Effective Wave Factorization for a Stochastic Schrödinger Equation
Ao Zhang, Jinqiao Duan · arXiv (Cornell University) · 2020
We study the homogenization of a stochastic Schrödinger equation with a large periodic potential in solid state physics. Denoting by $\varepsilon$ the period, the potential is scaled as $\varepsilon^{-2}$. 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.