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Asymptotic Analysis of Quantum Dynamics in Crystals： the Bloch-Wigner Transform, Bloch Dynamics and Berry Phase

Weinan、Jianfeng、Lü、Xu、Yang

2013Acta Scientiarum Naturalium Universitatis SunyatseniMathematics被引 1

摘要

We study the semi-classical limit of the Schro¨dinger equation in a crystal in the presence of an external potential and magnetic field. We first introduce the Bloch-Wigner transform and derive the asymptotic equations governing this transform in the semi-classical setting. For the second part, we focus on the appearance of the Berry curvature terms in the asymptotic equations. These terms play a crucial role in many important physical phenomena such as the quantum Hall effect. We give a simple derivation of these terms in different settings using asymptotic analysis.

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