Random attractors for damped stochastic fractional Schr\"odinger equation on $\mathbb{R}^{n}$

Abstract

We study the random attractors associated with the stochastic fractional Schr\"odinger equation on $\mathbb{R}^n$. Utilizing the stochastic Strichartz estimates for the damped fractional Schr\"odinger equation with Gaussian noise, we show the existence and uniqueness of a global solution to the damped stochastic fractional nonlinear Schr\"odinger equation in $H^{\alpha}(\mathbb{R}^n)$. Furthermore, we demonstrate that this equation defines an infinite-dimensional dynamical system, which possesses a global attractor in $H^{\alpha}(\mathbb{R}^n)$.