{
  "abstract": "We establish a Widom trace formula for spatial compressions of exact spectral projections of semiclassical Schrödinger operators. The potential is smooth near a compact classically allowed region, and the observation domain lies strictly inside that region. For every continuous spectral function with positive power decay at both endpoints, we obtain a trace formula at scale $h^{1-n}\\log h^{-1}$ whose coefficient separates into a boundary integral and a universal spectral functional. This yields the exact von Neumann and Rényi entanglement asymptotics for every fixed positive order, and proves their universal ratios to the particle-number variance. The proof combines commutator estimates in every fixed positive Schatten class with a local trace formula obtained from a boundary-adapted normal form and a Hardy model. In dimensions $n\\ge2$, a positive partition and the known variance asymptotic control the grazing contribution; in one dimension all boundary Fermi points are transverse. A harmonic-oscillator counterexample shows that continuity and weighted integrability alone are insufficient for the trace formula.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29076",
  "author_total": 2,
  "authors": [
    {
      "name": "Pan Ma"
    },
    {
      "name": "Daoyuan Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5gqzr035dwraf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29076",
  "fulltext_url": null,
  "id": "5gqzr035dwraf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29076",
  "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-ph"
    ],
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      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7223226295",
  "pdf_url": "https://arxiv.org/pdf/2610.29076",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5gqzr035dwraf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.29076",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29076"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Widom asymptotics for spatial compressions of Schrödinger spectral projections",
  "title_text": "Widom asymptotics for spatial compressions of Schrödinger spectral projections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/5gqzr035dwraf",
  "venue": "arXiv",
  "versions": []
}