{
  "abstract": "We study three identical bosons with contact attraction of strength mu on the square lattice at total quasimomentum K = 0 and K = pi. First, at K = 0, for all sufficiently large mu there are exactly two eigenvalues below the essential spectrum. The trimer branch follows from Kato perturbation theory at the simple isolated eigenvalue 3 of the pair-contact operator, uniformly in K; the atom-dimer branch follows from a Feshbach-Schur reduction whose limiting equation coincides with the second Birman-Schwinger (Faddeev) eigenvalue of the finite-rank principal part. The spectral gap between the two branches grows linearly in mu. Second, at K = pi the trimer branch is unchanged up to O(mu^-2), the two-particle threshold equals -mu + 4 exactly, and the gap to it is 2mu - 2 plus lower order corrections. The second bound state disappears because the exchange operator changes sign, S_pi = -S_0: the s-channel eigenvalue that exceeds 1 at K = 0 becomes negative, while the only positive atom-dimer channel at K = pi is the odd p-channel, bounded by 2 - 4/pi < 1. Consequently the operator has exactly one eigenvalue below the threshold minus 36/(mu - 10). Third, the ground state is exponentially localized in the relative coordinates. The decay exponent is positive unconditionally; under a non-cancellation hypothesis it is bounded above by log(3mu) plus lower order terms, while finite-volume computations indicate the slowest tail is the atom-dimer dissociation channel with decay rate one half log(2mu). A dictionary between the principal-part method, Kato theory, and the atom-dimer threshold matrix is given, together with the three-dimensional constants for comparison.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02488",
  "author_total": 4,
  "authors": [
    {
      "name": "Janikul Abdullaev"
    },
    {
      "name": "Abdumalik Eshniyozov"
    },
    {
      "name": "Abdikhurayra Toshturdiev"
    },
    {
      "name": "Mikhail Dolgopolov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/891xcq6yz798j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02488",
  "fulltext_url": null,
  "id": "891xcq6yz798j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02488",
  "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"
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    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7207757153",
  "pdf_url": "https://arxiv.org/pdf/2609.02488",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/891xcq6yz798j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2609.02488",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02488"
    }
  ],
  "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": "Precise spectral asymptotics, exponential localization, and spectral gap estimates for the three-boson lattice Schrödinger operator",
  "title_text": "Precise spectral asymptotics, exponential localization, and spectral gap estimates for the three-boson lattice Schrödinger operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/891xcq6yz798j",
  "venue": "arXiv",
  "versions": []
}