Asymptotic analysis of quantum dynamics in crystals: The Bloch-Wigner transform, Bloch dynamics and Berry phase

Journal Article

We study the semi-classical limit of the Schrödinger 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. © 2013 Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg.

Full Text

Duke Authors

Cited Authors

  • E, W; Lu, JF; Yang, X

Published Date

  • 2013

Published In

Volume / Issue

  • 29 / 3

Start / End Page

  • 465 - 476

International Standard Serial Number (ISSN)

  • 0168-9673

Digital Object Identifier (DOI)

  • 10.1007/s10255-011-0095-5