Existence of invariant measures for the stochastic damped Schr\"odinger   equation
  In this paper, we address the long time behaviour of solutions of the stochastic Schrodinger equation in $\mathbb{R}^d$. We prove the existence of an invariant measure and establish asymptotic compactness of solutions, implying in particular the existence of an ergodic measure. 
Ibrahim Ekren, Igor Kukavica, and Mohammed Ziane
math.AP