Ergodic results for the stochastic nonlinear Schrödinger equation with large damping

Abstract

Abstract We study a nonlinear Schrödinger equation with a linear damping, i.e. a zero-order dissipation, and an additive noise. Working in $${\mathbb {R}}^d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mi>d</mml:mi> </mml:msup> </mml:math> with $$d\le 3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>d</mml:mi> <mml:mo>≤</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> , we prove the uniqueness of the invariant measure when the damping coefficient is sufficiently large.

Topics & Concepts