Exponential mixing for nonlinear Schrödinger equations perturbed by bounded degenerate noise

Fuente: arXiv
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Main Authors: Chen, Yuxuan, Xiang, Shengquan, Zhang, Zhifei
Format: Preprint
Published: 2026
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_version_ 1866918432136495104
author Chen, Yuxuan
Xiang, Shengquan
Zhang, Zhifei
author_facet Chen, Yuxuan
Xiang, Shengquan
Zhang, Zhifei
contents We prove the exponential convergence to a unique invariant measure for locally damped nonlinear Schrödinger 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_05911
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Exponential mixing for nonlinear Schrödinger equations perturbed by bounded degenerate noise
Chen, Yuxuan
Xiang, Shengquan
Zhang, Zhifei
Analysis of PDEs
Dynamical Systems
Optimization and Control
Probability
35Q55, 37A25, 37L15, 37L55, 93C20
We prove the exponential convergence to a unique invariant measure for locally damped nonlinear Schrödinger 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.
title Exponential mixing for nonlinear Schrödinger equations perturbed by bounded degenerate noise
topic Analysis of PDEs
Dynamical Systems
Optimization and Control
Probability
35Q55, 37A25, 37L15, 37L55, 93C20
url https://arxiv.org/abs/2604.05911