{
  "abstract": "Nuclear spin diffusion is often summarized by a single diffusion coefficient, but this coarse-grained description can fail in dilute solids where positional disorder and long-range dipolar couplings generate a broad distribution of hopping rates. We develop a continuous-time random-walk (CTRW) description of $^{13}$C polarization transport in natural-abundance diamond (1.1%), constructing the rate matrix from dipolar-mediated flip-flop couplings and sampling exact continuous-time trajectories. Although site-to-site hopping is Markovian, the disorder-averaged dynamics give rise to emergent, anomalous transport. The empirical waiting-time distribution exhibits a heavy tail with exponent $α=0.64$ and exponential cutoff $t_{\\rm cutoff}=19$ s; the mean jump length becomes correlated with the waiting time $τ$ for $τ\\gtrsim0.1$ s; and the mean-squared displacement grows sublinearly in both step number and physical time, with exponents $γ=0.56$ and $δ=0.87$ respectively. We trace the microscopic origin of these signatures to geometric trapping: polarization can rapidly exchange within strongly coupled clusters, including dimers, while weak inter-cluster links control long-range exploration. A kinetic percolation construction links global transport to inter-cluster crossing times, and identifies a corresponding crossing time of $\\sim20$ s, consistent with $t_{\\rm cutoff}$. Finally, mapping paramagnetic impurities onto hard-sphere traps connects the CTRW framework to classic studies of trapping in reaction-diffusion theory and reproduces the qualitative timescale of experimentally measured relaxation, whereas a continuum diffusion equation description does not. These results show that dilute dipolar spin networks require a microscopic, network-resolved transport description beyond the Fickian diffusion equation.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22626",
  "author_total": 3,
  "authors": [
    {
      "name": "Cooper M. Selco"
    },
    {
      "name": "Christian Bengs"
    },
    {
      "name": "Ashok Ajoy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/etpdk1mbpk9pd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22626",
  "fulltext_url": null,
  "id": "etpdk1mbpk9pd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.22626",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2607.22626",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/etpdk1mbpk9pd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "2607.22626",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22626"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Continuous-Time Random Walk Description of Anomalous Spin Transport in Dilute Dipolar Networks",
  "title_text": "Continuous-Time Random Walk Description of Anomalous Spin Transport in Dilute Dipolar Networks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/etpdk1mbpk9pd",
  "venue": "arXiv",
  "versions": []
}