{
  "abstract": "In 2015, Liu, Qu (Commun. Math. Phys., Vol. 338) show that the Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian admits a positive lower bound independent of the coupling constant lambda: dim_H sigma(H_{tm,lambda}) ge (log 2) / (140log 2.1). In this paper, we prove that the spectrum of the Thue--Morse Hamiltonian has full Hausdorff dimension for any lambda in mathbb{R}: dim_H sigma(H_{tm,lambda})=1.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Computer Science, Beijing Institute of Technology, Beijing, 100081, Peoples’s Republic of China",
    "Department of Mathematics, Tsinghua University, Beijing, 100084, Peoples’s Republic of China"
  ],
  "article_type": null,
  "arxiv": "2609.12782",
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Qinghui Liu",
      "orcid": "0000-0001-8325-0723"
    },
    {
      "affs": [
        1
      ],
      "name": "Yan-Hui Qu",
      "orcid": "0000-0001-8168-7702"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8br79bq18w6f.bib",
  "cited_by": 10,
  "doi": "10.48550/arxiv.2609.12782",
  "fulltext_url": null,
  "id": "a8br79bq18w6f",
  "issns": [
    "2331-8422"
  ],
  "landing_url": "https://arxiv.org/abs/2609.12782",
  "language": "en",
  "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.DS"
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      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
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  "openalex": "W3100024583",
  "pdf_url": "https://arxiv.org/pdf/2609.12782",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": "Cornell University",
  "ris": "https://research.draconitic.com/paper/a8br79bq18w6f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W3100024583",
      "source": "openalex",
      "url": "https://arxiv.org/abs/2609.12782"
    },
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      "native_id": "2609.12782",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12782"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "The Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian",
  "title_text": "The Hausdorff dimension of the spectrum of the Thue-Morse Hamiltonian",
  "type": "preprint",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/a8br79bq18w6f",
  "venue": "arXiv (Cornell University)",
  "versions": []
}