{
  "abstract": "Covariance dynamics on the positive-definite cone are commonly described by gradient flows, which encode dissipative relaxation but obscure the underlying phase-space structure. We construct a finite-dimensional Hamiltonian lift of covariance dynamics on Sym$^+_n$ equipped with the Bures--Wasserstein metric. The natural mechanical Lagrangian yields canonical momentum $Π=\\tfrac12 L_Σ[\\dotΣ]$, where $L_Σ$ is the Lyapunov operator, and explicit Hamiltonian $\\mathcal{H}(Σ,Π) = 2{\\rm tr}(ΠΣΠ)+V(Σ)$. Adding Rayleigh dissipation recovers the Bures--Wasserstein gradient flow in the overdamped limit. For a spectral-floor and trace-control potential, the quadratic fluctuation Hamiltonian around the isotropic equilibrium separates trace and traceless modes; the baseline stiffness diverges as $(s-ν)^{-2}$ as the equilibrium covariance approaches the floor. The construction identifies a conservative parent system for constrained Bures--Wasserstein covariance relaxation and fixes the local stiffness scale induced by the spectral floor.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.16380",
  "author_total": 1,
  "authors": [
    {
      "name": "Christian Kerskens"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83s18m21qsqzn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.16380",
  "fulltext_url": null,
  "id": "83s18m21qsqzn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.16380",
  "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.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.16380",
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83s18m21qsqzn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2607.16380",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.16380"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Hamiltonian Lift of Bures--Wasserstein Covariance Dynamics with a Spectral Floor",
  "title_text": "Hamiltonian Lift of Bures--Wasserstein Covariance Dynamics with a Spectral Floor",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/83s18m21qsqzn",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.physleta.2026.132215",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}