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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 Anderson localization ： ウィキペディア英語版 Anderson localization In condensed matter physics, Anderson localization, also known as strong localization, is the absence of diffusion of waves in a ''disordered'' medium. This phenomenon is named after the American physicist P. W. Anderson, who was the first one to suggest the possibility of electron localization inside a semiconductor, provided that the degree of randomness of the impurities or defects is sufficiently large. Anderson localization is a general wave phenomenon that applies to the transport of electromagnetic waves, acoustic waves, quantum waves, spin waves, etc. This phenomenon is to be distinguished from weak localization, which is the precursor effect of Anderson localization (see below), and from Mott localization, named after Sir Nevill Mott, where the transition from metallic to insulating behaviour is ''not'' due to disorder, but to a strong mutual Coulomb repulsion of electrons. ==Introduction== In the original Anderson tight-binding model, the evolution of the wave function ''ψ'' on the ''d''-dimensional lattice Z''d'' is given by the Schrödinger equation :$i\; \backslash hbar\; \backslash dot\; =\; H\; \backslash psi~,$ where the Hamiltonian ''H'' is given by :$(H\; \backslash phi)(j)\; =\; E\_j\; \backslash phi(j)\; +\; \backslash sum\_\; V(|k-j|)\; \backslash phi(k)~,$ with ''E''''j'' random and independent, and interaction ''V''(''r'') falling off as ''r''−2 at infinity. For example, one may take ''E''''j'' uniformly distributed in (  +''W'' ), and : Starting with ''ψ''0 localised at the origin, one is interested in how fast the probability distribution $|\backslash psi|^2$ diffuses. Anderson's analysis shows the following: * if ''d'' is 1 or 2 and ''W'' is arbitrary, or if ''d'' ≥ 3 and ''W''/ħ is sufficiently large, then the probability distribution remains localized: ::$\backslash sum\_\; |\backslash psi(t,n)|^2\; |n|\; \backslash leq\; C$ :uniformly in ''t''. This phenomenon is called Anderson localization. * if ''d'' ≥ 3 and ''W''/ħ is small, :$\backslash sum\_\; |\backslash psi(t,n)|^2\; |n|\; \backslash approx\; D\; \backslash sqrt~,$ :where ''D'' is the diffusion constant. 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「Anderson localization」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.