{
  "abstract": "We solve exactly, for arbitrary finite channel number $N$, the Riccati dynamics of a quasi-one-dimensional random matrix Schrödinger operator with Hermitian white-noise potential in the $β=2$ unitary symmetry class. The associated Dyson--Riccati eigenvalue gas admits an exact free-fermion representation at any sample length $L$, which in the limit $L\\to \\infty$ expresses the density of states and the total Lyapunov growth rate exactly through a single Airy Hankel $τ$-function providing multichannel generalization of $N=1$ Halperin--Thouless formulas. The $τ-$function further admits an outgoing-contour Kontsevich matrix Airy integral representation. Its saddle-point and double-scaling analyses give, in a unified way, the finite-channel density Lifshitz tail, and the large-$N$ spectral edge. In particular, for $N\\gg 1$ the sharp $N=\\infty$ edge is softened within an $N^{-4/5}$ spectral window, with its profile governed by the tritronquée solution of Painlevé I. We conjecture universality of this quasi-one-dimensional scaling edge profile for a broad class of $β=2$ random band matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27154",
  "author_total": 2,
  "authors": [
    {
      "name": "Yan V. Fyodorov"
    },
    {
      "name": "Pierre Le Doussal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/327fymeykajg9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27154",
  "fulltext_url": null,
  "id": "327fymeykajg9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27154",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
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      "arxiv",
      "nlin.SI"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7223117291",
  "pdf_url": "https://arxiv.org/pdf/2610.27154",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/327fymeykajg9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:18Z",
      "native_id": "2610.27154",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27154"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Exact spectral integrability of a finite-channel random Schrödinger operator: from fermionization of the Dyson--Riccati gas to Kontsevich integral",
  "title_text": "Exact spectral integrability of a finite-channel random Schrödinger operator: from fermionization of the Dyson--Riccati gas to Kontsevich integral",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/327fymeykajg9",
  "venue": "arXiv",
  "versions": []
}