{
  "abstract": "Time ordering is a central obstacle in driven open-system dynamics governed by master equations with time-dependent rates. We derive explicit closed-form factorizations of the chronological and antichronological propagators for a time-dependent generator of the form $\\mathcal{L}(t)=α(t)A+β(t)B$, when the commutator $[A,B]$ is a simultaneous eigenoperator of the adjoint actions of $A$ and $B$, namely $[A,[A,B]]=λ_{A}[A,B]$ and $[B,[A,B]]=λ_{B}[A,B]$. In contrast to the disentangling procedure known as the Wei-Norman decomposition, our construction determines the factorization coefficients directly, without solving a coupled system of nonlinear differential equations. Applying this result to the bosonic gain-loss Lindblad equation, we obtain the exact dynamical map for arbitrary time-dependent gain and loss rates. The gain-loss master equation provides a canonical description of a driven harmonic oscillator coupled to a thermal bath. We benchmark the construction by deriving the time evolution of the Wigner function of an initial Fock state and comparing it with independent phase-space results. We further apply the resulting dynamical map to evaluate the code-space survival probability of a binomial bosonic code under driven gain-loss dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24617",
  "author_total": 1,
  "authors": [
    {
      "name": "Léonce Dupays"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5vkgfz8rt1tm0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24617",
  "fulltext_url": null,
  "id": "5vkgfz8rt1tm0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24617",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Non-Hermitian Physics"
    ]
  ],
  "openalex": "W7214011644",
  "pdf_url": "https://arxiv.org/pdf/2609.24617",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5vkgfz8rt1tm0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24617",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24617"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Explicit closed-form propagators for time-dependent gain-loss master equations",
  "title_text": "Explicit closed-form propagators for time-dependent gain-loss master equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/5vkgfz8rt1tm0",
  "venue": "arXiv",
  "versions": []
}