Effective approximation for a nonlocal stochastic Schrödinger equation with oscillating potential

We study the effective approximation for a nonlocal stochastic Schrödinger equation with rapidly oscillating, periodically time-dependent potential. use natural diffusive scaling of heterogeneous system and limit behavior as parameter tends to 0. This is motivated by data assimilation non-Gaussian uncertainties. The operator in this partial differential generator Lévy-type process (i.e., class anomalous diffusion processes), non-integrable jump kernel. With help two-scale convergence technique, we establish equation. More precisely, show that has it approximates original weakly Sobolev-type space strongly $$L^2$$ space. In particular, holds when fractional Laplacian.