{
  "abstract": "We establish a criterion of arithmetic $k$-polynomial spectral localization and $k$-polynomial dynamical localization in expectation for quasi-periodic long-range operators on $\\ell^2(\\mathbb{Z}^{d})$ with power-law hopping based on the quantitative $C^{k}$-reducibility of the dual Schrödinger cocycle. As the application, we prove both localization properties for power-law long-range perturbations of the Almost Mathieu Operators with sufficiently large couplings and Diophantine frequencies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.26012",
  "author_total": 4,
  "authors": [
    {
      "name": "Ao Cai"
    },
    {
      "name": "Huihui Lv"
    },
    {
      "name": "Yuan Shan"
    },
    {
      "name": "Xueyin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2wcn3y3f9arq5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.26012",
  "fulltext_url": null,
  "id": "2wcn3y3f9arq5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.26012",
  "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.DS"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214105384",
  "pdf_url": "https://arxiv.org/pdf/2609.26012",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2wcn3y3f9arq5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.26012",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.26012"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "Arithmetic $k$-Polynomial Dynamical Localization for $k$ Power-Law Quasi-Periodic Long-Range Operators on $\\ell^2(\\mathbb{Z}^d)$",
  "title_text": "Arithmetic k-Polynomial Dynamical Localization for k Power-Law Quasi-Periodic Long-Range Operators on ℓ^2(ℤ^d)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/2wcn3y3f9arq5",
  "venue": "arXiv",
  "versions": []
}