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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 Correlation function (statistical mechanics) ： ウィキペディア英語版 Correlation function (statistical mechanics) In statistical mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe how microscopic variables, such as spin and density, at different positions are related. More specifically, the correlation functions quantifies how microscopic variables co-vary with one another on average across space and time. A classic example of such spatial correlations is in ferro- and antiferromagnetic materials, where the spins prefer to align parallel and antiparallel with their nearest neighbors, respectively. The spatial correlation between spins in such materials is shown in the figure to the right. ==Definitions== The most common definition of a correlation function is the canonical ensemble (thermal) average of the scalar product of two random variables, $s\_1$ and $s\_2$, at positions $R$ and $R+r$ and times $t$ and $t+\backslash tau$: $C\; (r,\backslash tau)\; =\; \backslash langle\; \backslash mathbf(R,t)\; \backslash cdot\; \backslash mathbf(R+r,t+\backslash tau)\backslash rangle\backslash \; -\; \backslash langle\; \backslash mathbf(R,t)\; \backslash rangle\backslash langle\; \backslash mathbf(R+r,t+\backslash tau)\; \backslash rangle\backslash ,.$ Here the brackets, $\backslash langle\; ...\; \backslash rangle$, indicate the above-mentioned thermal average. It is a matter of convention whether one subtracts the uncorrelated average product of $s\_1$ and $s\_2$, $\backslash langle\; \backslash mathbf(R,t)\; \backslash rangle\backslash langle\; \backslash mathbf(R+r,t+\backslash tau)\; \backslash rangle$ from the correlated product, $\backslash langle\; \backslash mathbf(R,t)\; \backslash cdot\; \backslash mathbf(R+r,t+\backslash tau)\backslash rangle$, with the convention differing among fields. The most common uses of correlation functions are when $s\_1$ and $s\_2$ describe the same variable, such as a spin-spin correlation function, or a particle position-position correlation function in an elemental liquid or a solid (often called a Radial distribution function or a pair correlation function). Correlation functions between the same random variable are autocorrelation functions. However, in statistical mechanics, not all correlation functions are autocorrelation functions. For example, in multicomponent condensed phases, the pair correlation function between different elements is often of interest. Such mixed-element pair correlation functions are an example of cross-correlation functions, as the random variables $s\_1$ and $s\_2$ represent the average variations in density as a function position for two distinct elements. 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「Correlation function (statistical mechanics)」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.