{
  "abstract": "We study a free-energy minimization problem for a trapped semiclassical Bose gas with repulsive Coulomb self-interaction. Because the bosonic entropy density has zero recession slope, the natural relaxation is posed over nonnegative finite Radon measures on phase space, and a minimizer may have a singular component. We interpret this component as condensation within the relaxed semiclassical model. We prove existence and uniqueness at every positive temperature, derive the Euler-Lagrange contact condition and an obstacle-type formula for the condensed density, and establish sharp phase boundaries under only the standing continuity assumptions on the trap. At fixed mass there is a unique finite positive critical temperature, with condensation precisely below it. At fixed temperature there is a sharp critical mass, possibly infinite, separating normal and condensed minimizers. For harmonic traps we obtain a sharp confinement-strength dichotomy. We also prove an abstract conditional variational-stability statement for measure-valued curves that conserve mass and satisfy the free-energy inequality.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.26900",
  "author_total": 2,
  "authors": [
    {
      "name": "Gi-Chan Bae"
    },
    {
      "name": "Jinmyoung Seok"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3y0h1tg0237vg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.26900",
  "fulltext_url": null,
  "id": "3y0h1tg0237vg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.26900",
  "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.AP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7204546855",
  "pdf_url": "https://arxiv.org/pdf/2608.26900",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3y0h1tg0237vg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2608.26900",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.26900"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Measure-valued free-energy minimizers for trapped bosons with repulsive Coulomb interaction",
  "title_text": "Measure-valued free-energy minimizers for trapped bosons with repulsive Coulomb interaction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/3y0h1tg0237vg",
  "venue": "arXiv",
  "versions": []
}