Effective Approximation for a Nonlocal Stochastic Schrödinger Equation with Oscillating Potential

Abstract

We consider the homogenization of a nonlocal stochastic Schrödinger equation with a rapidly oscillating, periodically time-dependent potential. With help of a two-scale convergence technique, we establish a homogenization principle for this nonlocal stochastic partial differential equation. We explicitly derive the homogenized model. In particular, this homogenization principle holds when the nonlocal operator is the fractional Laplacian.