{
  "abstract": "In two dimensions, the kinetic and contact energies scale identically under dilation, a trap $V=r^s/s$ as $λ^{-s}$. We follow this balance through the power-law family $-2\\le s\\le4$, $s\\neq0$, for both signs of the coupling $g$, with rotation, using scaling bounds, radial solutions, Bogoliubov spectra, and two-dimensional imaginary-time states. Attraction collapses the cloud at the Townes coupling $g_{*}$ in every trap, with width $\\ell\\proptoδ^{1/(s+2)}$, $δ=1-|g|/g_{*}$; repulsion spreads it to a Thomas--Fermi (TF) radius $\\propto g^{1/(s+2)}$. A rotating collapse leaves the axis once the rotation frequency $Ω$ exceeds its dipole frequency, which softens only for $s>2$; in a quartic trap this happens at $δ\\simeq0.32\\,Ω^6$, within $3\\%$ of the Bogoliubov threshold; it then collapses on the minimum ring of the rotating-frame potential, which also empties a repulsive TF cloud at $Ω=(3g/π)^{1/6}$. For repulsive vortex states the TF energy error splits exactly into a density-gradient and a flow part of comparable or larger size. At $s=-2$ only the cutoff sets a length: the energy is exactly covariant with it, the condensate falls to the center for both signs, and repulsion leaves a halo of density $\\propto1/(gr^2)$ whose extent grows exponentially with $g$. Near collapse, split-step imaginary time has a first-order stationary bias invisible to residual tests.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04849",
  "author_total": 2,
  "authors": [
    {
      "name": "Dinh-Thi Nguyen"
    },
    {
      "name": "Bao-Duy Le"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6kd0cytpg694n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04849",
  "fulltext_url": null,
  "id": "6kd0cytpg694n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04849",
  "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",
      "cond-mat.quant-gas"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04849",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6kd0cytpg694n.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.04849",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04849"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Rotating two-dimensional Bose--Einstein condensates in power-law traps: collapse, Thomas--Fermi scaling, and the inverse-square endpoint",
  "title_text": "Rotating two-dimensional Bose--Einstein condensates in power-law traps: collapse, Thomas--Fermi scaling, and the inverse-square endpoint",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/6kd0cytpg694n",
  "venue": "arXiv",
  "versions": []
}