{
  "abstract": "We study the stationary spectrum of a coherently driven single-mode Kerr cavity in Bargmann--Fock space. For positive Kerr coupling the Hamiltonian is self-adjoint, bounded below, and has compact resolvent. For nonzero drive, a minimal-solution continued fraction yields an exact scalar spectral condition, with all eigenvalues simple. A Liouville transformation identifies the eigenvalue equation with a degenerate double-confluent Heun problem and classifies its singularities. An Olver-type Volterra construction gives normalized sectorial solutions at infinity with explicit error bounds. In the strong-drive regime, the leading turning-point energy coefficient is proved, whereas the next coefficient remains conditional on a stated global-connection conjecture; independent Bogoliubov and complex-WKB calculations provide consistency checks. A formal weak-drive expansion is verified from the Bargmann recurrence, and its upper-edge tridiagonal series is summed in closed form. Exploratory WKB iteration portraits are included only as visual aids and do not establish the conjectural global connection.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.16969",
  "author_total": 1,
  "authors": [
    {
      "name": "Maciej Janowicz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ft3ysh1c6d3ac.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.16969",
  "fulltext_url": null,
  "id": "ft3ysh1c6d3ac",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.16969",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7213426880",
  "pdf_url": "https://arxiv.org/pdf/2609.16969",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ft3ysh1c6d3ac.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:41Z",
      "native_id": "2609.16969",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.16969"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Operator-theoretic and analytic properties of a driven single-mode Kerr cavity in Bargmann space",
  "title_text": "Operator-theoretic and analytic properties of a driven single-mode Kerr cavity in Bargmann space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/ft3ysh1c6d3ac",
  "venue": "arXiv",
  "versions": []
}