{
  "abstract": "We prove the existence of an Efimov sequence in an internal gap of the essential spectrum of a three-particle lattice Hamiltonian. The system consists of two identical spinless fermions and one distinguishable particle on \\(\\Z^3\\), with repulsive pair interactions. For each fixed fermion-to-third-particle mass ratio \\(γ>γ_*\\approx13.6069657\\) and total quasi-momentum near \\(π\\mathbf1\\), the mixed zero-range coupling is tuned to a simultaneous upper-threshold resonance. Sufficiently strong nearest-neighbour repulsion between the fermions separates the upper fermion-pair two-cluster spectrum from the free three-particle band. Infinitely many discrete eigenvalues accumulate at the lower endpoint of the resulting gap, which coincides with the free upper edge. We establish logarithmic eigenvalue-counting asymptotics with the same positive coefficient as at zero fermion--fermion coupling. This coefficient also governs accumulation above the essential spectrum throughout the closed weak-coupling interval, including its critical endpoint. We classify the channel spectrum near the free upper edge for all nonnegative fermion couplings.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26284",
  "author_total": 1,
  "authors": [
    {
      "name": "Saidakhmat N. ~Lakaev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wxdpfkzqje3v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26284",
  "fulltext_url": null,
  "id": "2wxdpfkzqje3v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26284",
  "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.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7223034990",
  "pdf_url": "https://arxiv.org/pdf/2610.26284",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wxdpfkzqje3v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26284",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26284"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Efimov effect in an internal spectral gap of a three-particle lattice Hamiltonian",
  "title_text": "Efimov effect in an internal spectral gap of a three-particle lattice Hamiltonian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/2wxdpfkzqje3v",
  "venue": "arXiv",
  "versions": []
}