{
  "abstract": "Let \\[ A_ω=-\\partial_x^2+ρ\\dot B_x(ω), \\qquad ρ\\ne0, \\] be the Dirichlet Schrödinger operator on $(0,π)$ with a spatial Gaussian white-noise potential, realized pathwise via quasi-derivatives. Here $\\dot B_x$ denotes the distributional derivative of Brownian motion with respect to the spatial variable $x$. For $κ\\ne0$, we consider the cubic nonlinear Schrödinger equation \\[ i u_t=A_ωu+κ|u|^2u. \\] We first prove a zero-set theorem for locally real-analytic functions on classical Wiener space. As a consequence, on a single event of probability one, no nontrivial finitely supported integer combination of the random eigenvalues vanishes, and the quartic twist matrix is nonsingular for every finite tangential set. After fixing a path in this event, we combine these qualitative nondegeneracy properties with a partial quartic Birkhoff normal form adapted to the KAM scheme. For every finite nonempty tangential set \\(J\\) of cardinality \\(b\\), we obtain a Cantor family of linearly stable, real-analytic, small-amplitude invariant \\(b\\)-tori. The family is parametrized by a Cantor subset of \\([ν,2ν]^b\\) whose relative measure tends to one as \\(ν\\to0\\).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22808",
  "author_total": 3,
  "authors": [
    {
      "name": "Yingdu Dong"
    },
    {
      "name": "Wenwen Jian"
    },
    {
      "name": "Xiaoping Yuan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38sv0m10sfe5h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22808",
  "fulltext_url": null,
  "id": "38sv0m10sfe5h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22808",
  "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.DS"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7213999340",
  "pdf_url": "https://arxiv.org/pdf/2609.22808",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38sv0m10sfe5h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22808",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22808"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Almost-sure quenched KAM tori for cubic NLS with a spatial white-noise potential",
  "title_text": "Almost-sure quenched KAM tori for cubic NLS with a spatial white-noise potential",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/38sv0m10sfe5h",
  "venue": "arXiv",
  "versions": []
}