{"id":25734,"date":"2024-09-01T23:22:38","date_gmt":"2024-09-01T23:22:38","guid":{"rendered":"https:\/\/science-hub.click\/%E3%82%AB%E3%82%B7%E3%83%9F%E3%83%BC%E3%83%AB%E5%8A%B9%E6%9E%9C%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC\/"},"modified":"2024-09-01T23:22:38","modified_gmt":"2024-09-01T23:22:38","slug":"%E3%82%AB%E3%82%B7%E3%83%9F%E3%83%BC%E3%83%AB%E5%8A%B9%E6%9E%9C%E3%81%AB%E3%81%A4%E3%81%84%E3%81%A6%E8%A9%B3%E3%81%97%E3%81%8F%E8%A7%A3%E8%AA%AC","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=25734","title":{"rendered":"\u30ab\u30b7\u30df\u30fc\u30eb\u52b9\u679c\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac"},"content":{"rendered":"

\u5c0e\u5165<\/h2>

\u30ab\u30b7\u30df\u30fc\u30eb\u52b9\u679c \u306f<\/b>\u30011948 \u5e74\u306b\u30aa\u30e9\u30f3\u30c0\u306e\u7269\u7406\u5b66\u8005\u30d8\u30f3\u30c9\u30ea\u30c3\u30af\u30fb\u30ab\u30b7\u30df\u30fc\u30eb\u306b\u3088\u3063\u3066\u4e88\u6e2c\u3055\u308c\u305f\u3088\u3046\u306b\u30012 \u3064\u306e\u5c0e\u96fb\u6027\u306e\u5e2f\u96fb\u3057\u3066\u3044\u306a\u3044<\/i>\u5e73\u884c\u30d7\u30ec\u30fc\u30c8\u9593\u306e\u5f15\u529b\u3067\u3059\u3002\u91cf\u5b50\u771f\u7a7a<\/a><\/span>\u5909\u52d5\u306b\u3088\u308b\u3053\u306e\u52b9\u679c\u306f\u3001\u4ed6\u306e\u96fb\u6975\u5f62\u72b6\u306b\u3082\u5b58\u5728\u3057\u307e\u3059\u3002\u5b9f\u9a13\u7684\u306b\u306f\u3001\u93e1\u304c\u3088\u304f\u4f7f\u7528\u3055\u308c\u307e\u3059\u3002<\/p>

\n\"\"<\/figure>
\u30ab\u30b7\u30df\u30fc\u30eb\u306f\u5e73\u884c\u5e73\u677f\u306b\u529b\u3092\u52a0\u3048\u307e\u3059\u3002<\/div><\/div><\/div>
\n\"\"<\/figure>
\u30ab\u30b7\u30df\u30fc\u30eb\u306f\u5e73\u884c\u5e73\u677f\u306b\u529b\u3092\u52a0\u3048\u307e\u3059\u3002<\/div><\/div><\/div>
\n\"\u30ab\u30b7\u30df\u30fc\u30eb\u52b9\u679c\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\"<\/figure>

\u539f\u56e0<\/h2>

\u91cf\u5b50\u771f\u7a7a\u306e\u3086\u3089\u304e\u306f\u3059\u3079\u3066\u306e\u5834\u306e\u91cf\u5b50\u7406\u8ad6<\/a><\/span>\u306b\u5b58\u5728\u3057\u307e\u3059\u3002\u30ab\u30b7\u30df\u30fc\u30eb\u52b9\u679c\u306f<\/a><\/span>\u3001\u91cf\u5b50\u96fb\u6c17\u529b\u5b66<\/a><\/span>\u306e\u7406\u8ad6<\/a><\/span>\u306b\u3088\u3063\u3066\u8aac\u660e\u3055\u308c\u308b\u3001\u96fb\u78c1\u5834<\/a><\/span>\u306e\u5909\u52d5\u306b\u3088\u308b\u3082\u306e\u3067\u3059\u3002<\/p>

2 \u3064\u306e\u30d7\u30ec\u30fc\u30c8\u9593\u306e\u300c\u771f\u7a7a\u300d\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u3001\u6ce2\u9577\u304c 2 \u3064\u306e\u30d7\u30ec\u30fc\u30c8\u9593\u306e\u8ddd\u96e2\u3092\u6b63\u78ba\u306b\u5206\u5272\u3059\u308b\u5149\u5b50 (\u4eee\u60f3\u5149\u5b50\u3092\u542b\u3080) \u306e\u307f\u3092\u8003\u616e\u3057\u3066\u8a08\u7b97\u3055\u308c\u307e\u3059 (

$$ {\\scriptstyle n\\,\\lambda=L} $$<\/div>\u3053\u3053\u3067\u3001n \u306f\u6b63\u306e\u6574\u6570\u3001\u03bb \u306f\u5149\u5b50\u306e\u6ce2\u9577\u3001L \u306f 2 \u3064\u306e\u30d7\u30ec\u30fc\u30c8\u9593\u306e\u8ddd\u96e2\u3067\u3059)\u3002\u3053\u308c\u306f\u3001(\u3053\u308c\u3089 2 \u3064\u306e\u30d7\u30ec\u30fc\u30c8\u306e\u9593\u306e) \u771f\u7a7a\u306e\u30a8\u30cd\u30eb\u30ae\u30fc\u5bc6\u5ea6<\/a><\/span>\u304c\u3001\u3053\u308c\u3089 2 \u3064\u306e\u30d7\u30ec\u30fc\u30c8\u9593\u306b\u5b58\u5728\u3067\u304d\u308b\u5149\u5b50\u306e\u6570<\/a><\/span>\u306e\u95a2\u6570\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u307e\u3059\u3002<\/p>

\u30d7\u30ec\u30fc\u30c8\u304c\u8fd1\u3065\u304f\u307b\u3069\u3001\u30eb\u30fc\u30eb\u306b\u5f93\u3046\u5149\u5b50\u306e\u6570\u306f\u5c11\u306a\u304f\u306a\u308a\u307e\u3059

$$ {\\scriptstyle n\\,\\lambda=L} $$<\/div> \u3001\u6ce2\u9577\u304c L \u3088\u308a\u5927\u304d\u3044\u5149\u5b50\u306f\u9664\u5916\u3055\u308c\u308b\u305f\u3081\u3001\u30a8\u30cd\u30eb\u30ae\u30fc\u306f\u5c11\u306a\u304f\u306a\u308a\u307e\u3059\u3002<\/p>

\u3057\u305f\u304c\u3063\u3066\u3001\u3053\u308c\u3089 2 \u3064\u306e\u30d7\u30ec\u30fc\u30c8\u9593\u306e\u529b<\/a><\/span>\u3001\u3064\u307e\u308a L \u306b\u95a2\u3059\u308b\u30a8\u30cd\u30eb\u30ae\u30fc\u306e\u5c0e\u95a2\u6570<\/a><\/span>\u306f\u5f15\u529b\u3068\u306a\u308a\u307e\u3059\u3002<\/p>

\u5358\u4f4d\u9762\u7a4d\u3042\u305f\u308a\u306e\u529b\u306e\u8868\u73fe<\/h2>

(\u7279\u306b\u8a18\u8f09\u304c\u306a\u3044\u9650\u308a\u3001\u526f\u4f5c\u7528\u306f\u5e38\u306b\u7121\u8996\u3055\u308c\u307e\u3059)<\/p>

\u5bf8\u6cd5\u5206\u6790<\/a><\/span><\/span><\/h3>

\u4e92\u3044\u306b\u5e73\u884c\u3067\u8ddd\u96e2L<\/i><\/span>\u3060\u3051\u96e2\u308c\u305f\u3001\u8868\u9762S<\/i><\/span>\u306e 2 \u3064\u306e\u5927\u304d\u306a\u5e73\u3089\u306a\u91d1\u5c5e\u677f\u3092\u8003\u3048\u307e\u3059\u3002\u30d7\u30ec\u30fc\u30c8\u304c\u9577\u65b9\u5f62\u306e\u5834\u5408\u3001

$$ {\\scriptstyle S=D \\cdot H\\,} $$<\/div> \u30012 \u3064\u306e\u5e73\u884c\u30d7\u30ec\u30fc\u30c8\u9593\u306e\u9593\u9694L \u306f<\/i><\/span>\u3001\u9577\u3055D<\/i><\/span>\u304a\u3088\u3073H<\/i><\/span>\u306b\u6bd4\u3079\u3066\u5c0f\u3055\u3044<\/i>\u3067\u3059\u3002\u6b21\u306b\u3001\u30a8\u30c3\u30b8\u52b9\u679c\u3092\u7121\u8996\u3057\u3066\u5358\u4f4d\u9762\u7a4d\u3042\u305f\u308a\u306e\u529b\u3092<\/i>\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>

\u3055\u3089\u306b\u3001\u30d7\u30ec\u30fc\u30c8\u306f\u7121\u9650\u306e\u5c0e\u96fb\u7387<\/a><\/span>\u3092\u6301\u3064\u5b8c\u5168\u306a\u5c0e\u4f53<\/i>\u3067\u3042\u308a\u3001\u5e2f\u96fb\u3057\u3066\u3044\u306a\u3044\u3068\u4eee\u5b9a\u3055\u308c\u307e\u3059\u3002\u3053\u306e\u52b9\u679c\u306f\u91cf\u5b50\u8ad6\u7684\u304a\u3088\u3073\u76f8\u5bfe\u8ad6\u7684\u8d77\u6e90\u306e\u3082\u306e\u3067\u3042\u308b\u305f\u3081\u3001\u30ab\u30b7\u30df\u30fc\u30eb\u306e\u5358\u4f4d\u9762\u7a4d\u3042\u305f\u308a\u306e\u529b\u306f 2 \u3064\u306e\u57fa\u672c\u5b9a\u6570c<\/i><\/span> (\u771f\u7a7a\u4e2d\u306e\u5149<\/a><\/span>\u306e\u901f\u5ea6) \u3068 c \u306b\u4f9d\u5b58\u3059\u308b\u3068\u4e88\u60f3\u3055\u308c\u307e\u3059\u3002

$$ {\\hbar} $$<\/div> \uff08\u884c\u52d5\u91cf\uff09\u3002\u3055\u3089\u306b\u3001\u305d\u306e\u52b9\u679c\u306f\u30d7\u30ec\u30fc\u30c8\u9593\u306e\u8ddd\u96e2L<\/i><\/span>\u306b\u3082\u4f9d\u5b58\u3059\u308b\u53ef\u80fd\u6027\u304c\u9ad8\u304f\u306a\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u5358\u4f4d\u9762\u7a4d\u3042\u305f\u308a\u306e\u529b\u306f<\/i>\u6b21\u306e\u3088\u3046\u306b\u8868\u3055\u308c\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059\u3002 <\/p>
$$ {\\frac{dF}{dS} \\ = \\ k \\ L^{\\alpha} \\ c^{\\beta} \\ \\hbar^{\\gamma}} $$<\/div><\/td><\/tr><\/table>

\u3053\u3053\u3067\u3001 k \u306f<\/i><\/span>\u7d14\u7c8b\u306a\u7121\u6b21\u5143<\/a><\/span>\u6570\u3067\u3042\u308a\u3001 \u03b1\u3001\u03b2\u3001\u03b3 \u306e<\/span>3 \u3064\u306e\u6570\u304c\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002\u6b21\u5143\u89e3\u6790\u306b\u3088\u308a\u3001\u6b21\u306e\u9023\u7acb\u65b9\u7a0b\u5f0f\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>
$$ {\\left\\{\\begin{matrix} \\gamma \\ & = \\ + \\ 1 \\\\ \\alpha \\ + \\ \\beta \\ + \\ 2 \\, \\gamma \\ & = \\ – \\ 1 \\\\ – \\ \\beta \\ – \\ \\gamma \\ & = \\ – \\ 2 \\end{matrix}\\right.} $$<\/div><\/td><\/tr><\/table>

\u305d\u306e\u4e00\u610f\u306e<\/i>\u89e3\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059: \u03b2 = \u03b3 = 1<\/span>

$$ {\\alpha = – \\, 4} $$<\/div> \u3001 \u3069\u3061\u3089\u304b \uff1a <\/p>
$$ {\\frac{dF}{dS} \\ = \\ k \\ \\frac{\\hbar \\, c}{L^4}} $$<\/div><\/td><\/tr><\/table>

\u30ab\u30b7\u30df\u30fc\u30eb\u306e\u6b63\u78ba\u306a\u7d50\u679c<\/span><\/h3>

1948 \u5e74\u306b\u30ab\u30b7\u30df\u30fc\u30eb\u306b\u3088\u3063\u3066\u884c\u308f\u308c\u305f\u6b63\u78ba\u306a\u8a08\u7b97\u3067\u306f\u3001\u71b1\u529b\u5b66\u7684<\/a><\/span>\u6e29\u5ea6\u304c<\/a><\/span>\u5168\u304f\u30bc\u30ed\u3067\u3042\u308bT<\/i> = 0<\/span> K \u3068\u4eee\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u5b9a\u6570k<\/i><\/span>\u306e\u30bc\u30ed\u4ee5\u5916\u306e\u8ca0\u306e<\/i>\u5024\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ { \\frac{dF}{dS} \\ = \\ – \\ \\frac{\\pi^2}{240} \\ \\frac{\\hbar \\, c}{L^4} } $$<\/div><\/td><\/tr><\/table><\/center>

\u30de\u30a4\u30ca\u30b9\u8a18\u53f7\u306f\u3001\u3053\u306e\u529b\u304c\u9b45\u529b\u7684\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002\u3053\u306e\u8a08\u7b97\u306b\u8208\u5473\u306e\u3042\u308b\u8aad\u8005\u306f\u3001Duplantier \u306e\u30ec\u30d3\u30e5\u30fc\u8a18\u4e8b\u3067\u8a73\u3057\u304f\u8aac\u660e\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u8ddd\u96e2L<\/i>\u3060\u3051\u96e2\u308c\u305f\u9818\u57dfA<\/i>\u306e 2 \u3064\u306e\u30d7\u30ec\u30fc\u30c8\u9593\u306e\u30ab\u30b7\u30df\u30fc\u30eb\u5f15\u529b\u306e\u30ce\u30eb\u30e0<\/a><\/span>\u306f\u3001\u6b21\u306e\u5f0f\u3067\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002 <\/p>
$$ {F \\ = \\ \\frac{\\pi^2}{240} \\ \\frac{\\hbar \\, c}{L^4} \\ A} $$<\/div><\/td><\/tr><\/table>

\u6709\u9650\u6e29\u5ea6\u306e\u5f71\u97ff<\/span><\/h3>

\u5b9f\u969b\u306e\u5b9f\u9a13\u306f\u3059\u3079\u3066\u6709\u9650\u6e29\u5ea6T<\/i> > 0<\/span>\u3067\u884c\u308f\u308c\u308b\u305f\u3081\u3001\u672c\u8cea\u7684\u306b\u9ed2\u4f53<\/a><\/span>\u653e\u5c04<\/a><\/span>\u306b\u3088\u308b\u3053\u308c\u3089\u306e\u6e29\u5ea6\u306e\u5f71\u97ff\u3092\u63a8\u5b9a\u3059\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002 \u300c\u9006\u6e29\u5ea6\u300d \u03b2 = 1\/( kT<\/i> )<\/i><\/span>\u3092\u5c0e\u5165\u3057\u307e\u3057\u3087\u3046\u3002\u3053\u3053\u3067\u3001 k<\/i><\/span>\u306f\u30dc\u30eb\u30c4\u30de\u30f3\u5b9a\u6570<\/a><\/span>\u3067\u3059\u3002\u6b21\u5143\u5206\u6790\u306b\u3088\u308a\u3001\u30d1\u30e9\u30e1\u30fc\u30bf\u304c\u6b21\u306e\u3068\u304a\u308a\u3067\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u3002 <\/p>
$$ {\\alpha \\ = \\ \\frac{\\pi \\beta \\hbar c}{L}} $$<\/div><\/td><\/tr><\/table>

\u7121\u6b21\u5143\u3067\u3059\u3002\u6b21\u306b\u3001\u73fe\u5b9f\u7684\u306a\u77ed\u8ddd\u96e2\u306e\u9650\u754c\u3092\u691c\u8a0e\u3057\u307e\u3059\u3002

$$ {L \\to 0} $$<\/div>\u56fa\u5b9a\u6e29\u5ea6T<\/i><\/span>\u3067\u3001\u6b21\u306e\u5834\u5408\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002
$$ {\\alpha \\gg 1} $$<\/div> \u3002\u3053\u306e\u5236\u9650\u3067\u306f\u3001\u6b21\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>
$$ { \\frac{dF}{dS} \\ = \\ – \\ \\frac{\\pi^2}{240} \\ \\frac{\\hbar \\, c}{L^4} \\ – \\ \\frac{\\pi^2}{45} \\ \\frac{1}{\\beta} \\ \\frac{1}{(\\beta \\hbar c)^3} \\ + \\ \\frac{1}{\\beta} \\ \\frac{\\pi}{L^3} \\ e^{- \\, \\alpha} \\ + \\ O(e^{- \\, 2 \\, \\alpha})} $$<\/div><\/td><\/tr><\/table>

\u7b2c 1 \u9805\u306f\u30bc\u30ed\u6e29\u5ea6\u3067\u306e\u30ab\u30b7\u30df\u30fc\u30eb\u9805\u3001\u7b2c 2 \u9805\u306f\u7121\u9650<\/a><\/span>\u4f53\u7a4d<\/a><\/span>\u306e\u9ed2\u4f53\u653e\u5c04\u306b\u3088\u308b\u5f15\u529b\u5bc4\u4e0e\u3001\u7b2c 3 \u9805\u306f\u9ed2\u4f53\u653e\u5c04\u5bc4\u4e0e\u4e0a\u306e\u30d7\u30ec\u30fc\u30c8\u306b\u3088\u308b\u6709\u9650\u30b5\u30a4\u30ba\u88dc\u6b63\u306b\u5bfe\u5fdc\u3057\u307e\u3059\u3002<\/p>

\u5ba4\u6e29\u3067:

$$ { T \\sim 300 \\ K} $$<\/div>\u305d\u3057\u3066\u73fe\u5b9f\u7684\u306a\u9593\u9694\u306e\u305f\u3081\u306b
$$ { L \\sim 0.5 \\ \\mu m} $$<\/div> \u3001\u306e\u6570\u5024
$$ {\\alpha \\sim 48} $$<\/div> : \u9ed2\u4f53\u653e\u5c04\u306e\u5bc4\u4e0e\u306b\u95a2\u3059\u308b\u6709\u9650\u30b5\u30a4\u30ba\u88dc\u6b63\u306b\u5bfe\u5fdc\u3059\u308b\u7b2c 3 \u9805\u3002
$$ {e^{- \\, \\alpha}} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001\u5b9f\u969b\u306b\u306f\u5b8c\u5168\u306b\u7121\u8996\u3067\u304d\u307e\u3059<\/i>\u3002<\/p>

\u7b2c 1 \u9805\u306b\u5bfe\u3059\u308b\u7b2c 2 \u9805\u306e\u6bd4\u7387 (\u6b21\u5143\u306a\u3057) \u306b\u3064\u3044\u3066\u306f\u3001\u6b21\u306e\u5024\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>
$$ { \\gamma \\ = \\ \\frac{\\mathrm{corps ~ noir}}{\\mathrm{Casimir ~ a ~} T = 0} \\ = \\ \\frac{240}{45} \\ \\frac{L^4}{(\\beta \\hbar c)^4} \\ \\sim \\ 10^{-4} } $$<\/div><\/td><\/tr><\/table>

\u901a\u5e38\u306e\u5b9f\u9a13\u6761\u4ef6\u4e0b\u3067\u306f\u3001\u3042\u305f\u304b\u3082\u6e29\u5ea6\u304c\u30bc\u30ed\u3067\u3042\u308b\u304b\u306e\u3088\u3046\u306b\u3059\u3079\u3066\u304c\u8d77\u3053\u308a\u307e\u3059<\/i>\u3002\u8a73\u7d30\u306a\u5206\u6790\u306b\u8208\u5473\u306e\u3042\u308b\u8aad\u8005\u306f\u3001Duplantier \u306e\u30ec\u30d3\u30e5\u30fc\u8a18\u4e8b\u3092\u53c2\u7167\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p><\/div>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. \u062a\u0623\u062b\u064a\u0631 \u0643\u0627\u0632\u064a\u0645\u064a\u0631 \u2013 arabe<\/a><\/li>
  2. \u042d\u0444\u0435\u043a\u0442 \u041a\u0430\u0437\u0456\u043c\u0456\u0440\u0430 \u2013 bi\u00e9lorusse<\/a><\/li>
  3. \u0415\u0444\u0435\u043a\u0442 \u043d\u0430 \u041a\u0430\u0437\u0438\u043c\u0438\u0440 \u2013 bulgare<\/a><\/li>
  4. Efecte Casimir \u2013 catalan<\/a><\/li>
  5. Casimir\u016fv jev \u2013 tch\u00e8que<\/a><\/li>
  6. Casimir-effekten \u2013 danois<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u30ab\u30b7\u30df\u30fc\u30eb\u52b9\u679c\u306b\u3064\u3044\u3066\u8a73\u3057\u304f\u89e3\u8aac\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n