{
  "abstract": "The exponential decay of an unstable quantum state, as described by standard Markovian theories such as Fermi's Golden Rule, assumes a simple, structureless environment. However, in complex environments characterized by disorder, long-range interactions, or strong fluctuations, local decay rates fluctuate, leading to non-Markovian dynamics and power-law ``long-time tails.'' In this paper, we apply the recently proposed \\textit{hyperstatistics} framework to the problem of quantum decay in such complex environments. By considering a $γ$-distribution of local decay rates across mesoscopic domains, we derive a macroscopic survival probability governed by a $q$-exponential function. We then use the $q$-generalized Gamma function, defined via the Mellin transform of the $q$-exponential, to calculate the moments of the decay-time distribution. We show that the mean quantum lifetime is $\\langle t\\rangle = \\int_0^\\infty P(t)\\,dt= [\\langleΓ\\rangle(2-q)]^{-1},$ and is therefore finite for $q<2$. The convergence of the second moment, and hence of the lifetime variance, instead requires the stricter condition $q<3/2$. These results provide a refined physical interpretation: for $1<q<3/2$ both the mean lifetime and its variance are finite; for $3/2\\le q<2$ the mean lifetime remains finite but lifetime fluctuations become infinitely broad; and for $q\\ge2$ the mean lifetime itself diverges, corresponding to a truly trapped, localized, or Griffiths-like regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22190",
  "author_total": 1,
  "authors": [
    {
      "name": "Nicola Fabiano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8angd63srk0xh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22190",
  "fulltext_url": null,
  "id": "8angd63srk0xh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22190",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3109|Statistical Mechanics and Entropy"
    ]
  ],
  "openalex": "W7214010917",
  "pdf_url": "https://arxiv.org/pdf/2609.22190",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8angd63srk0xh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2609.22190",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22190"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Non-Markovian Quantum Decay in Complex Environments: A Hyperstatistical Approach",
  "title_text": "Non-Markovian Quantum Decay in Complex Environments: A Hyperstatistical Approach",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/8angd63srk0xh",
  "venue": "arXiv",
  "versions": []
}