论文标题
随机Schrödinger方程的有效波分解
Effective Wave Factorization for a Stochastic Schrödinger Equation
论文作者
论文摘要
我们研究具有固态物理学周期性巨大潜力的随机schrödinger方程的均质化。用$ \ varepsilon $表示该时期，电势被缩放为$ \ varepsilon^{ - 2} $。在对相关细胞问题的光谱特性的一般假设下，我们证明该溶液可以被近似分解为快速振荡的细胞特征功能和有效方程缓慢变化的溶液的乘积。我们的方法基于两尺度收敛和Bloch波理论。
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.
