{
  "abstract": "Spread complexity has emerged as a useful probe of quantum chaos, yet the microscopic spectral origin of its characteristic finite-time peak remains incompletely understood. We develop an analytic framework that relates spread complexity directly to local spectral statistics. Starting from an energy-space representation of the Krylov kernel, we show that the kernel is approximately banded, leading to a rapidly convergent diagonal expansion dominated by nearby levels in the ordered spectrum. Motivated by this structure, we propose an approximate kernel-universality hypothesis: after unfolding, the Krylov kernel is well approximated by that of a uniform lattice. Combining this universal kernel with local spectral statistics yields a simple analytic expression for spread complexity in terms of the Fourier transforms of the $k$-th nearest-neighbour spacing distributions. In particular, at leading order, the finite-time peak is controlled by the Fourier transform of the nearest-neighbour spacing distribution. The resulting framework describes both chaotic random-matrix ensembles and the integrable Poisson limit, identifies the spectral origin of the complexity peak and its late-time behaviour, and provides a direct connection between Krylov dynamics and spectral statistics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.07412",
  "author_total": 3,
  "authors": [
    {
      "name": "Pallab Basu"
    },
    {
      "name": "Suman das"
    },
    {
      "name": "Bigboy Madlala"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5exnynkc1kxga.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.07412",
  "fulltext_url": null,
  "id": "5exnynkc1kxga",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.07412",
  "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.stat-mech"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3109|Quantum chaos and dynamical systems"
    ]
  ],
  "openalex": "W7202145846",
  "pdf_url": "https://arxiv.org/pdf/2608.07412",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5exnynkc1kxga.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:19Z",
      "native_id": "2608.07412",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.07412"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Analytic Spread Complexity from Level Statistics: From Chaos to Integrability",
  "title_text": "Analytic Spread Complexity from Level Statistics: From Chaos to Integrability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:19Z",
  "url": "https://research.draconitic.com/paper/5exnynkc1kxga",
  "venue": "arXiv",
  "versions": []
}