Effective Wave Factorization for a Stochastic Schrödinger Equation

2020/05/13 by Ao Zhang, Zhang, Ao, Jinqiao Duan +1
Computer Science · Engineering · #35B27 #60H15 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2005.06298

openalex publication_date 2020/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the homogenization of a stochastic Schrödinger equation with a large periodic potential in solid state physics. Denoting by ε the period, the potential is scaled as ε^-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.

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