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We study the nonlinear Schr\"odinger equation with linear damping, i.e. azero 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 dampingcoefficient is sufficiently large.

Ergodic results for the stochastic nonlinear Schr\"odinger equation with large damping