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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 Byers-Yang theorem ： ウィキペディア英語版 Byers-Yang theorem In quantum mechanics, the Byers-Yang theorem states that all physical properties of a doubly connected system (an annulus) enclosing a magnetic flux $\backslash Phi$ through the opening are periodic in the flux with period $\backslash Phi\_0=h/e$ (the magnetic flux quantum). The theorem was first stated and proven by Nina Byers and Chen-Ning Yang (1961), and further developed by Felix Bloch (1970). ==Proof== An enclosed flux $\backslash Phi$ corresponds to a vector potential $A(r)$ inside the annulus with a line integral $\backslash oint\_C\; A\backslash cdot\; dl=\backslash Phi$ along any path $C$ that circulates around once. One can try to eliminate this vector potential by the gauge transformation :$\backslash psi\text{'}(\backslash )=\backslash exp\backslash left(\backslash frac\backslash sum\_j\backslash chi(r\_j)\backslash right)\backslash psi(\backslash )$ of the wave function $\backslash psi(\backslash )$ of electrons at positions $r\_1,r\_2,\backslash ldots$. The gauge-transformed wave function satisfies the same Schrödinger equation as the original wave function, but with a different magnetic vector potential $A\text{'}(r)=A(r)+\backslash nabla\backslash chi(r)$. It is assumed that the electrons experience zero magnetic field $B(r)=\backslash nabla\backslash times\; A(r)=0$ at all points $r$ inside the annulus, the field being nonzero only within the opening (where there are no electrons). It is then always possible to find a function $\backslash chi(r)$ such that $A\text{'}(r)=0$ inside the annulus, so one would conclude that the system with enclosed flux $\backslash Phi$ is equivalent to a system with zero enclosed flux. However, for any arbitrary $\backslash Phi$ the gauge transformed wave function is no longer single-valued: The phase of $\backslash psi\text{'}$ changes by :$\backslash delta\backslash phi=(e/\backslash hbar)\backslash oint\_C\backslash nabla\backslash chi(r)\backslash cdot\; dl=2\backslash pi\backslash Phi/\backslash Phi\_0$ whenever one of the coordinates $r\_n$ is moved along the ring to its starting point. The requirement of a single-valued wave function therefore restricts the gauge transformation to fluxes $\backslash Phi$ that are an integer multiple of $\backslash Phi\_0$. Systems that enclose a flux differing by a multiple of $h/e$ are equivalent. 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「Byers-Yang theorem」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.