{
  "abstract": "We consider the Wigner--Smith time-delay matrix of a chaotic cavity with broken time-reversal symmetry, a finite number $M$ of equivalent open channels, and a uniform tunnel barrier of reflection probability $R$. Exact random-matrix results for nonideal coupling are known at the level of the joint matrix distribution, whereas explicit finite-channel formulas for Schur moments are much less developed. We show that every Schur moment of the nonideal Wigner--Smith matrix factorizes into its ideal-coupling inverse-Laguerre value and a barrier factor given by a circular unitary ensemble (CUE) average of a Schur polynomial. A dual-Cauchy generating function reduces the latter to a Toeplitz determinant with a rational symbol, placing the barrier problem within the classical theory of exact CUE characteristic-polynomial ratios. For one-row partitions, specializing the exact CUE ratio formula gives a closed generating function for all barrier coefficients and therefore all finite delay-time moments in the allowed range $n\\le M$. The exact ratio formula decomposes into a sector visible to the semiclassical expansion and an additional contribution proportional to $R^{M+1}$, which is invisible to every algebraic order in $1/M$. For the second moment, this contribution exactly reproduces the exponentially small term in the known random-matrix expression for $\\langleτ_W^2\\rangle$ that is absent from the semiclassical expansion. We also derive an exact finite sum for all one-column partitions and an exact complement symmetry for Schur averages inside the $M\\times M$ square. The new contribution therefore lies not in the underlying CUE ratio identities, which are classical, but in combining them with the exact nonideal Wigner--Smith mapping and extracting the resulting finite-channel time-delay formulas and corrections to semiclassical Schur-moment conjectures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04170",
  "author_total": 1,
  "authors": [
    {
      "name": "Israel F. Araujo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1t79qyrq6538b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04170",
  "fulltext_url": null,
  "id": "1t79qyrq6538b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04170",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3109|Quantum chaos and dynamical systems"
    ]
  ],
  "openalex": "W7220665306",
  "pdf_url": "https://arxiv.org/pdf/2610.04170",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1t79qyrq6538b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.04170",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04170"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact Finite-Channel Schur Moments of the Wigner-Smith Matrix with a Tunnel Barrier",
  "title_text": "Exact Finite-Channel Schur Moments of the Wigner-Smith Matrix with a Tunnel Barrier",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1t79qyrq6538b",
  "venue": "arXiv",
  "versions": []
}