{
  "abstract": "In this paper, we study the existence of ground states for two-component attractive Bose--Einstein condensates with displaced harmonic trapping potentials \\[ V_1(x)=|x-x_1|^2 \\ \\text{and}\\ V_2(x)=|x-x_2|^2, \\] where $x_1\\neq x_2\\in\\mathbb R^2$. For intraspecies interactions $a_1,a_2\\in (0,a^*)$, we focus on the critical interspecies coupling \\[ β=β^*:=a^*+\\sqrt{(a^*-a_1)(a^*-a_2)} \\] and prove that there exists a separation threshold $d_c\\in(0,\\infty)$ such that the corresponding constrained minimization problem admits no minimizer when $0<|x_1-x_2|<d_c$, whereas it admits a minimizer when $|x_1-x_2|\\geq d_c$. The threshold is given by $d_c=Λ_*^{-1/4}$, where $Λ_*$ is characterized by an auxiliary variational problem and attained. Our results extend the previous work of Guo et al. [J. Funct. Anal. 276 (2019)] and complete the existence classification of ground states for two-component attractive Bose--Einstein condensates with harmonic trapping potentials.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05183",
  "author_total": 2,
  "authors": [
    {
      "name": "Shubin Yu"
    },
    {
      "name": "Chun-Lei Tang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8a9g40zqn1kgw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05183",
  "fulltext_url": null,
  "id": "8a9g40zqn1kgw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05183",
  "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.AP"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7220736139",
  "pdf_url": "https://arxiv.org/pdf/2610.05183",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8a9g40zqn1kgw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05183",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05183"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "A separation threshold for ground states of two-component attractive Bose--Einstein condensates in displaced harmonic traps",
  "title_text": "A separation threshold for ground states of two-component attractive Bose--Einstein condensates in displaced harmonic traps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/8a9g40zqn1kgw",
  "venue": "arXiv",
  "versions": []
}