Effective Wave Factorization for a Stochastic Schrödinger Equation

Abstract

We study the homogenization of a stochastic Schrödinger 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.