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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 Dynamic structure factor ： ウィキペディア英語版 Dynamic structure factor In condensed matter physics, the dynamic structure factor is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization of the structure factor which considers correlations in both space ''and'' time. Experimentally, it can be accessed most directly by inelastic neutron scattering. The dynamic structure factor is most often denoted $S(\backslash vec,\backslash omega)$, where $\backslash vec$ (sometimes $\backslash vec$) is a wave vector (or wave number for isotropic materials), and $\backslash omega$ a frequency (sometimes stated as energy, $\backslash hbar\backslash omega$). It is defined as:〔 〕 :$S(\backslash vec,\backslash omega)\; \backslash equiv\; \backslash frac\backslash int\_^\; F(\backslash vec,t)\backslash mbox(i\backslash omega\; t)\; dt$ Here $F(\backslash vec,t)$, is called the intermediate scattering function and can be measured by neutron spin echo spectroscopy. The intermediate scattering function is the spatial Fourier transform of the van Hove function $G(\backslash vec,t)$:〔G. Vineyard, "Scattering of Slow Neutrons by a Liquid", Phys. Rev. 110, 999-1010 (1958).〕 :$F(\backslash vec,t)\; \backslash equiv\; \backslash int\; G(\backslash vec,t)\backslash exp\; (-i\backslash vec\backslash cdot\backslash vec)\; d\backslash vec$ Thus we see that the dynamical structure factor is the spatial ''and'' temporal Fourier transform of van Hove's time-dependent pair correlation function. It can be shown (see below), that the intermediate scattering function is the correlation function of the Fourier components of the density $\backslash rho$: :$F(\backslash vec,t)\; =\; \backslash frac\backslash langle\; \backslash rho\_\}\; \backslash rangle$ The dynamic structure is exactly what is probed in coherent inelastic neutron scattering. The differential cross section is : :$\backslash frac\; =\; a^2\backslash left(\backslash frac\backslash right)^\; S(\backslash vec,\backslash omega)$ where $a$ is the scattering length. ==The van Hove Function== The van Hove Function for a spatially uniform system containing $N$ point particles is defined as:〔 :$G(\backslash vec,t)\; =\; \backslash langle\; \backslash frac\; \backslash int\; \backslash sum\_^\backslash sum\_^N\; \backslash delta()\backslash delta()\; d\backslash vec\text{'}\; \backslash rangle$ It can be rewritten as: :$G(\backslash vec,t)\; =\; \backslash langle\; \backslash frac\backslash int\; \backslash rho(\backslash vec\text{'}+\backslash vec,t)\backslash rho(\backslash vec\text{'},0)\; d\backslash vec\text{'}\backslash rangle$ In an isotropic sample (with scalar ''r''), ''G(r,t)'' is a time dependent radial distribution function. 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「Dynamic structure factor」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.