Quantitative bounds on the rate of approach to equilibrium for some one-dimensional stochastic nonlinear Schrödinger equations

We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schrödinger equation with diffusive forcing. Equilibrium is described by a generalized grand canonical ensemble. Our...

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Published inNonlinearity Vol. 32; no. 4; pp. 1352 - 1374
Main Authors Carlen, Eric A, Fröhlich, Jürg, Lebowitz, Joel, Wang, Wei-Min
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.04.2019
Subjects
entropy
equilibrium
log Sobolev inequality
Online AccessGet full text
ISSN0951-7715
1361-6544
DOI10.1088/1361-6544/aae69c

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Summary:We establish quantitative bounds on the rate of approach to equilibrium for a system with infinitely many degrees of freedom evolving according to a one-dimensional focusing nonlinear Schrödinger equation with diffusive forcing. Equilibrium is described by a generalized grand canonical ensemble. Our analysis also applies to the easier case of defocusing nonlinearities.
Bibliography:NON-102745.R1
London Mathematical Society
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/aae69c