{
  "abstract": "We investigate the spectral statistics of random perturbations of semiclassical Schrödinger operators on compact manifolds, near energy levels corresponding to chaotic classical dynamics. The prototypical example is that of an operator $h^2Δ+V(x)$ that is perturbed by a smooth potential $h^αV_ω$ with $α\\in (0,1)$, and $V_ω$ is a random potential that decorrelates on distances $h^β$, with $0<β<2α$. We show that for a generic perturbation, the spectral fluctuations of the smoothed counting function of eigenvalues obey a universal behavior at a certain mesoscopic scale, which is coherent with the predictions of random matrix theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09869",
  "author_total": 1,
  "authors": [
    {
      "name": "Julien Moy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6y9cmfcyd01gt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09869",
  "fulltext_url": null,
  "id": "6y9cmfcyd01gt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09869",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
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      "arxiv",
      "math.SP"
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      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
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  "openalex": "W7221056639",
  "pdf_url": "https://arxiv.org/pdf/2610.09869",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6y9cmfcyd01gt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:37Z",
      "native_id": "2610.09869",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09869"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Smooth spectral statistics of random perturbations of Schrödinger operators near Anosov energy levels",
  "title_text": "Smooth spectral statistics of random perturbations of Schrödinger operators near Anosov energy levels",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/6y9cmfcyd01gt",
  "venue": "arXiv",
  "versions": []
}