{
  "abstract": "We study the hard-core variant of the Simplified Approach to the ground state of the dilute Bose gas. The hard-core potential has been the subject of renewed attention, and is physically relevant to realistic atomic Bose gases. The hard-core Simple Equation is an integro-differential equation, and we construct its solution via a monotone iteration scheme and prove existence and uniqueness (in a restricted sense) of the solution. The energy per particle $e$ and the density $ρ$ of the solution are shown to satisfy the Lee-Huang-Yang formula $e = 2πρ(1 + \\frac{128}{15\\sqrtπ}\\sqrtρ + o(\\sqrtρ))$ as $ρ\\to 0$, and the condensate fraction $η$ predicted by the hard-core Simple Equation is shown to satisfy $η= 1 - \\frac{8}{3\\sqrtπ}\\sqrtρ + o(\\sqrtρ)$ as $ρ\\to 0$, in agreement with Bogolyubov's theory. We thus extend results of Carlen, Jauslin, Lieb to the hard-core case. The hard-core equation is defined on its own terms, and the proofs proceed by approximating the hard-core potential with the soft-core potentials $m\\,χ_{\\{|x| \\le 1\\}}$ of increasing height $m$: at fixed energy, we establish the $L^1$ convergence of the corresponding solutions and the convergence of their densities at an $O(m^{-1/2})$ rate, and we show that the Lee-Huang-Yang expansions of the energy and of the condensate fraction for the soft-core equations hold with errors uniform in $m$, so that they survive the hard-core limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05293",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohamed El Hedi Bahri"
    },
    {
      "name": "Ian Jauslin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkbv20k2zz7m7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05293",
  "fulltext_url": null,
  "id": "fkbv20k2zz7m7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05293",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05293",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fkbv20k2zz7m7.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:25Z",
      "native_id": "2611.05293",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05293"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The Lee-Huang-Yang Formula in the Hard-Core Simplified Approach to the Bose gas",
  "title_text": "The Lee-Huang-Yang Formula in the Hard-Core Simplified Approach to the Bose gas",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/fkbv20k2zz7m7",
  "venue": "arXiv",
  "versions": []
}