首页 | 本学科首页   官方微博 | 高级检索  
     检索      


Asymptotic analysis of quantum dynamics in crystals: the Bloch-Wigner transform, Bloch dynamics and Berry phase
Authors:Weinan E  Jian-feng Lu  Xu Yang
Institution:1 Department of Mathematics, Princeton University, Princeton, NJ 08544, USA 2 Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA 3 School of Mathematical Sciences, Peking University, Beijing, 100871, China
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.
Keywords:semiclassical limit  Bloch-Wigner transform  Bloch dynamics  Berry phase  asymptotic analysis
本文献已被 CNKI 维普 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号