{
  "abstract": "We study the stochastic Schrödinger equation $ i\\partial_t u_{\\varepsilon} = H_{\\varepsilon} u_{\\varepsilon} $ with $ H_{\\varepsilon} = -Δ+ V(x/\\varepsilon) $, where V is a stationary ergodic sub-Gaussian field with exponential mixing. We establish the optimal algebraic error rate $ \\varepsilon^{d/2} $ in $ L^2(Ω; L^2_x) $ for every $ d\\ge1 $, prove it sharp by a matching lower bound when $ \\widehat{R}(0)>0 $, and upgrade the convergence of Zhang--Bal from convergence in probability to almost sure convergence. We further establish a Gaussian fluctuation central limit theorem with explicit covariance. The limiting fluctuation satisfies $ i\\partial_t \\mathcal{G} = (-Δ+ \\bar{V})\\mathcal{G} + \\sqrt{\\widehat R(0)}\\,\\dot W(t,x) $, a linear random Schrödinger equation driven by additive space-time white noise, where $ \\bar{V} = \\mathbb{E}[V] $ is the effective potential.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03014",
  "author_total": 1,
  "authors": [
    {
      "name": "Fanfei Meng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5eytnhjf91sdd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03014",
  "fulltext_url": null,
  "id": "5eytnhjf91sdd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03014",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03014",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5eytnhjf91sdd.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03014",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03014"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stochastic Homogenization of Schrödinger Equations with Exponentially Mixing Sub-Gaussian Potentials",
  "title_text": "Stochastic Homogenization of Schrödinger Equations with Exponentially Mixing Sub-Gaussian Potentials",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/5eytnhjf91sdd",
  "venue": "arXiv",
  "versions": []
}