Approach to Equilibrium for the Stochastic NLS

J. L. Lebowitz, Ph Mounaix, W. M. Wang

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We study the approach to equilibrium, described by a Gibbs measure, for a system on a d-dimensional torus evolving according to a stochastic nonlinear Schrödinger equation (SNLS) with a high frequency truncation. We prove exponential approach to the truncated Gibbs measure both for the focusing and defocusing cases when the dynamics is constrained via suitable boundary conditions to regions of the Fourier space where the Hamiltonian is convex. Our method is based on establishing a spectral gap for the non self-adjoint Fokker-Planck operator governing the time evolution of the measure, which is uniform in the frequency truncation N. The limit N → ∞ is discussed.

Original languageEnglish (US)
Pages (from-to)69-84
Number of pages16
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - Jul 2013

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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