{
  "abstract": "We study spectral measures of one-dimensional quasiperiodic Schrödinger operators. For subcritical Schrödinger operator with Diophantine frequency, we prove sharp measurable-set bounds, answering a question of Avila and Jitomirskaya \\cite{AJ}; we prove optimal Fourier decay and the sharp decay order of the time-averaged quantum return probability, confirming a conjecture of Aloisio, Carvalho, and de Oliveira \\cite{ACO} and a prediction of Zhong and Mosseri \\cite{ZhongMosseri}. For the subcritical almost Mathieu operator, we establish summable square-root envelopes for the spectral density, with an optimal density-one formulation of the lower bound, thereby answering a question of Avila \\cite{Aqi}. These results follow from a general theorem for reflectionless measures under a summable square-root Craig-type condition. We establish an exact residue expansion of the squared Borel transform, which connects local density blow-up with long-time averaged return probabilities: the endpoint residues determine both the square-root edge profiles and the leading coefficient of the time-averaged return probability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18259",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhenfu Wang"
    },
    {
      "name": "Qi Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3017k14kxtzb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18259",
  "fulltext_url": null,
  "id": "b3017k14kxtzb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18259",
  "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.DS"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7221827527",
  "pdf_url": "https://arxiv.org/pdf/2610.18259",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3017k14kxtzb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.18259",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18259"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Square-Root Profiles and Sharp Fourier Decay of Quasiperiodic Spectral Measures",
  "title_text": "Square-Root Profiles and Sharp Fourier Decay of Quasiperiodic Spectral Measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/b3017k14kxtzb",
  "venue": "arXiv",
  "versions": []
}