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

Weinan E, Jian feng Lu, Xu Yang

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)465-476
Number of pages12
JournalActa Mathematicae Applicatae Sinica
Volume29
Issue number3
DOIs
StatePublished - Jul 1 2013

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Keywords

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

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