{
  "abstract": "In this paper, we consider one-dimensional discrete Schrödinger operators \\begin{align} Hu(n)=(Δ+V)u(n)\\nonumber \\end{align} on $\\ell^2(\\mathbb{N})$ with a self-adjoint boundary condition at $n=0$, where $Δ$ denotes the discrete Laplacian and $V(n)$ is a real-valued perturbation satisfying $$V(n)=\\frac{O(1)}{1+n}.$$ We determine the sharp transition for the asymptotic coefficient of \\(V\\) governing the existence and nonexistence of embedded eigenvalues.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03224",
  "author_total": 3,
  "authors": [
    {
      "name": "Jifeng Chu"
    },
    {
      "name": "Wencai Liu"
    },
    {
      "name": "Kang Lyu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0z9z9f0y4d9jd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03224",
  "fulltext_url": null,
  "id": "0z9z9f0y4d9jd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03224",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.03224",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0z9z9f0y4d9jd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:31Z",
      "native_id": "2609.03224",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03224"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Optimal bounds for embedded eigenvalues of one-dimensional discrete Schrödinger operators with decaying potentials",
  "title_text": "Optimal bounds for embedded eigenvalues of one-dimensional discrete Schrödinger operators with decaying potentials",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/0z9z9f0y4d9jd",
  "venue": "arXiv",
  "versions": []
}