Exponential mixing for nonlinear Schr\"odinger equations perturbed by bounded degenerate noise
Analysis of PDEs
2026-04-08 v1 Dynamical Systems
Optimization and Control
Probability
Abstract
We prove the exponential convergence to a unique invariant measure for locally damped nonlinear Schr\"odinger equations, perturbed by bounded noise acting on only two Fourier modes. To tackle the lack of smoothing effect, we introduce asymptotic compactness of linearized system to enhance the coupling method. Inspired by [14,33,39], we establish a new criterion for exponential mixing. Elements from global stability, nonlinear smoothing, and geometric control are combined when applying this criterion.
Keywords
Cite
@article{arxiv.2604.05911,
title = {Exponential mixing for nonlinear Schr\"odinger equations perturbed by bounded degenerate noise},
author = {Yuxuan Chen and Shengquan Xiang and Zhifei Zhang},
journal= {arXiv preprint arXiv:2604.05911},
year = {2026}
}