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arXiv · 2005.06298

Effective Wave Factorization for a Stochastic Schr\"{o}dinger Equation

Ao Zhang·Jinqiao Duan
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Abstract

We study the homogenization of a stochastic Schr\"odinger 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.

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Ao Zhang, Jinqiao Duan. 2020-05-13. Effective Wave Factorization for a Stochastic Schr\"{o}dinger Equation. https://arxiv.org/abs/2005.06298

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