{
  "abstract": "We investigate the existence of ground states for two-component Bose--Einstein condensates with intraspecies interactions $a_1, a_2 \\in (0, a^*)$ and interspecies interaction $β>0$. By carefully investigating an associated auxiliary minimization problem, we prove the existence of a unique, continuous, critical surface $γ= γ(a_1, a_2)$ between $β_*:= \\sqrt{(a^* - a_1) (a^* - a_2)}$ and $β^*:= a^* - \\frac{a_1 + a_2}{2}$. This surface provides a complete classification for the existence of minimizers: ground states exist for $β\\in (0,γ)$ and do not exist for $β> γ$. Additionally, when the trapping potentials are continuous at a common zero point, there is no ground state for $β= γ$. Our results close the gap case $β\\in [β_*, β^*]$ when $a_1\\ne a_2$ in literature, significantly extending the results in \\cite{Bao-Cai-1,guoBlowupSolutionsTwo2017a}.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27316",
  "author_total": 4,
  "authors": [
    {
      "name": "Wenshuai Peng"
    },
    {
      "name": "Xiaoyu Zeng"
    },
    {
      "name": "Qidi Zhang"
    },
    {
      "name": "Huan-Song Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/486zwvb5q08sr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27316",
  "fulltext_url": null,
  "id": "486zwvb5q08sr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27316",
  "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.FA"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W7214217401",
  "pdf_url": "https://arxiv.org/pdf/2609.27316",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/486zwvb5q08sr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27316",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27316"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Critical surface for two component Bose-Einstein Condensates",
  "title_text": "Critical surface for two component Bose-Einstein Condensates",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/486zwvb5q08sr",
  "venue": "arXiv",
  "versions": []
}