{
  "abstract": "We study magnetic Bloch eigenvalue problems for two-dimensional magnetic Schrödinger operators with nonuniform periodic magnetic fields and periodic scalar potentials, and develop a hybrid Fourier-finite difference discretization. A Landau-type gauge is constructed by solving a periodic Poisson equation. Under the integer magnetic flux condition, the magnetic Bloch boundary conditions are incorporated through shifts of Fourier-mode indices. The method combines link-variable-based covariant central differences in the $x$-direction with a Fourier pseudospectral discretization in the $y$-direction, yielding a Hermitian discrete Hamiltonian. The resulting eigenvalue problems are solved using a LOBPCG method. Under appropriate regularity assumptions, we establish a fully discrete consistency residual estimate of order $O(h_1^2+N_2^{-s})$. With suitable spectral separation and eigenspace dimension-preserving conditions, error estimates of the same order are derived for isolated eigenvalues and their associated eigenspaces. Numerical experiments show second-order convergence in the finite difference direction and rapid error reduction with increasing Fourier resolution, and illustrate band degeneracies and eigenstate distributions in nonuniform periodic magnetic fields.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05950",
  "author_total": 2,
  "authors": [
    {
      "name": "Xueyang Li"
    },
    {
      "name": "Yuanwei Lai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5b2qzpb06h6qg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05950",
  "fulltext_url": null,
  "id": "5b2qzpb06h6qg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05950",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05950",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5b2qzpb06h6qg.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:20:56Z",
      "native_id": "2611.05950",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05950"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Magnetic Bloch eigenvalue problems in nonuniform periodic magnetic fields: a Fourier-finite difference approach",
  "title_text": "Magnetic Bloch eigenvalue problems in nonuniform periodic magnetic fields: a Fourier-finite difference approach",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/5b2qzpb06h6qg",
  "venue": "arXiv",
  "versions": []
}