{
  "abstract": "A uniform magnetic field completely suppresses long-time dispersion for the Euclidean Landau Hamiltonian. We show that negative curvature fundamentally changes this behavior. For the Landau Hamiltonian with arbitrary field strength $B\\in\\mathbb R$ on the hyperbolic plane $\\mathbb H$, we establish sharp dispersive estimates for the Schrödinger evolution on the absolutely continuous spectral subspace. The decay is $|t|^{-1}$ at short times and, strikingly, improves to $|t|^{-3/2}$ at large times whenever $B\\notin\\frac12+\\mathbb Z$. At half-integer fields, we identify a threshold resonance and isolate its leading contribution, which yields the slower but sharp rate $|t|^{-1/2}$. Thus the long-time dynamics exhibit a resonance-driven dichotomy with no analogue in the flat constant-field problem. Our analysis is based on an explicit representation of the magnetic Schrödinger kernel together with a precise separation of the Landau levels and threshold profile. As a further consequence, for every nonthreshold field we obtain global-in-time Strichartz estimates on the absolutely continuous spectral subspace throughout the full hyperbolic admissible region.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12999",
  "author_total": 4,
  "authors": [
    {
      "name": "Huanqing Guo"
    },
    {
      "name": "Haoran Wang"
    },
    {
      "name": "Junyong Zhang"
    },
    {
      "name": "Jiqiang Zheng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/238s3q6y1b1ph.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12999",
  "fulltext_url": null,
  "id": "238s3q6y1b1ph",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12999",
  "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"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212692108",
  "pdf_url": "https://arxiv.org/pdf/2609.12999",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/238s3q6y1b1ph.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12999",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12999"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Dispersive estimates for the Landau Hamiltonian on the hyperbolic plane",
  "title_text": "Dispersive estimates for the Landau Hamiltonian on the hyperbolic plane",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/238s3q6y1b1ph",
  "venue": "arXiv",
  "versions": []
}