{
  "abstract": "We analyze thermalization and eigenstate thermalization in the random free fermion model, a quadratic Hamiltonian with a Gaussian Orthogonal Ensemble hopping matrix, by an exact random-matrix calculation. For a single-particle observable $A$ we compute the ensemble average and fluctuations of $\\operatorname{Tr}(Aρ(t))$: we derive the relaxation envelope $g^2(t/τ_λ)$ with $τ_λ= \\hbar/(2η\\sqrt{N})$ and its oscillatory $|t|^{-3}$ tail, both properties of the semicircular limiting density, and we show that the variance of the fluctuations is $O(1/N)$, so that the relaxation profile self-averages at fixed scaled time. Incorporating particle-number conservation, we prove a factorization theorem for the energy-shell statistics of the many-body eigenstates: the energy-independent ETH structure follows from the statistical independence of the eigenvector matrix and the spectrum, and at fixed realization the energy constraint enters only through a covariance subtraction of relative order $1/N$. A controlled eigenvector--eigenvalue correlation deformation $H(\\varepsilon)=H_0+\\varepsilon H_1$ then generates, at first order in $\\varepsilon$, the energy dependence of the diagonal energy-resolved slope and of the off-diagonal spectral function, a single-particle diagnostic of the ETH structure in the allowed particle-hole sector. Correlation-function fluctuations and the single-particle spectral form factor finally identify the subleading $O(1/N)$ late-time fingerprints of two-level spectral correlations. The model thus separates eigenbasis chaos from spectral chaos and identifies the statistical origin of energy-independent versus energy-dependent ETH.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01414",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiao-Kan Guo"
    },
    {
      "name": "Zhiqiang Huang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/57tfrzwhy5f71.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01414",
  "fulltext_url": null,
  "id": "57tfrzwhy5f71",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01414",
  "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"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7216274782",
  "pdf_url": "https://arxiv.org/pdf/2610.01414",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/57tfrzwhy5f71.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.01414",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01414"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "On thermalization in random free fermions: Statistical origins and energy-dependent ETH structure",
  "title_text": "On thermalization in random free fermions: Statistical origins and energy-dependent ETH structure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/57tfrzwhy5f71",
  "venue": "arXiv",
  "versions": []
}