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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 Peierls substitution ： ウィキペディア英語版 Peierls substitution The Peierls substitution method, named after the original work by R. Peierls is a widely employed approximation for describing tightly-bound electrons in the presence of a slowly varying magnetic vector potential. In the presence of an external vector potential $\backslash mathbf$ the second quantization translation operators, which form the kinetic part of the Hamiltonian in the tight-binding framework, are simply - $$\backslash mathbf\_x\; =\; \backslash boldsymbol^\backslash dagger\_\backslash boldsymbol\_e^\_y\; =\; \backslash boldsymbol^\backslash dagger\_\backslash boldsymbol\_e^=\backslash frac\backslash int\_m^\; A\_x(x,n)\backslash textx,\; \backslash quad\; \backslash theta^y\_=\backslash frac\backslash int\_n^\; A\_y(m,y)\; \backslash texty$$. The number of flux quanta per plaquette $\backslash phi\_$ is related to the lattice curl of the phase factor, $$ \boldsymbol\times\theta_=\Delta_x\theta^y_-\Delta_y\theta^x_=\left(\theta^y_-\theta^y_-\theta^x_+\theta^x_\right)= $$$$ \frac\int_\cdot \text\mathbf=2\pi\frac\int \mathbf \cdot \text\mathbf=2\pi\phi_ and the total flux through the lattice is $\backslash Phi=\backslash Phi\_0\backslash sum\_\backslash phi\_$ with $\backslash Phi\_0=hc/e$ in cgs units (and $\backslash Phi\_0=2\backslash pi$ in natural units). In addition, it is related to the accumulated phase of a single particle state, $|\backslash psi\backslash rangle=\backslash boldsymbol\_|0\backslash rangle$ surrounding a plaquette: $$ \mathbf_y^\dagger \mathbf_x^\dagger \mathbf_y\mathbf_x|\psi\rangle=\mathbf_y^\dagger \mathbf_x^\dagger \mathbf_y |i+1,j\rangle e^_y^\dagger \mathbf_x^\dagger |i+1,j+1\rangle e^ \right)}= $$$$ \quad\quad \mathbf_y^\dagger |i,j+1\rangle e^-\theta^x_ \right)}= |i,j\rangle e^-\theta^x_-\theta^y_ \right)}=|i,j\rangle e^{i2\pi \phi_{m,n}} ==Introduction== Here we give a short derivation of the Peierls substitution. Although the derivation is not very rigorous it is illuminating. 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「Peierls substitution」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.