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

作者：Weinan, E.^*; Lu, Jian-feng; Yang, Xu

来源：Acta Mathematicae Applicatae Sinica-English Series, 2013, 29(3): 465-476.

DOI：10.1007/s10255-011-0095-5

• semiclassical limit
• Bloch-Wigner transform
• Bloch dynamics
• Berry phase
• asymptotic analysis

We study the semi-classical limit of the Schrodinger 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.

• 出版日期2013
• 单位北京大学