{
  "abstract": "We consider the weakly damped stochastic nonlinear Schrödinger (NLS) equation on the real line, driven by a noise that is white in time and smooth in space. Assuming that the noise is sufficiently non-degenerate, we prove that the equation has a unique stationary measure in the class of probability measures concentrated on $H^2$, and establish polynomial mixing in the dual-Lipschitz metric over $H^1$. We do not impose any restriction on the size of the damping. The proof is based on a coupling argument, whose key ingredient is a Foiaş-Prodi-type estimate in the $H^1$-norm, derived by means of a Lyapunov functional adapted to the linearized NLS dynamics. To compensate for the loss of compactness, we combine this estimate with a truncated Poincaré inequality and a space-time weight function quantifying the spatial decay of solutions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08935",
  "author_total": 2,
  "authors": [
    {
      "name": "Vahagn Nersesyan"
    },
    {
      "name": "Tianyi Pan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5pwdg85pbnb9r.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08935",
  "fulltext_url": null,
  "id": "5pwdg85pbnb9r",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08935",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212022459",
  "pdf_url": "https://arxiv.org/pdf/2609.08935",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5pwdg85pbnb9r.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:01Z",
      "native_id": "2609.08935",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08935"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Polynomial mixing for the weakly damped stochastic nonlinear Schrödinger equation on the whole space",
  "title_text": "Polynomial mixing for the weakly damped stochastic nonlinear Schrödinger equation on the whole space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/5pwdg85pbnb9r",
  "venue": "arXiv",
  "versions": []
}