{
  "abstract": "We compute the full probability distribution of the moment of inertia I \\propto \\sum_{i=1}^N \\vec{r}_i^{\\,2} I ∝ ∑ i = 1 N r → i 2 of a gas of N N noninteracting bosons trapped in a harmonic potential V(r) = (1/2)\\, m\\, \\omega^2 r^2 V ( r ) = ( 1 / 2 ) m ω 2 r 2 , in all dimensions and at all temperature. The appropriate thermodynamic limit in a trapped Bose gas consists in taking the limit N\\to ∞ N → ∞ and \\omega\\to 0 ω → 0 with their product \\rho = N \\omega^d ρ = N ω d fixed, where \\rho ρ plays the role analogous to the density in a translationally invariant system. In this thermodynamic limit and in dimensions d;gt 1 d > 1 , the harmonically trapped Bose gas undergoes a Bose-Einstein condensation (BEC) transition as the density \\rho ρ crosses a critical value \\rho_c(\\beta) ρ c ( β ) , where \\beta β denotes the inverse temperature. We show that the nature of the condensation is different for 1<d≤ 2 1 < d ≤ 2 and d;gt 2 d > 2 . Near the condensation transition, for simplicity, we provide the analysis only for d;gt 2 d > 2 . We show that the probability distribution P_\\beta(I,N) P β ( I , N ) of I I admits a large deviation form P_\\beta(I,N) \\sim e^{-V \\Phi(I/V)} P β ( I , N ) ∼ e − V Φ ( I / V ) where V = \\omega^{-d} \\gg 1 V = ω − d ≫ 1 . We compute explicitly the rate function \\Phi(z) Φ ( z ) and show that it exhibits a singularity at a critical value z=z_c z = z c where its second derivative undergoes a discontinuous jump. In addition, on the condensed side, the rate function \\Phi(z) Φ ( z ) becomes independent of \\rho ρ for z<z_c z < z c . We show that the existence of z_c z c and the associated freezing below z_c z c is directly related to the existence of a BEC transition and it disappears when the system does not have a BEC transition as in d ≤ 1 d ≤ 1 . An interesting consequence of our results is that even if the actual system is in the fluid phase, i.e., when \\rho < \\rho_c(\\beta) ρ < ρ c ( β ) , by measuring the distribution of I I and analysing the singularity in the associated rate function, one can get a signal of the BEC transition in d;gt 1 d > 1 . This provides a real space diagnostic for the BEC transition in the noninteracting Bose gas.",
  "abstract_shown": true,
  "affiliations": [
    "Tata Institute of Fundamental Research",
    "Laboratoire de Physique Théorique et Modèles Statistiques",
    "University of Paris-Saclay",
    "Laboratory of Theoretical and High Energy Physics"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Manas Kulkarni"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Satya N. Majumdar"
    },
    {
      "affs": [
        3
      ],
      "name": "Grégory Schehr",
      "orcid": "0000-0001-6648-5213"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ywgk2vjt3352.bib",
  "cited_by": 0,
  "doi": "10.21468/scipostphys.21.4.102",
  "fulltext_url": null,
  "id": "6ywgk2vjt3352",
  "issns": [
    "2542-4653"
  ],
  "landing_url": "http://scipost.org/SciPostPhys.21.4.102",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0",
  "metadata_licence": null,
  "native_subjects": [
    [
      "feed-journal",
      "physics/general"
    ],
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      "openalex",
      "3107|Cold Atom Physics and Bose-Einstein Condensates"
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  "openalex": "W4416354439",
  "pdf_url": "https://scipost.org/10.21468/SciPostPhys.21.4.102/pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": "Stichting SciPost",
  "ris": "https://research.draconitic.com/paper/6ywgk2vjt3352.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "10.21468/scipostphys.21.4.102",
      "source": "feed-scipost",
      "url": "http://scipost.org/SciPostPhys.21.4.102"
    },
    {
      "first_seen": "2026-10-30T12:17:57Z",
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      "source": "crossref",
      "url": "https://scipost.org/10.21468/SciPostPhys.21.4.102"
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  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Cold Atom Physics and Bose-Einstein Condensates",
      "subfield": "amo"
    }
  ],
  "title": "The distribution of the moment of inertia for harmonically trapped noninteracting Bosons at finite temperature: Large deviations",
  "title_text": "The distribution of the moment of inertia for harmonically trapped noninteracting Bosons at finite temperature: Large deviations",
  "type": "peer-reviewed",
  "updated_at": "2026-11-02T12:20:43Z",
  "url": "https://research.draconitic.com/paper/6ywgk2vjt3352",
  "venue": "SciPost",
  "versions": []
}