{
  "abstract": "The complex spacing ratio is the complex displacement from a reference eigenvalue to its nearest neighbor divided by the corresponding displacement to its next-to-nearest neighbor. Its statistics provide a useful diagnostic of spectral correlations and nonintegrability in open quantum systems. Here, starting from the exact joint eigenvalue probability densities, we derive finite-$N$ complex-spacing-ratio distributions for the Gaussian ensembles of non-Hermitian random matrices in classes AI$^†$ and AII$^†$, realized by complex symmetric and complex self-dual random matrices, respectively. In class AII$^†$, we obtain an exact algebraic expression for arbitrary $N$ and explicitly evaluate the distributions and representative moments for $N=3, 4, 5, 6$. In class AI$^†$, although the joint density retains a noncompact integral over nonunitary eigenvector degrees of freedom, we analytically derive a normalized one-dimensional integral representation for $N=3$ and determine the asymptotic behavior, including a logarithmic correction to the cubic level repulsion and a nonanalytic contribution to the angular density. We further confirm these analytical results through direct numerical diagonalization of non-Hermitian random matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35230",
  "author_total": 1,
  "authors": [
    {
      "name": "Kohei Kawabata"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/231a8fxxgs95n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35230",
  "fulltext_url": null,
  "id": "231a8fxxgs95n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.35230",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3109|Quantum chaos and dynamical systems"
    ]
  ],
  "openalex": "W7214783532",
  "pdf_url": "https://arxiv.org/pdf/2609.35230",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/231a8fxxgs95n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.35230",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35230"
    }
  ],
  "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:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact probability distributions of complex spacing ratios in non-Hermitian random matrices",
  "title_text": "Exact probability distributions of complex spacing ratios in non-Hermitian random matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/231a8fxxgs95n",
  "venue": "arXiv",
  "versions": []
}