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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 Ginzburg–Landau theory ： ウィキペディア英語版 Ginzburg–Landau theory In physics, Ginzburg–Landau theory, named after Vitaly Lazarevich Ginzburg and Lev Landau, is a mathematical physical theory used to describe superconductivity. In its initial form, it was postulated as a phenomenological model which could describe type-I superconductors without examining their microscopic properties. Later, a version of Ginzburg–Landau theory was derived from the Bardeen-Cooper-Schrieffer microscopic theory by Lev Gor'kov, thus showing that it also appears in some limit of microscopic theory and giving microscopic interpretation of all its parameters. ==Introduction== Based on Landau's previously-established theory of second-order phase transitions, Ginzburg and Landau argued that the free energy, ''F'', of a superconductor near the superconducting transition can be expressed in terms of a complex order parameter field, ''ψ'', which is nonzero below a phase transition into a superconducting state and is related to the density of the superconducting component, although no direct interpretation of this parameter was given in the original paper. Assuming smallness of ''|ψ|'' and smallness of its gradients, the free energy has the form of a field theory. :$F\; =\; F\_n\; +\; \backslash alpha\; |\backslash psi|^2\; +\; \backslash frac\; |\backslash psi|^4\; +\; \backslash frac\; \backslash left|\; \backslash left(-i\backslash hbar\backslash nabla\; -\; 2e\backslash mathbf\; \backslash right)\; \backslash psi\; \backslash right|^2\; +\; \backslash frac$ where ''Fn'' is the free energy in the normal phase, ''α'' and ''β'' in the initial argument were treated as phenomenological parameters, ''m'' is an effective mass, ''e'' is the charge of an electron, A is the magnetic vector potential, and $\backslash mathbf=\backslash nabla\; \backslash times\; \backslash mathbf$ is the magnetic field. By minimizing the free energy with respect to variations in the order parameter and the vector potential, one arrives at the Ginzburg–Landau equations :$\backslash alpha\; \backslash psi\; +\; \backslash beta\; |\backslash psi|^2\; \backslash psi\; +\; \backslash frac\; \backslash left(-i\backslash hbar\backslash nabla\; -\; 2e\backslash mathbf\; \backslash right)^2\; \backslash psi\; =\; 0$ :$\backslash nabla\; \backslash times\; \backslash mathbf\; =\; \backslash mu\_\backslash mathbf\; \backslash ;\backslash ;\; ;\; \backslash ;\backslash ;\; \backslash mathbf\; =\; \backslash frac\; \backslash mathrm\; \backslash left\backslash$ where j denotes the dissipation-less electric current density and ''Re'' the ''real part''. The first equation — which bears some similarities to the time-independent Schrödinger equation, but is principally different due to a nonlinear term — determines the order parameter, ''ψ''. The second equation then provides the superconducting current. 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「Ginzburg–Landau theory」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.