{
  "abstract": "We study the block Anderson Hamiltonian \\(H_L=λΨ_L+\\mathcal V\\) on the discrete torus \\((\\mathbb Z/L\\mathbb Z)^d\\), \\(d\\geq2\\), where \\(Ψ_L\\) is the nearest-neighbor Laplacian and \\(\\mathcal V\\) consists of independent \\(W^d\\times W^d\\) GOE blocks. In the weak-disorder limit \\(λ\\to\\infty\\), we establish an entrywise local law, a spatial scaling limit for the squared resolvent entries, time-averaged dynamical delocalization, and lower bounds on the localization length of most bulk eigenfunctions. Particularly, we allow the block size to be fixed or grow above a polylogarithmic threshold. In sufficiently large polynomial volumes, the dynamical estimates hold for \\(C_δ(λ+W/λ)\\leq T\\leq λ^{1+κ_d^{\\rm BA}-δ}\\), with a dimension-dependent exponent \\(κ_d^{\\rm BA}>0\\), and the spreading scale is \\(\\sqrt{(λ^3+λW)T}\\). This identifies a transition at \\(W\\asympλ^2\\) between \\(λ^{3/2}\\sqrt T\\) and \\(\\sqrt{λWT}\\). The proof combines Gaussian moment estimates with deterministic stability of a matrix Dyson equation. A partial Bloch transform handles fixed blocks, while scalar reduction controls growing blocks. A Feshbach--Schur reduction of the block \\(T\\)-equation separates a single scalar diffusion mode from the stable internal cell modes. A renewal expansion and exact cell counting give a positive representation of the diffusion coefficient and control the fourth moment uniformly across the block-size transition. Notably, our argument does not require an enumeration of Feynman diagrams.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00598",
  "author_total": 1,
  "authors": [
    {
      "name": "Haoxuan Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6t0vsegydpyew.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00598",
  "fulltext_url": null,
  "id": "6t0vsegydpyew",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00598",
  "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-ph"
    ],
    [
      "arxiv",
      "math.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00598",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6t0vsegydpyew.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:20:59Z",
      "native_id": "2611.00598",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00598"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Quantum Diffusion and the Block-Size Crossover in the Block Anderson Model",
  "title_text": "Quantum Diffusion and the Block-Size Crossover in the Block Anderson Model",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/6t0vsegydpyew",
  "venue": "arXiv",
  "versions": []
}