{
  "abstract": "We derive the canonical-ensemble scaling of Tan's contact for $N$ harmonically trapped Tonks--Girardeau bosons at finite temperature in the large-$N$ limit. The leading scaling coefficient reproduces the local-density-approximation result and is obtained from a contour-integral representation of the canonical partition function followed by a saddle-point reduction to a phase-space integral with a self-consistent scaled chemical potential. The subleading coefficient is the central new object of this work: it admits an explicit representation in terms of universal phase-space integrals of the Fermi factor, having closed-form Sommerfeld and virial limits, and is identified with the canonical-versus-grand-canonical ensemble difference at fixed mean particle number. In the high-temperature Boltzmann regime the ratio of subleading to leading coefficients collapses to a universal value, traceable to the Poissonian particle-number statistics of the dilute grand-canonical gas. We construct Padé approximants for both scaling functions that interpolate uniformly between the low-temperature Sommerfeld and high-temperature virial regimes; for the subleading coefficient we report a form that is uniformly accurate on our working range of temperatures and asymptotically correct beyond. The scaling law is verified against canonical contour-integration data across the full temperature range, and the experimental visibility of the ensemble correction is quantified: for the mesoscopic particle numbers and temperatures of current one-dimensional experiments it reaches the several-percent level.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.15994",
  "author_total": 1,
  "authors": [
    {
      "name": "Felipe Taha Sant'Ana"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/06s3h1a2f3aah.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.15994",
  "fulltext_url": null,
  "id": "06s3h1a2f3aah",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.15994",
  "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",
      "cond-mat.stat-mech"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2605.15994",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/06s3h1a2f3aah.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:52Z",
      "native_id": "2605.15994",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.15994"
    }
  ],
  "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:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Canonical-ensemble scaling of Tan's contact in the trapped Tonks--Girardeau gas",
  "title_text": "Canonical-ensemble scaling of Tan's contact in the trapped Tonks--Girardeau gas",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:52Z",
  "url": "https://research.draconitic.com/paper/06s3h1a2f3aah",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1103/4nlt-wdl7",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}