Approach to Equilibrium for the Stochastic NLS

作者：Lebowitz J L^*; Mounaix Ph; Wang W M

来源：Communications in Mathematical Physics, 2013, 321(1): 69-84.

DOI：10.1007/s00220-012-1632-7

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 Schrodinger 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 -> a is discussed.

• 出版日期2013-7
• 单位rutgers