{
  "abstract": "We prove polynomial mixing for the defocusing damped cubic stochastic nonlinear Schrödinger equation on the three-dimensional torus under saturating smooth finite rank Brownian forcing. The mixing rate is measured in the $p$-Wasserstein metric induced by the $H^1$ distance for every $1\\le p<\\infty$. We also obtain sharp geometric characterizations of saturation. The proof is based on a polynomial mixing criterion built on a stable--compact decomposition of the exact solution differences with polynomial moment control of the logarithmic path amplification. Dense Malliavin range allows the compact defect to be compensated by finite-dimensional Cameron--Martin shifts, producing a block multiplier with negative mean logarithm. A logarithmic transportation gauge, combined with a renewal--reset coupling scheme, then yields mixing at every prescribed polynomial order in the weaker $L^2$ distance. A stationary regularity gain to $H^{2-}$ then enables us to upgrade the convergence to $H^1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08645",
  "author_total": 3,
  "authors": [
    {
      "name": "Rongchang Liu"
    },
    {
      "name": "Kening Lu"
    },
    {
      "name": "Lin Shi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bw5284f5zjgj7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08645",
  "fulltext_url": null,
  "id": "bw5284f5zjgj7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08645",
  "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": "W7212026751",
  "pdf_url": "https://arxiv.org/pdf/2609.08645",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bw5284f5zjgj7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08645",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08645"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Polynomial mixing for the 3D damped cubic nonlinear Schrödinger equation with degenerate noise",
  "title_text": "Polynomial mixing for the 3D damped cubic nonlinear Schrödinger equation with degenerate noise",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/bw5284f5zjgj7",
  "venue": "arXiv",
  "versions": []
}