[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/294548#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/294548","headline":"\u30dc\u30fc\u30b9\u6c17\u4f53 – Wikipedia","name":"\u30dc\u30fc\u30b9\u6c17\u4f53 – Wikipedia","description":"\u7406\u60f3\u30dc\u30fc\u30b9\u6c17\u4f53\uff08\u82f1: Bose gas\uff09\u3068\u306f\u3001\u53e4\u5178\u7684\u306a\u7406\u60f3\u6c17\u4f53\u306b\u985e\u4f3c\u3057\u305f\u91cf\u5b50\u529b\u5b66\u7684\u306a\u76f8\u306e\u3053\u3068\u3002\u6574\u6570\u5024\u306e\u30b9\u30d4\u30f3\u3092\u3082\u3064\u30dc\u30fc\u30b9\u7c92\u5b50\u304b\u3089\u69cb\u6210\u3055\u308c\u3001\u30dc\u30fc\u30b9\u2013\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u7d71\u8a08\u306b\u5f93\u3046\u3002\u30dc\u30fc\u30b9\u7c92\u5b50\u306e\u7d71\u8a08\u529b\u5b66\u306f\u3001\u30b5\u30c6\u30a3\u30a8\u30f3\u30c9\u30e9\u30fb\u30dc\u30fc\u30b9\u304c\u5149\u5b50\u306b\u304a\u3044\u3066\u958b\u62d3\u3057\u305f\u3002\u30a2\u30eb\u30d9\u30eb\u30c8\u30fb\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306f\u8cea\u91cf\u3092\u6301\u3064\u7c92\u5b50\u306b\u5bfe\u3057\u3066\u30dc\u30fc\u30b9\u7d71\u8a08\u3092\u62e1\u5f35\u3059\u308b\u3068\u3068\u3082\u306b\u3001\u30dc\u30fc\u30b9\u7c92\u5b50\u306e\u7406\u60f3\u6c17\u4f53\u304c\u5341\u5206\u306b\u4f4e\u6e29\u3067\u51dd\u7e2e\u3057\u3001\u53e4\u5178\u7684\u306a\u7406\u60f3\u6c17\u4f53\u3068\u306f\u6319\u52d5\u304c\u7570\u306a\u308b\u3053\u3068\u3092\u793a\u3057\u305f\u3002\u3053\u306e\u51dd\u7e2e\u306f\u30dc\u30fc\u30b9\uff1d\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u51dd\u7e2e\u3068\u547c\u3070\u308c\u308b\u3002 Table of Contents \u30c8\u30fc\u30de\u30b9\uff1d\u30d5\u30a7\u30eb\u30df\u8fd1\u4f3c[\u7de8\u96c6]\u57fa\u5e95\u72b6\u614b\u306e\u7d44\u307f\u5165\u308c[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6] \u30c8\u30fc\u30de\u30b9\uff1d\u30d5\u30a7\u30eb\u30df\u8fd1\u4f3c[\u7de8\u96c6] \u7406\u60f3\u30dc\u30fc\u30b9\u6c17\u4f53\u306e\u71b1\u529b\u5b66\u306f\u3001\u30b0\u30e9\u30f3\u30c9\u30ab\u30ce\u30cb\u30ab\u30eb\u5206\u5e03\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u308b\u3002\u30dc\u30fc\u30b9\u6c17\u4f53\u306e\u30b0\u30e9\u30f3\u30c9\u30ab\u30ce\u30cb\u30ab\u30eb\u5206\u5e03\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b\u3002 Z(z,\u03b2,V)=\u220fi(1\u2212ze\u2212\u03b2\u03f5i)\u2212gi{displaystyle {mathcal {Z}}(z,beta ,V)=prod _{i}left(1-ze^{-beta epsilon _{i}}right)^{-g_{i}}} \u3053\u306e\u7a4d\u306e\u305d\u308c\u305e\u308c\u306e\u9805\u306f\u3001\u56fa\u6709\u306e\u30a8\u30cd\u30eb\u30ae\u30fc \u03b5i \u306b\u76f8\u5f53\u3059\u308b\u3002gi \u306f\u30a8\u30cd\u30eb\u30ae\u30fc","datePublished":"2022-04-26","dateModified":"2022-04-26","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/c9645c498c9701c88b89b8537773dd7c?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/11\/book.png","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/0a282294791d26f45eb72c900bef1afe006a9720","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/0a282294791d26f45eb72c900bef1afe006a9720","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/294548","about":["Wiki"],"wordCount":7682,"articleBody":"\u7406\u60f3\u30dc\u30fc\u30b9\u6c17\u4f53\uff08\u82f1: Bose gas\uff09\u3068\u306f\u3001\u53e4\u5178\u7684\u306a\u7406\u60f3\u6c17\u4f53\u306b\u985e\u4f3c\u3057\u305f\u91cf\u5b50\u529b\u5b66\u7684\u306a\u76f8\u306e\u3053\u3068\u3002\u6574\u6570\u5024\u306e\u30b9\u30d4\u30f3\u3092\u3082\u3064\u30dc\u30fc\u30b9\u7c92\u5b50\u304b\u3089\u69cb\u6210\u3055\u308c\u3001\u30dc\u30fc\u30b9\u2013\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u7d71\u8a08\u306b\u5f93\u3046\u3002\u30dc\u30fc\u30b9\u7c92\u5b50\u306e\u7d71\u8a08\u529b\u5b66\u306f\u3001\u30b5\u30c6\u30a3\u30a8\u30f3\u30c9\u30e9\u30fb\u30dc\u30fc\u30b9\u304c\u5149\u5b50\u306b\u304a\u3044\u3066\u958b\u62d3\u3057\u305f\u3002\u30a2\u30eb\u30d9\u30eb\u30c8\u30fb\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306f\u8cea\u91cf\u3092\u6301\u3064\u7c92\u5b50\u306b\u5bfe\u3057\u3066\u30dc\u30fc\u30b9\u7d71\u8a08\u3092\u62e1\u5f35\u3059\u308b\u3068\u3068\u3082\u306b\u3001\u30dc\u30fc\u30b9\u7c92\u5b50\u306e\u7406\u60f3\u6c17\u4f53\u304c\u5341\u5206\u306b\u4f4e\u6e29\u3067\u51dd\u7e2e\u3057\u3001\u53e4\u5178\u7684\u306a\u7406\u60f3\u6c17\u4f53\u3068\u306f\u6319\u52d5\u304c\u7570\u306a\u308b\u3053\u3068\u3092\u793a\u3057\u305f\u3002\u3053\u306e\u51dd\u7e2e\u306f\u30dc\u30fc\u30b9\uff1d\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u51dd\u7e2e\u3068\u547c\u3070\u308c\u308b\u3002  Table of Contents\u30c8\u30fc\u30de\u30b9\uff1d\u30d5\u30a7\u30eb\u30df\u8fd1\u4f3c[\u7de8\u96c6]\u57fa\u5e95\u72b6\u614b\u306e\u7d44\u307f\u5165\u308c[\u7de8\u96c6]\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]\u30c8\u30fc\u30de\u30b9\uff1d\u30d5\u30a7\u30eb\u30df\u8fd1\u4f3c[\u7de8\u96c6]\u7406\u60f3\u30dc\u30fc\u30b9\u6c17\u4f53\u306e\u71b1\u529b\u5b66\u306f\u3001\u30b0\u30e9\u30f3\u30c9\u30ab\u30ce\u30cb\u30ab\u30eb\u5206\u5e03\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u308b\u3002\u30dc\u30fc\u30b9\u6c17\u4f53\u306e\u30b0\u30e9\u30f3\u30c9\u30ab\u30ce\u30cb\u30ab\u30eb\u5206\u5e03\u95a2\u6570\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b\u3002  Z(z,\u03b2,V)=\u220fi(1\u2212ze\u2212\u03b2\u03f5i)\u2212gi{displaystyle {mathcal {Z}}(z,beta ,V)=prod _{i}left(1-ze^{-beta epsilon _{i}}right)^{-g_{i}}}\u3053\u306e\u7a4d\u306e\u305d\u308c\u305e\u308c\u306e\u9805\u306f\u3001\u56fa\u6709\u306e\u30a8\u30cd\u30eb\u30ae\u30fc \u03b5i \u306b\u76f8\u5f53\u3059\u308b\u3002gi \u306f\u30a8\u30cd\u30eb\u30ae\u30fc \u03b5i \u3092\u6301\u3064\u72b6\u614b\u306e\u6570\u3001z \u306f\u7d76\u5bfe\u6d3b\u91cf(\u307e\u305f\u306f\u30d5\u30ac\u30b7\u30c6\u30a3\u30fc)\u3067\u3001\u5316\u5b66\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb  \u03bc \u3092\u7528\u3044\u3066\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u3002z(\u03b2,\u03bc)=e\u03b2\u03bc{displaystyle z(beta ,mu )=e^{beta mu }}\u03b2 \u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u3002  \u03b2=1kT{displaystyle beta ={frac {1}{kT}}}\u3053\u3053\u3067 k \u306f\u30dc\u30eb\u30c4\u30de\u30f3\u5b9a\u6570\u3001T \u306f\u6e29\u5ea6\u3067\u3042\u308b\u3002\u5168\u3066\u306e\u71b1\u529b\u5b66\u7684\u306a\u91cf\u306f\u30b0\u30e9\u30f3\u30c9\u30ab\u30ce\u30cb\u30ab\u30eb\u5206\u5e03\u95a2\u6570\u304b\u3089\u5c0e\u51fa\u3055\u308c\u308b\u305f\u3081\u3001\u5168\u3066\u306e\u71b1\u529b\u5b66\u7684\u306a\u91cf\u306f\uff13\u3064\u306e\u5909\u6570 z\u3001\u03b2\uff08\u307e\u305f\u306f T \uff09\u3001V \u306e\u307f\u306e\u95a2\u6570\u3068\u3057\u3066\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u5168\u3066\u306e\u504f\u5fae\u5206\u4fc2\u6570\u306f\u3001\uff13\u3064\u306e\u5909\u6570\u306e\u3046\u3061\uff11\u3064\u3092\u5909\u6570\u3068\u3057\u3001\u6b8b\u308a\u306e\uff12\u3064\u306f\u5b9a\u6570\u3068\u3059\u308b\u3053\u3068\u3067\u6c42\u3081\u3089\u308c\u308b\u3002\u3053\u3053\u3067\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u7121\u6b21\u5143\u306e\u30b0\u30e9\u30f3\u30c9\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3092\u6271\u3046\u3068\u4fbf\u5229\u3067\u3042\u308b\u3002\u03a9=\u2212ln\u2061(Z)=\u2211igiln\u2061(1\u2212ze\u2212\u03b2\u03f5i).{displaystyle Omega =-ln({mathcal {Z}})=sum _{i}g_{i}ln left(1-ze^{-beta epsilon _{i}}right).}\u5e73\u5747\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u6e96\u4f4d\u9593\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u5dee\u3068\u6bd4\u3079\u3066\u5927\u304d\u3044\u3068\u4eee\u5b9a\u3059\u308b\u30c8\u30fc\u30de\u30b9\uff1d\u30d5\u30a7\u30eb\u30df\u8fd1\u4f3c\u3092\u9069\u7528\u3059\u308b\u3068\u3001\u4e0a\u8a18\u306e\u548c\u306f\u7a4d\u5206\u3067\u7f6e\u304d\u63db\u3048\u3089\u308c\u308b\u3002\u03a9\u2248\u222b0\u221eln\u2061(1\u2212ze\u2212\u03b2E)dg.{displaystyle Omega approx int _{0}^{infty }ln left(1-ze^{-beta E}right),dg.}\u7e2e\u9000\u5ea6 dg \u306f\u4e00\u822c\u7684\u306a\u516c\u5f0f\u306b\u3088\u3063\u3066\u591a\u304f\u306e\u7570\u306a\u308b\u72b6\u6cc1\u3092\u8868\u73fe\u3059\u308b\u3002dg=1\u0393(\u03b1)E\u03b1\u22121Ec\u03b1\u00a0dE{displaystyle dg={frac {1}{Gamma (alpha )}},{frac {E^{,alpha -1}}{E_{c}^{alpha }}}~dE}\u3053\u3053\u3067 \u03b1 \u306f\u5b9a\u6570\u3001Ec \u306f\u81e8\u754c\u30a8\u30cd\u30eb\u30ae\u30fc\u3001\u0393 \u306f\u30ac\u30f3\u30de\u95a2\u6570\u3067\u3042\u308b\u3002\u305f\u3068\u3048\u3070\u7bb1\u306e\u4e2d\u306e\u8cea\u91cf\u3092\u6301\u3064\u30dc\u30fc\u30b9\u6c17\u4f53\u3067\u306f \u03b1 = 3\/2 \u3067\u3001\u81e8\u754c\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b\u30021(\u03b2Ec)\u03b1=Vf\u039b3{displaystyle {frac {1}{(beta E_{c})^{alpha }}}={frac {Vf}{Lambda ^{3}}}}\u3053\u3053\u3067 \u039b \u306f\u71b1\u7684\u6ce2\u9577\u3067\u3042\u308b\u3002\u8abf\u548c\u30c8\u30e9\u30c3\u30d7\u4e2d\u306e\u8cea\u91cf\u3092\u6301\u3064\u30dc\u30fc\u30b9\u6c17\u4f53\u3067\u306f \u03b1 = 3 \u3067\u3001\u81e8\u754c\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b\u30021(\u03b2Ec)\u03b1=f(\u210f\u03c9\u03b2)3{displaystyle {frac {1}{(beta E_{c})^{alpha }}}={frac {f}{(hbar omega beta )^{3}}}}\u3053\u3053\u3067 V(r) = m\u03c92r2 \/ 2 \u306f\u8abf\u548c\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u3067\u3042\u308b\u3002Ec \u306f\u4f53\u7a4d\u3060\u3051\u306e\u95a2\u6570\u3067\u3042\u308b\u3002\u3053\u306e\u30b0\u30e9\u30f3\u30c9\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306e\u65b9\u7a0b\u5f0f\u306f\u3001\u9805\u5225\u306b\u88ab\u7a4d\u5206\u95a2\u6570\u306e\u30c6\u30a4\u30e9\u30fc\u7d1a\u6570\u3092\u7a4d\u5206\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001 \u307e\u305f\u306f Li1(zexp(\u2212\u03b2E)) \u306e\u30e1\u30ea\u30f3\u5909\u63db\u306b\u6bd4\u4f8b\u3059\u308b\u3068\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u3053\u3067 Lis(x) \u306f\u591a\u91cd\u5bfe\u6570\u95a2\u6570\u3067\u3042\u308b\u3002\u89e3\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b\u3002\u03a9\u2248\u2212Li\u03b1+1(z)(\u03b2Ec)\u03b1{displaystyle Omega approx -{frac {{textrm {Li}}_{alpha +1}(z)}{left(beta E_{c}right)^{alpha }}}}\u3053\u306e\u30dc\u30fc\u30b9\u6c17\u4f53\u306b\u304a\u3051\u308b\u9023\u7d9a\u4f53\u8fd1\u4f3c\u306e\u554f\u984c\u70b9\u306f\u3001\u57fa\u5e95\u72b6\u614b\u304c\u5b9f\u8cea\u7684\u306b\u7121\u8996\u3055\u308c\u308b\u3053\u3068\u3067\u3001\u30bc\u30ed\u30a8\u30cd\u30eb\u30ae\u30fc\u3067\u7e2e\u9000\u5ea6\u304c\u30bc\u30ed\u306b\u306a\u308b\u3053\u3068\u3067\u3042\u308b\u3002\u3053\u306e\u554f\u984c\u70b9\u306f\u30dc\u30fc\u30b9\uff1d\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u51dd\u7e2e\u3092\u6271\u3046\u3068\u304d\u306b\u306f\u91cd\u5927\u3067\u3001\u6b21\u7ae0\u3067\u6271\u3046\u3002\u57fa\u5e95\u72b6\u614b\u306e\u7d44\u307f\u5165\u308c[\u7de8\u96c6]\u5168\u7c92\u5b50\u6570\u306f\u30b0\u30e9\u30f3\u30c9\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u304b\u3089\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b\u3002N=\u2212z\u2202\u03a9\u2202z\u2248Li\u03b1(z)(\u03b2Ec)\u03b1{displaystyle N=-z{frac {partial Omega }{partial z}}approx {frac {{textrm {Li}}_{alpha }(z)}{(beta E_{c})^{alpha }}}}\u591a\u91cd\u5bfe\u6570\u95a2\u6570\u9805\u306f\u5b9f\u3067\u6b63\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u305a\u3001\u6700\u5927\u5024\u306f z = 1 \u306e\u3068\u304d\u3067 \u03b6(\u03b1) \u306b\u7b49\u3057\u3044\u3002\u3053\u3053\u3067 \u03b6 \u306f\u30ea\u30fc\u30de\u30f3\u30bc\u30fc\u30bf\u95a2\u6570\u3067\u3042\u308b\u3002N \u3092\u56fa\u5b9a\u3059\u308b\u3068\u3001\u03b2 \u306e\u6700\u5927\u5024\u306f\u81e8\u754c\u5024 \u03b2c \u3067\u3001\u3053\u306e\u3068\u304d\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308b\u3002N=\u03b6(\u03b1)(\u03b2cEc)\u03b1{displaystyle N={frac {zeta (alpha )}{(beta _{c}E_{c})^{alpha }}}}\u3053\u308c\u306f\u81e8\u754c\u6e29\u5ea6 Tc = 1\/k\u03b2c \u306b\u76f8\u5f53\u3057\u3001\u3053\u308c\u4ee5\u4e0b\u3067\u306f\u30c8\u30fc\u30de\u30b9\uff1d\u30d5\u30a7\u30eb\u30df\u8fd1\u4f3c\u306f\u7834\u7dbb\u3059\u308b\u3002\u4e0a\u8a18\u306e\u65b9\u7a0b\u5f0f\u306f\u81e8\u754c\u6e29\u5ea6\u306b\u3064\u3044\u3066\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002Tc=(N\u03b6(\u03b1))1\/\u03b1Eck{displaystyle T_{c}=left({frac {N}{zeta (alpha )}}right)^{1\/alpha }{frac {E_{c}}{k}}}\u305f\u3068\u3048\u3070 \u03b1 = 3\/2 \u3067\u3001\u4e0a\u8ff0\u306e\u5024 Ec \u3092\u7528\u3044\u308b\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308b\u3002Tc=(NVf\u03b6(3\/2))2\/3h22\u03c0mk{displaystyle T_{c}=left({frac {N}{Vfzeta (3\/2)}}right)^{2\/3}{frac {h^{2}}{2pi mk}}}\u3055\u3089\u306b\u3001\u3053\u3053\u3067\u306f\u81e8\u754c\u6e29\u5ea6\u4ee5\u4e0b\u306e\u7d50\u679c\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u306f\u3067\u304d\u306a\u3044\u3002\u306a\u305c\u306a\u3089\u4e0a\u8a18\u306e\u65b9\u7a0b\u5f0f\u3092\u7528\u3044\u305f\u7c92\u5b50\u6570\u306f\u8ca0\u306b\u306a\u308b\u304b\u3089\u3067\u3042\u308b\u3002\u3053\u3053\u3067\u306e\u554f\u984c\u70b9\u306f\u3001\u30c8\u30fc\u30de\u30b9\uff1d\u30d5\u30a7\u30eb\u30df\u8fd1\u4f3c\u306f\u57fa\u5e95\u72b6\u614b\u306e\u7e2e\u9000\u5ea6\u3092\uff10\u3068\u3057\u3066\u3044\u308b\u3053\u3068\u3067\u3001\u3053\u308c\u306f\u9593\u9055\u3063\u3066\u3044\u308b\u3002\u51dd\u7e2e\u3092\u53d7\u3051\u5165\u308c\u308b\u57fa\u5e95\u72b6\u614b\u304c\u7121\u3044\u305f\u3081\u65b9\u7a0b\u5f0f\u304c\u7834\u7dbb\u3059\u308b\u3002\u3057\u304b\u3057\u4e0a\u8a18\u306e\u65b9\u7a0b\u5f0f\u306f\u52b1\u8d77\u72b6\u614b\u3067\u306f\u7c92\u5b50\u6570\u3092\u6bd4\u8f03\u7684\u6b63\u78ba\u306b\u8a55\u4fa1\u3057\u3066\u304a\u308a\u3001\u305d\u3053\u3078\u57fa\u5e95\u72b6\u614b\u3092\u5358\u7d14\u306b\u4ed8\u3051\u52a0\u3048\u308b\u3053\u3068\u306f\u60aa\u3044\u8fd1\u4f3c\u3067\u306f\u306a\u3044\u3053\u3068\u304c\u308f\u304b\u308b\u3002N=N0+Li\u03b1(z)(\u03b2Ec)\u03b1{displaystyle N=N_{0}+{frac {{textrm {Li}}_{alpha }(z)}{(beta E_{c})^{alpha }}}}\u3053\u3053\u3067 N0 \u306f\u57fa\u5e95\u72b6\u614b\u51dd\u7e2e\u306e\u7c92\u5b50\u6570\u3067\u3001\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u308b\u3002N0=g0z1\u2212z{displaystyle N_{0}={frac {g_{0},z}{1-z}}}  \u56f31\uff1a\u6b63\u898f\u5316\u3055\u308c\u305f\u6e29\u5ea6 \u03c4 \u3068\u69d8\u3005\u306a\u30dc\u30fc\u30b9\u6c17\u4f53\u30d1\u30e9\u30e1\u30fc\u30bf\u3068\u306e\u95a2\u4fc2\u3002\u03b1 \u306e\u5024\u306f3\/2\u3002\u5b9f\u7dda\u306f N = 10,000 \u306e\u5834\u5408\u3067\u3001\u70b9\u7dda\u306f N = 1,000 \u306e\u5834\u5408\u3002\u9ed2\u7dda\u306f\u52b1\u8d77\u7c92\u5b50\u306e\u5272\u5408\u3002\u9752\u7dda\u306f\u51dd\u96c6\u7c92\u5b50\u306e\u5272\u5408\u3002\u8d64\u7dda\u306f\u5316\u5b66\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306e\u8ca0\u6570\u3002\u7dd1\u7dda\u306f z \u306e\u5024\u3002k\u03b5c = 1 \u3068\u4eee\u5b9a\u3057\u305f\u3002\u3053\u306e\u65b9\u7a0b\u5f0f\u306f\u7d76\u5bfe\u96f6\u5ea6\u307e\u3067\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u56f3\uff11\u306b \u03b1 = 3\/2 \u306b\u304a\u3051\u308b\u3053\u306e\u65b9\u7a0b\u5f0f\u306e\u89e3\u306e\u7d50\u679c\u3092\u793a\u3059\u3002\u3053\u308c\u306f\u7bb1\u306e\u4e2d\u306e\u30dc\u30fc\u30b9\u6c17\u4f53\u306b\u76f8\u5f53\u3057\u3001k = \u03b5c = 1 \u3068\u3059\u308b\u3002\u5b9f\u7dda\u306f N = 10,000 \u306e\u5834\u5408\u3001\u70b9\u7dda\u306f N = 1,000 \u306e\u5834\u5408\u3092\u793a\u3059\u3002\u9ed2\u7dda\u306f\u52b1\u8d77\u7c92\u5b50\u306e\u5272\u5408 1 \u2212 N0\/N \u3001\u9752\u7dda\u306f\u51dd\u7e2e\u7c92\u5b50\u306e\u5272\u5408 N0\/N \u3067\u3001\u8d64\u7dda\u306f\u5316\u5b66\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb \u03bc \u306b\u30de\u30a4\u30ca\u30b9\u7b26\u53f7\u3092\u3064\u3051\u305f\u3082\u306e\u3001\u7dd1\u7dda\u306f z \u306e\u5024\u3067\u3042\u308b\u3002\u6a2a\u8ef8\u306f\u6b21\u306e\u3088\u3046\u306b\u5b9a\u7fa9\u3055\u308c\u308b\u6b63\u898f\u5316\u3055\u308c\u305f\u6e29\u5ea6 \u03c4 \u3067\u3042\u308b\u3002\u03c4=TTc{displaystyle tau ={frac {T}{T_{c}}}}\u03bc \u3084 z \u306f\u4f4e\u6e29\u306e\u6975\u9650\u3067 \u03c4\u03b1 \u3068\u7dda\u5f62\u306b\u306a\u308a\u3001N0\/N \u306f\u9ad8\u6e29\u306e\u6975\u9650\u3067 1\/\u03c4\u03b1 \u3068\u7dda\u5f62\u306b\u306a\u308b\u3053\u3068\u304c\u4f3a\u3048\u308b\u3002\u7c92\u5b50\u6570\u304c\u5897\u52a0\u3059\u308b\u3068\u3001\u51dd\u7e2e\u306e\u5272\u5408\u3068\u52b1\u8d77\u306e\u5272\u5408\u306f\u81e8\u754c\u6e29\u5ea6\u3067\u4e0d\u9023\u7d9a\u306b\u306a\u308b\u3002\u7c92\u5b50\u6570\u306e\u65b9\u7a0b\u5f0f\u306f\u6b63\u898f\u5316\u3055\u308c\u305f\u6e29\u5ea6\u3067\u8868\u3055\u308c\u308b\u3002N=g0z1\u2212z+N\u00a0Li\u03b1(z)\u03b6(\u03b1)\u00a0\u03c4\u03b1{displaystyle N={frac {g_{0},z}{1-z}}+N~{frac {{textrm {Li}}_{alpha }(z)}{zeta (alpha )}}~tau ^{alpha }}N \u3068 \u03c4 \u304c\u4e0e\u3048\u3089\u308c\u308b\u3068\u3001\u3053\u306e\u65b9\u7a0b\u5f0f\u306f \u03c4\u03b1 \u306b\u3064\u3044\u3066\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u3001z \u306b\u3064\u3044\u3066\u306e\u7d1a\u6570\u89e3\u306f\u3001\u03c4\u03b1 \u306e\u3079\u304d\u4e57\u307e\u305f\u306f \u03c4\u03b1 \u306e\u9006\u3079\u304d\u4e57\u3067\u306e\u6f38\u8fd1\u5c55\u958b\u3068\u3057\u3066\u306e\u7d1a\u6570\u306e\u53cd\u8ee2\u306e\u65b9\u6cd5\u306b\u3088\u3063\u3066\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u3053\u308c\u3089\u306e\u5c55\u958b\u304b\u3089\u3001T = 0 \u8fd1\u304f\u3067\u306e\u30ac\u30b9\u306e\u632f\u308b\u821e\u3044\u3092\u77e5\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002T \u304c\u7121\u9650\u5927\u3067\u30de\u30af\u30b9\u30a6\u30a7\u30eb-\u30dc\u30eb\u30c4\u30de\u30f3\u5206\u5e03\u3068\u306a\u308b\u3002\u7279\u306b\u6211\u3005\u304c\u8208\u5473\u304c\u3042\u308b\u306e\u306f T \u304c\u7121\u9650\u5927\u306e\u3068\u304d\u3067\u3001\u3053\u308c\u306f\u4e0a\u8a18\u306e\u5c55\u958b\u304b\u3089\u5bb9\u6613\u306b\u6c7a\u5b9a\u3059\u308b\u3002\u7c92\u5b50\u6570\u306b\u5bfe\u3059\u308b\u65b9\u7a0b\u5f0f\u306b\u57fa\u5e95\u72b6\u614b\u3092\u52a0\u3048\u308b\u3053\u3068\u306f\u3001\u7b49\u4fa1\u306a\u57fa\u5e95\u72b6\u614b\u306e\u9805\u3092\u30b0\u30e9\u30f3\u30c9\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306b\u52a0\u3048\u308b\u3053\u3068\u306b\u76f8\u5f53\u3059\u308b\u3002\u03a9=g0ln\u2061(1\u2212z)\u2212Li\u03b1+1(z)(\u03b2Ec)\u03b1{displaystyle Omega =g_{0}ln(1-z)-{frac {{textrm {Li}}_{alpha +1}(z)}{left(beta E_{c}right)^{alpha }}}}\u5168\u3066\u306e\u71b1\u529b\u5b66\u7684\u306a\u6027\u8cea\u306f\u3001\u30b0\u30e9\u30f3\u30c9\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u304b\u3089\u8a08\u7b97\u3055\u308c\u308b\u3002\u4ee5\u4e0b\u306e\u8868\u3067\u306f\u4f4e\u6e29\u3068\u9ad8\u6e29\u306e\u6975\u9650\u3001\u7c92\u5b50\u6570\u304c\u7121\u9650\u5927\u306e\u6975\u9650\u3067\u306e\u69d8\u3005\u306a\u71b1\u529b\u5b66\u7684\u306a\u91cf\u3092\u793a\u3059\u3002\u53b3\u5bc6\u306a\u7d50\u679c\u306f\u7b49\u53f7 (=) \u3067\u8868\u3057\u3001\u03c4\u03b1 \u306e\u7d1a\u6570\u306e\u6700\u521d\u306e\u6570\u9805\u306e\u307f\u306e\u7d50\u679c\u306f\u8fd1\u4f3c\u8a18\u53f7\u3067\u8868\u3057\u3066\u3044\u308b\u3002\u91cf\u4e00\u822c\u306e\u5834\u5408T\u226aTc{displaystyle Tll T_{c},}T\u226bTc{displaystyle Tgg T_{c},}z\u2248\u03b6(\u03b1)\u03c4\u03b1\u2212\u03b62(\u03b1)2\u03b1\u03c42\u03b1{displaystyle approx {frac {zeta (alpha )}{tau ^{alpha }}}-{frac {zeta ^{2}(alpha )}{2^{alpha }tau ^{2alpha }}}}=1{displaystyle =1,}\u51dd\u7e2e\u3057\u3066\u3044\u306a\u3044\u7c92\u5b50\u306e\u5272\u54081\u2212N0N{displaystyle 1-{frac {N_{0}}{N}},}=Li\u03b1(z)\u03b6(\u03b1)\u03c4\u03b1{displaystyle ={frac {{textrm {Li}}_{alpha }(z)}{zeta (alpha )}},tau ^{alpha }}=\u03c4\u03b1{displaystyle =tau ^{alpha },}=1{displaystyle =1,}\u72b6\u614b\u65b9\u7a0b\u5f0fPV\u03b2N=\u2212\u03a9N{displaystyle {frac {PVbeta }{N}}=-{frac {Omega }{N}},}=Li\u03b1+1(z)\u03b6(\u03b1)\u03c4\u03b1{displaystyle ={frac {{textrm {Li}}_{alpha !+!1}(z)}{zeta (alpha )}},tau ^{alpha }}=\u03b6(\u03b1+1)\u03b6(\u03b1)\u03c4\u03b1{displaystyle ={frac {zeta (alpha !+!1)}{zeta (alpha )}},tau ^{alpha }}\u22481\u2212\u03b6(\u03b1)2\u03b1+1\u03c4\u03b1{displaystyle approx 1-{frac {zeta (alpha )}{2^{alpha !+!1}tau ^{alpha }}}}\u30ae\u30d6\u30b9\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fcG=ln\u2061(z){displaystyle G=ln(z),}=ln\u2061(z){displaystyle =ln(z),}=0{displaystyle =0,}\u2248ln\u2061(\u03b6(\u03b1)\u03c4\u03b1)\u2212\u03b6(\u03b1)2\u03b1\u03c4\u03b1{displaystyle approx ln left({frac {zeta (alpha )}{tau ^{alpha }}}right)-{frac {zeta (alpha )}{2^{alpha }tau ^{alpha }}}}\u5168\u3066\u306e\u91cf\u306f\u3001\u9ad8\u6e29\u306e\u6975\u9650\u3092\u3068\u308b\u3068\u53e4\u5178\u7684\u306a\u7406\u60f3\u6c17\u4f53\u306e\u5024\u306b\u8fd1\u3065\u3044\u3066\u3044\u304f\u3002\u4e0a\u8a18\u306e\u5024\u3092\u7528\u3044\u3066\u3001\u4ed6\u306e\u71b1\u529b\u5b66\u7684\u306a\u91cf\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u305f\u3068\u3048\u3070\u3001\u5185\u90e8\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u5727\u529b\u00d7\u4f53\u7a4d\u3068\u306e\u95a2\u4fc2\u306f\u3001\u3059\u3079\u3066\u306e\u6e29\u5ea6\u306b\u308f\u305f\u3063\u3066\u53e4\u5178\u7684\u306a\u7406\u60f3\u6c17\u4f53\u3068\u540c\u3058\u3067\u3042\u308b\u3002U=\u2202\u03a9\u2202\u03b2=\u03b1PV{displaystyle U={frac {partial Omega }{partial beta }}=alpha PV}\u5b9a\u7a4d\u6bd4\u71b1\u306b\u304a\u3044\u3066\u3082\u540c\u69d8\u3067\u3042\u308b\u3002Cv=\u2202U\u2202T=k(\u03b1+1)U\u03b2{displaystyle C_{v}={frac {partial U}{partial T}}=k(alpha +1),Ubeta }\u30a8\u30f3\u30c8\u30ed\u30d4\u30fc\u306f\u6b21\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b\u3002TS=U+PV\u2212G{displaystyle TS=U+PV-G,}\u9ad8\u6e29\u306e\u6975\u9650\u3092\u3068\u308b\u3068\u3001\u6b21\u5f0f\u304c\u5f97\u3089\u308c\u308b\u3002TS=(\u03b1+1)+ln\u2061(\u03c4\u03b1\u03b6(\u03b1)){displaystyle TS=(alpha +1)+ln left({frac {tau ^{alpha }}{zeta (alpha )}}right)}\u3053\u308c\u306f \u03b1 = 3\/2 \u3067\u306f\u5358\u306a\u308b\u30b6\u30c3\u30af\u30fc\u30eb\u30fb\u30c6\u30c8\u30ed\u30fc\u30c7\u65b9\u7a0b\u5f0f\u3092\u66f8\u304d\u63db\u3048\u305f\u3082\u306e\u3067\u3042\u308b\u3002\u30c7\u30eb\u30bf\u76f8\u4e92\u4f5c\u7528\u3092\u3082\u30641\u6b21\u5143\u30dc\u30fc\u30b9\u7c92\u5b50\u306f\u30d5\u30a7\u30eb\u30df\u7c92\u5b50\u3068\u3057\u3066\u632f\u308b\u821e\u3044\u3001\u30d1\u30a6\u30ea\u306e\u6392\u4ed6\u539f\u7406\u306b\u5f93\u3046\u3002\u30c7\u30eb\u30bf\u76f8\u4e92\u4f5c\u7528\u3092\u3082\u30641\u6b21\u5143\u30dc\u30fc\u30b9\u7c92\u5b50\u306f\u30d9\u30fc\u30c6\u4eee\u8a2d\u306b\u3088\u308a\u53b3\u5bc6\u306b\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u308b\u3002\u30d0\u30eb\u30af\u81ea\u7531\u30a8\u30cd\u30eb\u30ae\u30fc\u3068\u71b1\u529b\u5b66\u7684\u30dd\u30c6\u30f3\u30b7\u30e3\u30eb\u306f\u694a\u632f\u5be7\u306b\u3088\u3063\u3066\u8a08\u7b97\u3055\u308c\u305f\u3002\uff11\u6b21\u5143\u306e\u5834\u5408\u306b\u304a\u3051\u308b\u76f8\u95a2\u95a2\u6570\u3082\u8a55\u4fa1\u3055\u308c\u305f\u3002\uff11\u6b21\u5143\u30dc\u30fc\u30b9\u6c17\u4f53\u306f\u91cf\u5b50\u7684\u306a\u975e\u7dda\u5f62\u30b7\u30e5\u30ec\u30fc\u30c7\u30a3\u30f3\u30ac\u30fc\u65b9\u7a0b\u5f0f\u3068\u7b49\u4fa1\u3067\u3042\u308b\u3002\u95a2\u9023\u9805\u76ee[\u7de8\u96c6]\u53c2\u8003\u6587\u732e[\u7de8\u96c6]"},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki21\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/jp\/wiki21\/archives\/294548#breadcrumbitem","name":"\u30dc\u30fc\u30b9\u6c17\u4f53 – Wikipedia"}}]}]