A stochastic thermalization of the Discrete Nonlinear Schr\"odinger Equation
Mathematical Physics
2021-09-06 v1 Statistical Mechanics
Analysis of PDEs
math.MP
Probability
Abstract
We introduce a mass conserving stochastic perturbation of the discrete nonlinear Schr\"odinger equation that models the action of a heat bath at a given temperature. We prove that the corresponding canonical Gibbs distribution is the unique invariant measure. In the one-dimensional cubic focusing case on the torus, we prove that in the limit for large time, continuous approximation, and low temperature, the solution converges to the steady wave of the continuous equation that minimizes the energy for a given mass.
Keywords
Cite
@article{arxiv.2109.01389,
title = {A stochastic thermalization of the Discrete Nonlinear Schr\"odinger Equation},
author = {Amirali Hannani and Stefano Olla},
journal= {arXiv preprint arXiv:2109.01389},
year = {2021}
}