{
  "abstract": "We prove polynomial upper bounds on spectral gaps of quasi-periodic Schrödinger operators with small $C^{k}$ potentials and Diophantine frequencies. For sufficiently large $k$, the decay exponent is $k-34τ$, where $τ$ is the Diophantine exponent. We construct examples with lower bounds along infinitely many gap labels, showing that the leading coefficient $1$ of $k$ is asymptotically optimal. The proof uses quantitative reducibility and the Moser-Pöschel argument.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26977",
  "author_total": 3,
  "authors": [
    {
      "name": "Ao Cai"
    },
    {
      "name": "Yang Gao"
    },
    {
      "name": "Jiawei He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/am107bnn0q083.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26977",
  "fulltext_url": null,
  "id": "am107bnn0q083",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26977",
  "language": null,
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  "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-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ],
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      "arxiv",
      "math.SP"
    ],
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      "2610|Spectral Theory in Mathematical Physics"
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  "openalex": "W7223150475",
  "pdf_url": "https://arxiv.org/pdf/2610.26977",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/am107bnn0q083.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:04Z",
      "native_id": "2610.26977",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26977"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators",
  "title_text": "Polynomial Spectral Gap Estimates for Finitely Differentiable Quasi-Periodic Schrödinger Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/am107bnn0q083",
  "venue": "arXiv",
  "versions": []
}