{
  "abstract": "We study a spin-balanced unitary Fermi superfluid bound by an attractive $1/r$ interaction within an extended Thomas--Fermi density functional. Its large-particle-number limit is the Lane--Emden polytrope of index $3/2$. We prove the leading gradient correction to the ground-state energy and strong convergence of the density amplitude. A rescaled surface problem predicts the next energy correction and the leading integrated density error. Matching a vortex core to the polytropic bulk gives the energetic threshold of a singly quantized central vortex, including the constant beyond the leading logarithm. Linearizing the same surface problem predicts a local energetic threshold for collective surface excitations that, in the natural TF frequency units, decreases more slowly with particle number than the central-vortex threshold. Radial stationary, spherical Bogoliubov--Poisson, and axisymmetric real-time calculations test the predicted energy corrections and vortex matching, and resolve finite-size surface-mode minima whose approach to the continuum surface coefficient is followed to $N\\simeq4\\times10^6$. For the reference gradient coefficient the vortex constant is $c_1=-0.535$, and the surface Landau scale is $1.417\\,ω_K(\\hbar_{\\rm eff}^2/2R_{\\rm TF})^{1/6}\\propto N^{-1/9}$; sector energies at $N\\simeq4.6\\times10^5$, computed after the fit, agree with the extrapolated vortex threshold to $10^{-4}$. These results distinguish the accuracy of the Thomas--Fermi bulk from the gradient physics that controls the surface and vortex core, and separate vortex energetics from the open problem of nonlinear vortex entry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24565",
  "author_total": 1,
  "authors": [
    {
      "name": "Bao-Duy Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8msnm4skf7h48.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24565",
  "fulltext_url": null,
  "id": "8msnm4skf7h48",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24565",
  "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",
      "cond-mat.quant-gas"
    ],
    [
      "openalex",
      "3107|Cold Atom Physics and Bose-Einstein Condensates"
    ]
  ],
  "openalex": "W7222996251",
  "pdf_url": "https://arxiv.org/pdf/2610.24565",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8msnm4skf7h48.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:52Z",
      "native_id": "2610.24565",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24565"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Surface corrections and vortex energetics in the Thomas--Fermi limit of a self-bound unitary Fermi superfluid",
  "title_text": "Surface corrections and vortex energetics in the Thomas--Fermi limit of a self-bound unitary Fermi superfluid",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:41Z",
  "url": "https://research.draconitic.com/paper/8msnm4skf7h48",
  "venue": "arXiv",
  "versions": []
}