Ergodic results for the stochastic nonlinear Schrödinger equation with large damping

Abstract

We study the nonlinear Schrödinger equation with linear damping, i.e. a zero order dissipation, and additive noise. Working in $R^d$ with d = 2 or d = 3, we prove the uniqueness of the invariant measure when the damping coefficient is sufficiently large.

27 pages