{
  "abstract": "We prove exponentially slow thermalization for the quantum random energy model (QREM) under Davies dynamics. The QREM is the $n$-qubit Hamiltonian $H=ΓT+U$, where $U$ assigns independent Gaussian energies with variance equal to the system size to computational-basis configurations and $T$ is the transverse field generated by single-qubit Pauli $X$ operators. Let $β_c=\\sqrt{2\\log 2}$ be the freezing inverse temperature of the classical random energy model. For every inverse temperature $β>β_c$ and every transverse-field strength $0\\leqΓ<Γ_c(β)$, where $e^{ββ_c}=2\\cosh(βΓ_c(β))$, we show that the mixing time of the dissipative Davies dynamics associated with single-qubit Pauli system--bath couplings grows exponentially with the system size, almost surely; the bound is unchanged if the standard zero-Bohr-frequency dephasing terms are included. The result is uniform over all Davies rates satisfying detailed balance and a polynomial upper bound and does not assume primitivity. In the spin-glass phase, the Gibbs weight is carried by a sparse family of deep classical configurations that are separated by an extensive Hamming distance. A localization theorem for the QREM [Manai, Warzel, Comm. Math. Phys. 402, 1259 (2023)] transfers this geometry to the corresponding low-energy quantum eigenstates. Consequently, the Gibbs weight of the intermediate spectral sector is exponentially small, while single-qubit bath operators have exponentially small matrix elements between the two macroscopic sides of the bottleneck. A Davies-specific flux estimate then converts these two facts into an exponential lower bound on the mixing time. This gives a rigorous open-system dynamical manifestation of the frozen, localized low-energy structure of the QREM throughout its equilibrium spin-glass phase below the quantum transition line.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.08064",
  "author_total": 2,
  "authors": [
    {
      "name": "Giacomo De Palma"
    },
    {
      "name": "Emanuele Mingione"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9ehj46g7xq4gd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.08064",
  "fulltext_url": null,
  "id": "9ehj46g7xq4gd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.08064",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.08064",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9ehj46g7xq4gd.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2611.08064",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.08064"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exponential mixing time for the Davies dynamics of the quantum random energy model",
  "title_text": "Exponential mixing time for the Davies dynamics of the quantum random energy model",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:48Z",
  "url": "https://research.draconitic.com/paper/9ehj46g7xq4gd",
  "venue": "arXiv",
  "versions": []
}