Exponential mixing for nonlinear Schrödinger equations perturbed by bounded degenerate noise
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918432136495104 |
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| 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 |
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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 |