{
  "abstract": "We present a direct and nonrecursive construction that maps an arbitrary planar polynomial dissipative flow $\\dotα=h(α,α^*)$ to an open quantum system in Gorini--Kossakowski--Sudarshan--Lindblad form. Given the homogeneous components of the classical drift, the corresponding Hamiltonian and collapse-operator blocks are obtained algebraically and independently at each degree. No recursive cancellation of lower-order terms is required: in the large-amplitude limit $|α|\\sim S\\to\\infty$, ordering-generated lower-degree terms are parametrically suppressed, while mean-field closure yields the prescribed leading $O(S)$ drift for semiclassically localized states. This provides a simple and systematic route from dissipative classical dynamics to explicit open-quantum-system realizations, without claiming a unique microscopic quantization of the classical flow. We demonstrate the construction for stable fixed points, a Hopf bifurcation, and a bistable-ring flow. The corresponding Liouvillian spectra recover the classical relaxation exponents, the radial Floquet exponent and neutral phase direction of a limit cycle, and the separation between local relaxation and inter-ring switching in the bistable case. These examples show that the construction can be used not only to analyze a given quantum model, but also to design open quantum systems with prescribed classical dynamical structures in the semiclassical limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15632",
  "author_total": 1,
  "authors": [
    {
      "name": "Tingfei Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ajmvfmqec8h1b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15632",
  "fulltext_url": null,
  "id": "ajmvfmqec8h1b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15632",
  "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",
      "nlin.CD"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7213267428",
  "pdf_url": "https://arxiv.org/pdf/2609.15632",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ajmvfmqec8h1b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.15632",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15632"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:nlin.CD",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "A Nonrecursive Lindblad Quantization of Dissipative Polynomial Dynamics",
  "title_text": "A Nonrecursive Lindblad Quantization of Dissipative Polynomial Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:25Z",
  "url": "https://research.draconitic.com/paper/ajmvfmqec8h1b",
  "venue": "arXiv",
  "versions": []
}