{
  "abstract": "For chaotic many-body systems as well as the random energy model, the logarithm of the (scaled) spectral form factor (SFF) exhibits two robust properties at late times: (i) self-averaging and (ii) a reflected-Gumbel distribution. Here, we demonstrate that both properties break down for $N$ non-interacting fermions on a lattice of size $L$ with an incommensurate single-particle spectrum. We show that the logarithm of the SFF, upon rescaling by $1/\\sqrt{L}$, follows the Airy distribution, in stark contrast to the reflected-Gumbel law. Moreover, it is no longer self-averaging, as its mean and standard deviation are of the same order. While deviations from reflected-Gumbel statistics are generically expected for non-interacting systems, we find that an interacting integrable model exhibits reflected-Gumbel statistics at late times, mirroring the chaotic case and distinguishing it from non-interacting fermions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41393",
  "author_total": 3,
  "authors": [
    {
      "name": "Oscar Martin"
    },
    {
      "name": "Satya N. Majumdar"
    },
    {
      "name": "Laura Foini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ppc1e28mzz59.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41393",
  "fulltext_url": null,
  "id": "2ppc1e28mzz59",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41393",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41393",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ppc1e28mzz59.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:15Z",
      "native_id": "2610.41393",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41393"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Airy distribution of the quenched spectral form factor in non-interacting fermions",
  "title_text": "Airy distribution of the quenched spectral form factor in non-interacting fermions",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:51Z",
  "url": "https://research.draconitic.com/paper/2ppc1e28mzz59",
  "venue": "arXiv",
  "versions": []
}