Effective wave factorization for a stochastic Schrodinger equation

PHYSICA D-NONLINEAR PHENOMENA

卷:411

Article

Zhang, Ao^1,2  Duan, Jinqiao³ 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Peoples R China

[2] Huazhong Univ Sci & Technol, Ctr Math Sci, Wuhan 430074, Peoples R China

[3] IIT, Dept Appl Math, Chicago, IL 60616 USA

关键词: Homogenization;    Stochastic Schrodinger equation;    Multiplicative noise;    Two-scale convergence;    Bloch wave;    Variational solution;   

DOI  :  10.1016/j.physd.2020.132573

来源: Elsevier

【 摘 要 】

We study the homogenization of a stochastic Schrodinger equation with a large periodic potential in solid state physics. Denoting by epsilon the period, the potential is scaled as epsilon(-2). Under a generic assumption on the spectral properties of the associated cell problem, we prove that the solution can be approximately factorized as the product of a fast oscillating cell eigenfunction and of a slowly varying solution of an effective equation. Our method is based on two-scale convergence and Bloch waves theory. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free