{
  "abstract": "We study eigenstate fluctuations of the particle number in the nearest-neighbour free-fermion model on the periodic cubic lattice $(\\mathbb{Z}/L\\mathbb{Z})^d$. For every fixed dimension, every particle number, every subvolume, and every normalized energy eigenstate, we prove a bound of order $NL^{d-1}$ for the particle-number variance. The corresponding eigenstate-thermalization estimate is of order $L^{d-1}/(Nη^2)$ for fluctuations of relative size $η$. In particular, at positive particle density the bound decays as the inverse linear size. The proof decomposes the centered particle-number operator according to one-particle energy transfer and treats the zero- and nonzero-transfer components separately. The nonzero-transfer part is controlled by a sharp resonance bound, proved from Mann's theorem on relations among roots of unity, while the zero-transfer part is estimated by a Hilbert-Schmidt argument. These bounds are optimal in every dimension: the maximal nonzero-gap multiplicity has order $L^{d-1}$, and suitable many-body eigenstates realize matching variance lower bounds and show that the concentration bound cannot be improved in estimates uniform in the tolerance parameter.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.12701",
  "author_total": 5,
  "authors": [
    {
      "name": "Tristan Benoist"
    },
    {
      "name": "Vojkan Jakšić"
    },
    {
      "name": "Claude-Alain Pillet"
    },
    {
      "name": "Anna Szczepanek"
    },
    {
      "name": "Cornelia Vogel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/24v1cm82d8jgg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.12701",
  "fulltext_url": null,
  "id": "24v1cm82d8jgg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.12701",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.12701",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/24v1cm82d8jgg.ris",
  "sources": [
    {
      "first_seen": "2026-11-10T06:21:23Z",
      "native_id": "2611.12701",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.12701"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "One-Particle Resonances and Eigenstate Thermalization in Periodic Free-Fermion Lattices",
  "title_text": "One-Particle Resonances and Eigenstate Thermalization in Periodic Free-Fermion Lattices",
  "type": "preprint",
  "updated_at": "2026-11-10T06:21:37Z",
  "url": "https://research.draconitic.com/paper/24v1cm82d8jgg",
  "venue": "arXiv",
  "versions": []
}