{
  "abstract": "We compare two three-particle lattice models on the square lattice at total quasimomentum zero: three identical bosons with attractive contact interactions, and a two-fermion plus one distinguishable particle system with attractive interspecies contact. Using the Birman--Schwinger principle combined with symmetry reduction and strong-coupling asymptotics, we distinguish shared methodology from model-dependent spectral conclusions. For bosons, the ground-state energy behaves as minus three times the coupling plus six minus three over twice the coupling plus higher-order corrections, and exactly two bound states exist below the threshold for large coupling; the second lies at a finite distance 0.03542 below the threshold, a genuine eigenvalue rather than a threshold resonance. For fermions, the critical mass ratio is pi divided by pi minus two, approximately 2.75194; above it, a doubly degenerate level appears at strong coupling. Near onset, the binding energy follows a linear-over-logarithmic law. The results are compared with numerical finite-grid Faddeev computations and with recent three-dimensional classifications of threshold states.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37142",
  "author_total": 3,
  "authors": [
    {
      "name": "Janikul Abdullaev"
    },
    {
      "name": "Abdumalik Eshniyozov"
    },
    {
      "name": "Mikhail Dolgopolov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3e33m6cwrrca2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37142",
  "fulltext_url": null,
  "id": "3e33m6cwrrca2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37142",
  "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",
      "cond-mat.quant-gas"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7224111732",
  "pdf_url": "https://arxiv.org/pdf/2610.37142",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3e33m6cwrrca2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.37142",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37142"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "amo"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.quant-gas",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Threshold Criteria for Bosonic and Fermionic Trimers on a Square Lattice: A Birman--Schwinger Comparison",
  "title_text": "Threshold Criteria for Bosonic and Fermionic Trimers on a Square Lattice: A Birman--Schwinger Comparison",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/3e33m6cwrrca2",
  "venue": "arXiv",
  "versions": []
}