{
  "abstract": "The dynamical formation of a complete Bose-Einstein condensate and the asymptotic purification of trapped bosons coupled to a quantized radiation field are rigorously established. By tracking the macroscopic one-particle density matrix $κ_T$ through a nonlinear resonance cascade, it is demonstrated that radiative relaxation irreversibly depletes all excited trap modes, even when the initial macroscopic state $κ_0$ is genuinely mixed. Here $κ_T$ is an average, with respect to a de Finetti measure $μ_0$, over mean-field particle-field orbits, so that the mixedness of $κ_0$ reflects a statistical ensemble of orbits. Under the assumptions of a non-vanishing initial ground state component and strictly positive downward Fermi-Golden-Rule rates, strong trace-norm convergence to a pure condensate is proven, $$ \\lim_{T\\to\\infty} \\| κ_T-|χ_0\\rangle\\langleχ_0| \\|_{\\mathfrak{S}_1(\\mathfrak{h})} = 0 \\, . $$ Furthermore, the von Neumann entropy of the macroscopic one-particle density matrix is shown to vanish asymptotically, $$ \\lim_{T\\to\\infty}S[κ_T]=0 \\, , $$ without any claim of monotonicity in $T$. Thus, any initially mixed, positive-entropy state ($0<S[κ_0]<\\infty$) is purified to the ground state $|χ_0\\rangle\\langleχ_0|$. For the proof, we derive the Hartree hierarchy of the coupled system of bosons and photons from the finite-$N$ BBGKY hierarchy of the microscopic quantum many-body system, establishing trace-norm convergence in the mean-field limit as $N\\to\\infty$. The limits are taken successively; first $N\\to\\infty$, then the weak-coupling limit, and finally $T\\to\\infty$. Although the global particle-field evolution remains unitary, the macroscopic one-particle state converges to a pure state as energy and correlations are continuously radiated into the dispersive field.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17923",
  "author_total": 2,
  "authors": [
    {
      "name": "Thomas Chen"
    },
    {
      "name": "Ali Mezher"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4esz8ebm3rahr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17923",
  "fulltext_url": null,
  "id": "4esz8ebm3rahr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17923",
  "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.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Cold Atom Physics and Bose-Einstein Condensates"
    ]
  ],
  "openalex": "W7221798462",
  "pdf_url": "https://arxiv.org/pdf/2610.17923",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4esz8ebm3rahr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.17923",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17923"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Dynamical BEC formation and vanishing entropy for trapped bosons in non-relativistic QED via nonlinear resonance cascades",
  "title_text": "Dynamical BEC formation and vanishing entropy for trapped bosons in non-relativistic QED via nonlinear resonance cascades",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/4esz8ebm3rahr",
  "venue": "arXiv",
  "versions": []
}