{
  "abstract": "We consider a system of $N$ interacting bosons in a rotating harmonic trap in $\\mathbb{R}^2$, where the two-body interaction is attractive and scaled as $N^{2α}U(N^αx)$ with $0<α<1/12$, and the three-body interaction is repulsive and scaled as $N^{4β}W(N^βx,N^βy)$ with $0<β<1/24$. In the mean-field limit, the ground state energy is effectively described by a rotating cubic-quintic nonlinear Schrödinger functional. We analyze the collapse regime where the two-body coupling $a$ approaches the critical value $a_*$ and the three-body coupling $b$ tends to zero. The NLS ground states blow up with a universal profile given by the optimizer of the Gagliardo-Nirenberg inequality, and the energy satisfies $E^{\\mathrm{NLS}} = (1-ζ/4+o(1))\\mathcal{Q}{\\rm{pot}}\\ell_n^2$ with $ζ\\geqslant0$ determined by the relative rates of $a_n\\to a_*$ and $b_n\\searrow0$. From the many-body theory, we rigorously justify this effective description: the quantum ground state energy converges to the NLS energy with the same asymptotic expansion in the collapse regime, and the many-body ground states exhibit complete Bose-Einstein condensation onto the universal blow-up profile.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06466",
  "author_total": 3,
  "authors": [
    {
      "name": "Deke Li"
    },
    {
      "name": "Yuan Li"
    },
    {
      "name": "Qingxuan Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5y5wfzx4n9sk8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06466",
  "fulltext_url": null,
  "id": "5y5wfzx4n9sk8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06466",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212006212",
  "pdf_url": "https://arxiv.org/pdf/2609.06466",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5y5wfzx4n9sk8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.06466",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06466"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Condensation and Collapse in the Mean-Field Limit of Rotating 2D Bose Gases with Two-Body and Three-Body Interactions",
  "title_text": "Condensation and Collapse in the Mean-Field Limit of Rotating 2D Bose Gases with Two-Body and Three-Body Interactions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/5y5wfzx4n9sk8",
  "venue": "arXiv",
  "versions": []
}