{
  "abstract": "We study stochastic and sharp restart in a one-dimensional lackadaisical discrete-time quantum walk with self-loop weight $\\ell$. In the absence of restart, the dynamics has a flat band responsible for intrinsic localization and two dispersive bands supporting ballistic propagation. We compare two initially localized benchmark states: a flat-band-active state with finite flat-band overlap and a flat-band-dark state with zero flat-band overlap. For geometric stochastic restart with per-step restart probability $q$, the stationary mean-squared displacement scales as $q^{-2}$ as $q\\to0$. In the same limit, the restart-site occupation probability approaches the restart-free intrinsic localized value for the flat-band-active state, whereas for the flat-band-dark state it vanishes as $q\\ln(1/q)$. For power-law restart, where $p_m\\propto m^{-s}$ is the probability that the waiting time to the next restart is $m$ steps, a normalized stationary site-occupation distribution exists only for $s>2$, while the stationary absolute spatial moment of order $p$ is finite only for $s>p+2$. In the regime $1<s\\leq2$, at every fixed lattice site, the flat-band-active occupation converges to the intrinsic flat-band profile, while the flat-band-dark occupation tends to zero. We also consider monitored first detection with sharp restart, in which the walk is reinitialized after a fixed number $r$ of consecutive unsuccessful measurements. For fixed $r$, the mean first-detected-passage time of the flat-band-active state exhibits a minimum at an intermediate self-loop weight, whereas the flat-band-dark state approaches a ballistic detection limit as $\\ell\\to\\infty$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08973",
  "author_total": 1,
  "authors": [
    {
      "name": "Debraj Das"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3gabbte31y7r7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08973",
  "fulltext_url": null,
  "id": "3gabbte31y7r7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08973",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7212005490",
  "pdf_url": "https://arxiv.org/pdf/2609.08973",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3gabbte31y7r7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:52Z",
      "native_id": "2609.08973",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08973"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Restart and first detection in a lackadaisical quantum walk with flat-band localization",
  "title_text": "Restart and first detection in a lackadaisical quantum walk with flat-band localization",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:52Z",
  "url": "https://research.draconitic.com/paper/3gabbte31y7r7",
  "venue": "arXiv",
  "versions": []
}