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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク BBGKY hierarchy ： ウィキペディア英語版 BBGKY hierarchy In statistical physics, the BBGKY hierarchy (Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy, sometimes called Bogoliubov hierarchy) is a set of equations describing the dynamics of a system of a large number of interacting particles. The equation for an ''s''-particle distribution function (probability density function) in the BBGKY hierarchy includes the (''s'' + 1)-particle distribution function thus forming a coupled chain of equations. This formal theoretic result is named after Bogoliubov, Born, Green, Kirkwood, and Yvon. ==Formulation== The evolution of an ''N''-particle system is given by the Liouville equation for the probability density function $f\_N\; =\; f\_N(\backslash mathbf\_1\backslash dots\backslash mathbf\_N,\; \backslash mathbf\_1\; \backslash dots\; \backslash mathbf\_N,\; t)$ in ''6N'' dimensional phase space (3 space and 3 momentum coordinates per particle) :$$ \frac + \sum_^N \dot + \sum_^N \left( - \frac_i} - \sum_^N \frac_i} \right) \frac = 0. By integration over part of the variables, the Liouville equation can be transformed into a chain of equations where the first equation connects the evolution of one-particle probability density function with the two-particle probability density function, second equation connects the two-particle probability density function with the three-particle probability density function, and generally the ''s''-th equation connects the ''s''-particle probability density function $f\_s\; =\; f\_s(\backslash mathbf\_1\backslash dots\backslash mathbf\_s,\; \backslash mathbf\_1\; \backslash dots\; \backslash mathbf\_s,\; t)$ with the ''(s+1)''-particle probability density function: :$$ \frac + \sum_^s \dot + \sum_^s \left( - \frac_i} - \sum_^s \frac_i} \right) \frac = (N-s) \sum_^s \frac \int \frac_i}\cdot f_ \,d\mathbf_ d\mathbf_. Here $\backslash mathbf\_i,\; \backslash mathbf\_i$ are the coordinates and momentum for ''i''th particle, $\backslash Phi^(\backslash mathbf\_i)$ is the external field potential, and $\backslash Phi\_(\backslash mathbf\_i,\; \backslash mathbf\_j)$ is the pair potential for interaction between particles. The equation above for ''s''-particle distribution function is obtained by integration of the Liouville equation over the variables $\backslash mathbf\_\backslash dots\backslash mathbf\_N,\; \backslash mathbf\_\; \backslash dots\; \backslash mathbf\_N$. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「BBGKY hierarchy」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.