{
  "abstract": "We investigate single-excitation quantum walks across the one-to-two-dimensional crossover in diluted power-law hopping models. Using arrays of $\\ell$ coupled chains of length $L$, we identify the finite-size localization crossover from the longitudinal spreading of an initially localized excitation. The crossover filling is well described by an exponential approach to its two-dimensional value with increasing $\\ell$, defining a characteristic transverse scale $\\ell_e$, and effectively two-dimensional behavior emerges already for $\\ell\\ll L$. An independent spectral analysis shows that $\\ell_e$ is set by the transverse extent of the eigenstates participating in the dynamics, providing a microscopic interpretation of the dimensional crossover. Our results reveal an intrinsic eigenstate scale governing emergent dimensionality in diluted systems with power-law hopping, a regime directly relevant to recently developed arrays of polar molecules, Rydberg atoms, and other quantum simulators with long-range interactions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07856",
  "author_total": 2,
  "authors": [
    {
      "name": "G. A. Domínguez-Castro"
    },
    {
      "name": "L. Santos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a2c4n0a0dw5pe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07856",
  "fulltext_url": null,
  "id": "a2c4n0a0dw5pe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07856",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.dis-nn"
    ],
    [
      "openalex",
      "3107|Quantum many-body systems"
    ]
  ],
  "openalex": "W7221012457",
  "pdf_url": "https://arxiv.org/pdf/2610.07856",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a2c4n0a0dw5pe.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07856",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07856"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    }
  ],
  "title": "Emergent Dimensionality in Diluted Power-Law Quantum Walks",
  "title_text": "Emergent Dimensionality in Diluted Power-Law Quantum Walks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:22Z",
  "url": "https://research.draconitic.com/paper/a2c4n0a0dw5pe",
  "venue": "arXiv",
  "versions": []
}