{
  "abstract": "We develop a completely positive and trace-preserving non-Markovian transmon model with longitudinal Markovian dephasing and transverse renewal events motivated by a glassy two-level-system environment. A microscopic Hamiltonian identifies coupling subspaces; a normalized Prabhakar waiting-time law phenomenologically coarse grains slow defect reconfigurations. Forward chronological renewal histories yield an exact map-level Volterra equation, a noncommuting kernel--resolvent master equation, and an equivalent drift-conjugated Caputo-type representation with its required initial-value term. Without energy relaxation, Pauli-space dynamics splits into two one-dimensional subspaces and a coupled $(σ_y,σ_z)$ subspace supporting directional transfer between coherence and longitudinal polarization; $σ_x$ polarization is renewal-insensitive. For heavy-tailed waiting times with $0<α<1$, branch-cut analysis gives a generic $t^{-α}$ storage tail in longitudinal polarization generated from initial coherence and $O(t^{-1-α})$ reverse transfer; constant-rate Poisson renewal yields pole-generated exponential decay. Independent zero-temperature relaxation at finite $T_1$ exponentially cuts off these tails when its rate is below twice the pure-dephasing rate. We compare independent inverse-Laplace reconstructions of the waiting-time density, memory kernel, and selected qubit-response components to assess numerical accuracy. For the studied parameters, Prabhakar renewal gives larger forward-transfer magnitudes at the prescribed readout than both a scale-matched constant-rate Poisson reference and an inhomogeneous Poisson reference matching the full expected-count profile, including finite-$T_1$ tests. Both Poisson references yield larger evaluated finite-window peaks. Disorder-motivated renewal memory reshapes transmon decoherence selectively by state and direction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37270",
  "author_total": 2,
  "authors": [
    {
      "name": "Ruha Uğraş Erdoğan"
    },
    {
      "name": "Ferit Acar Savacı"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fcg04tp0hzpjs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37270",
  "fulltext_url": null,
  "id": "fcg04tp0hzpjs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37270",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7214928483",
  "pdf_url": "https://arxiv.org/pdf/2609.37270",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fcg04tp0hzpjs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.37270",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37270"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Directional transfer from coherence to longitudinal polarization and algebraic storage in a transmon with Markovian dephasing and a glassy environment: A non-Markovian fractional renewal model",
  "title_text": "Directional transfer from coherence to longitudinal polarization and algebraic storage in a transmon with Markovian dephasing and a glassy environment: A non-Markovian fractional renewal model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/fcg04tp0hzpjs",
  "venue": "arXiv",
  "versions": []
}