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.

中文翻译：

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随机Schrödinger方程的有效波分解

我们研究了在固态物理学中具有大周期电势的随机Schrödinger方程的均化。用...表示$\epsilon$ 在这段时期内，潜力被缩放为 ${\epsilon }^{-2}$。在有关细胞问题的光谱性质的一般假设下，我们证明了该解可以近似分解为快速振荡的细胞本征函数和有效方程的缓慢变化解的乘积。我们的方法基于两尺度收敛和布洛赫波理论。