span><\/p>\n


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\u5728\u672c\u8282\u4ee5\u53ca\u6574\u7bc7\u6587\u7ae0\u4e2d\uff0c\u65b9\u62ec\u53f7<>\u8868\u793a\u5176\u6240\u5305\u542b\u6570\u91cf\u7684\u5e73\u5747\u503c\u3002<\/span><\/p>\n


<\/span><\/p>\n

\u7cfb\u7edf\u7684\u5185\u80fd\u662f\u6bcf\u4e2a\u81ea\u7531\u5ea6\u76f8\u5173\u7684\u5e73\u5747\u80fd\u91cf\u4e4b\u548c\uff1a<\/span><\/p>\n


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\n

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<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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\u5982\u679c\u4e0e\u8be5\u81ea\u7531\u5ea6\u76f8\u5173\u7684\u80fd\u91cf\u9879\u53ef\u4ee5\u5199\u6210\u5982\u4e0b\u7b49\u5f0f\uff0c\u5219\u81ea\u7531\u5ea6Xi\u662f\u4e8c\u6b21\u7684<\/span><\/p>\n


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\u5176\u4e2dY\u662f\u5176\u4ed6\u4e8c\u6b21\u81ea\u7531\u5ea6\u7684\u7ebf\u6027\u7ec4\u5408\u3002<\/span><\/p>\n


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\u4f8b\u5982\uff1a\u5982\u679cX1 \u548c X2\u662f\u4e24\u4e2a\u81ea\u7531\u5ea6\uff0c\u800cE\u662f\u5173\u8054\u7684\u80fd\u91cf\uff1a<\/span><\/p>\n


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\u4f8b\u5982\uff0c\u5728\u725b\u987f\u529b\u5b66\u4e2d\uff0c\u4e00\u4e2a\u4e8c\u81ea\u7531\u5ea6\u7684\u52a8\u529b\u5b66\u7cfb\u7edf\u662f\u7531\u4e00\u7ec4\u5177\u6709\u6052\u5b9a\u7cfb\u6570\u7684\u9f50\u6b21\u7ebf\u6027\u5fae\u5206\u65b9\u7a0b homogeneous linear differential equations \u63a7\u5236\u7684\u3002<\/span><\/p>\n


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\u4e8c\u6b21\u72ec\u7acb\u7684\u81ea\u7531\u5ea6<\/span><\/strong><\/span><\/h3>\n

\u5982\u679c\u80fd\u91cf\u4e0e\u7cfb\u7edf\u7684\u5fae\u89c2\u72b6\u6001\u6709\u5173\uff0c\u5219X1,\u2009…\u2009,\u2009XN\u662f\u4e8c\u6b21\u72ec\u7acb\u7684\u81ea\u7531\u5ea6\uff0c\u5b83\u4eec\u53ef\u4ee5\u5199\u6210\uff1a<\/span><\/p>\n


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\u80fd\u91cf\u5747\u5206\u5b9a\u7406<\/span><\/strong><\/span><\/h3>\n

\u5728\u7edf\u8ba1\u529b\u5b66\u7684\u7ecf\u5178\u6781\u9650\u4e2d\uff0c\u5728\u70ed\u529b\u5b66\u5e73\u8861 Thermodynamic equilibrium\u72b6\u6001\u4e0b\uff0cN\u4e2a\u4e8c\u6b21\u4e14\u72ec\u7acb\u81ea\u7531\u5ea6\u7684\u7cfb\u7edf\u5185\u90e8\u80fd\u91cf\u4e3a\uff1a<\/span><\/p>\n


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<\/mjx-dbox><\/mjx-frac><\/mjx-mfrac><\/mjx-texatom><\/mjx-mstyle><\/mjx-math><\/mjx-container><\/p>\n

\u6b64\u65f6\uff0c\u4e0e\u81ea\u7531\u5ea6\u76f8\u5173\u7684\u5e73\u5747\u80fd\u91cf\u4e3a\uff1a<\/span><\/mjx-row><\/p>\n

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\u7531\u4e8e\u81ea\u7531\u5ea6\u662f\u72ec\u7acb\u7684\uff0c\u56e0\u6b64\u7cfb\u7edf\u7684\u5185\u90e8\u80fd\u91cf\u7b49\u4e8e\u6bcf\u4e2a\u81ea\u7531\u5ea6\u5e26\u6709\u7684\u5e73\u5747\u80fd\u91cf\u4e4b\u548c\uff0c\u7531\u6b64\u5f97\u5230\u4e86\u7ed3\u679c\u3002<\/span><\/p>\n


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\u603b\u7ed3<\/span><\/strong><\/strong><\/span><\/strong><\/strong><\/p>\n<\/section>\n

\n

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<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

<\/span>
<\/h2>\n

\u5c3d\u7ba1\u5728\u6570\u5b66\u4e0a\u5f88\u65b9\u4fbf\uff0c\u4f46\u5c06\u7cfb\u7edf\u72b6\u6001\u63cf\u8ff0\u4e3a\u76f8\u7a7a\u95f4\u4e2d\u7684\u4e00\u4e2a\u70b9\uff0c\u4ece\u6839\u672c\u4e0a\u8bb2\u662f\u4e0d\u51c6\u786e\u7684\u3002\u5728\u91cf\u5b50\u529b\u5b66\u4e2d\uff0c\u4f53\u7cfb\u8fd0\u52a8\u72b6\u6001\u7684\u81ea\u7531\u5ea6\u88ab\u6ce2\u51fd\u6570\u7684\u6982\u5ff5\u6240\u53d6\u4ee3\uff0c\u5e76\u4e14\u5bf9\u5e94\u4e8e\u5176\u4ed6\u81ea\u7531\u5ea6\u7684\u7b97\u5b50 Operator\u5177\u6709\u79bb\u6563\u7684\u5149\u8c31\u3002\u4f8b\u5982\uff0c\u7535\u5b50\u6216\u5149\u5b50\u7684\u672c\u5f81\u89d2\u52a8\u91cf\u7b97\u7b26 Angular momentum operator \uff08\u5bf9\u5e94\u4e8e\u8f6c\u52a8\u81ea\u7531\u5ea6\uff09\u53ea\u6709\u4e24\u4e2a\u7279\u5f81\u503c\u3002\u5f53\u8fd0\u52a8\u5177\u6709\u666e\u6717\u514b\u5e38\u6570 Planck constant\u7684\u91cf\u7ea7\u65f6\uff0c\u8fd9\u79cd\u79bb\u6563\u53d8\u5f97\u975e\u5e38\u660e\u663e\uff0c\u5e76\u4e14\u53ef\u4ee5\u533a\u5206\u51fa\u5404\u4e2a\u81ea\u7531\u5ea6\u3002<\/span><\/p>\n


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<\/strong>
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\u6587\u7ae0\u63a8\u8350<\/span><\/strong><\/span>
<\/h3>\n

Reactive Islands for Three Degrees-of-Freedom Hamiltonian Systems<\/strong><\/p>\n

https:\/\/pattern.swarma.org\/paper?id=3adc054e-9cde-11eb-9d35-0242ac170009<\/span><\/p>\n

\u672c\u6587\u7ae0\u8fdb\u4e00\u6b65\u63a2\u8ba8\u4e86\u4e09\u4e2a\u81ea\u7531\u5ea6\u65f6\u4e0d\u76f8\u5173\u54c8\u5bc6\u987f\u7cfb\u7edf\u7684\u53cd\u5e94\u5c9b\u7406\u8bba\u7684\u51e0\u4f55\u3001\u89e3\u6790\u548c\u8ba1\u7b97\u6846\u67b6\u3002\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u52a8\u529b\u5b66\u53d1\u751f\u5728\u76f8\u7a7a\u95f4\u7684\u4e94\u7ef4\u80fd\u91cf\u9762\u4e2d\uff0c\u5e76\u4e14\u7531\u4e09\u7ef4\u6b63\u5e38\u53cc\u66f2\u4e0d\u53d8\u7403\u7684\u56db\u7ef4\u7a33\u5b9a\u6d41\u5f62\u548c\u4e0d\u7a33\u5b9a\u6d41\u5f62\u63a7\u5236\u3002\u7a33\u5b9a\u6d41\u5f62\u548c\u4e0d\u7a33\u5b9a\u6d41\u5f62\u5177\u6709\u7403\u6807\u7684\u51e0\u4f55\u7ed3\u6784\uff0c\u5bf9\u6b64\u672c\u6587\u7ae0\u63d0\u4f9b\u4e86\u7814\u7a76\u8fd9\u4e9b\u7403\u6807\u53ca\u5176\u4ea4\u70b9\u51b3\u5b9a\u8f68\u8ff9\u52a8\u6001\u6f14\u5316\u7684\u65b9\u6cd5\u3002\u8fd9\u79cd\u51e0\u4f55\u56fe\u50cf\u662f\u901a\u8fc7\u62c9\u683c\u6717\u65e5\u63cf\u8ff0\u5b50\u7684\u8ba1\u7b97\u6280\u672f\u5b9e\u73b0\u7684\u3002\u5728\u4e00\u7ec4\u8f68\u8ff9\u4e2d\uff0c\u62c9\u683c\u6717\u65e5\u63cf\u8ff0\u7b26\u5141\u8bb8\u88ab\u8bc6\u522b\u6700\u63a5\u8fd1\u7a33\u5b9a\u6216\u4e0d\u7a33\u5b9a\u6d41\u5f62\u7684\u8f68\u8ff9\u3002\u5229\u7528\u622a\u9762\u4e0a\u6d41\u5f62\u7684\u8fd1\u4f3c\uff0c\u80fd\u591f\u8ba1\u7b97\u80fd\u91cf\u9762\u4e24\u4e2a\u533a\u57df\u4e4b\u95f4\u7684\u901a\u91cf\u3002
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<\/p>\n

\u80fd\u5747\u5206\u5b9a\u7406\u63a8\u5bfc\u53ca\u5e94\u7528<\/span><\/strong><\/span><\/p>\n

https:\/\/zhuanlan.zhihu.com\/p\/364116467<\/span><\/p>\n

\u80fd\u91cf\u5747\u5206\u5b9a\u7406\u662f\u7ecf\u5178\u7edf\u8ba1\u529b\u5b66\u975e\u5e38\u91cd\u8981\u7684\u7ed3\u8bba,\u672c\u6587\u7ae0\u4ecb\u7ecd\u4e86\u80fd\u91cf\u5747\u5206\u5b9a\u7406\u7684\u63a8\u5bfc\u4ee5\u53ca\u8fd0\u7528\u8303\u56f4\u3002<\/span><\/p>\n


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\u89c6\u9891\u63a8\u8350<\/span><\/strong><\/h3>\n

\u5927\u5b66\u7269\u74065.3 \u80fd\u91cf\u6309\u81ea\u7531\u5ea6\u5747\u5206\u5b9a\u7406<\/span><\/strong><\/span><\/p>\n

https:\/\/www.bilibili.com\/video\/av242881324\/<\/span><\/p>\n

\u6c14\u4f53\u7684\u70ed\u8fd0\u52a8\u91cf\u4e0e\u7ec4\u6210\u6c14\u4f53\u7684\u5206\u5b50\u7ed3\u6784\u6709\u5173\uff0c\u9664\u4e86\u5355\u539f\u5b50\u5206\u5b50\u53ef\u770b\u4f5c\u8d28\u70b9\uff08\u53ea\u6709\u5e73\u52a8\uff09\u5916\uff0c\u4e00\u822c\u7531\u4e8e\u4e24\u4e2a\u539f\u5b50\u4ee5\u4e0a\u7ec4\u6210\u7684\u5206\u5b50\u4e0d\u4ec5\u6709\u5e73\u52a8\uff0c\u800c\u4e14\u8fd8\u6709\u8f6c\u52a8\u548c\u5206\u5b50\u5185\u539f\u5b50\u95f4\u7684\u632f\u52a8\uff0c\u5176\u76f8\u5e94\u80fd\u91cf\u4e0d\u80fd\u5ffd\u7565\u3002\u4e3a\u6b64\uff0c\u9700\u8981\u5f15\u7528\u529b\u5b66\u4e2d\u5173\u4e8e\u81ea\u7531\u5ea6\u7684\u6982\u5ff5\u6765\u63cf\u8ff0\u5206\u5b50\u7ed3\u6784\u3002<\/span><\/p>\n


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\u8bfe\u7a0b\u63a8\u8350<\/strong><\/span><\/h3>\n

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