{
  "abstract": "We study a one-dimensional single-excitation model of a scalar photon field coupled to a continuum of two-level atoms with quadratic density. The resulting matrix Hamiltonian has an unbounded spatially varying coupling and is not semibounded. We prove that it is essentially self-adjoint and determine its spectrum explicitly. The continuous spectrum is the half-line $(-\\infty,Ω]$, where $Ω$ is the atomic resonance frequency, while the spectrum above $Ω$ consists of a strictly increasing sequence of simple eigenvalues. These eigenvalues are characterized by the interlaced zeros of the Airy function and its derivative and satisfy \\begin{align*} ω_n = \\left(\\frac{3πg n}{4}\\right)^{1/2} + \\fracΩ{4} + O(n^{-1/2}). \\end{align*} The analysis is based on a nonlinear spectral reduction that yields a confining massless relativistic oscillator above $Ω$ and an inverted oscillator below $Ω$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18421",
  "author_total": 2,
  "authors": [
    {
      "name": "Sam Johar"
    },
    {
      "name": "Joseph Kraisler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ahty2nzbabws4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18421",
  "fulltext_url": null,
  "id": "ahty2nzbabws4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18421",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "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.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "arxiv",
      "physics.optics"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7221822836",
  "pdf_url": "https://arxiv.org/pdf/2610.18421",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ahty2nzbabws4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:31Z",
      "native_id": "2610.18421",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18421"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.optics",
      "subfield": "optics-photonics"
    }
  ],
  "title": "Spectral Theory of an Exactly Solvable Quantum-Optical Oscillator",
  "title_text": "Spectral Theory of an Exactly Solvable Quantum-Optical Oscillator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/ahty2nzbabws4",
  "venue": "arXiv",
  "versions": []
}