{
  "annotation_id": "07c1eaba-60c2-4fb6-b47f-23b025a5db2e",
  "date_created": "2026-02-17T05:53:12.065000Z",
  "date_modified": "2026-02-17T05:53:12.065000Z",
  "file_hash": "55949be56a6860baaaedf465ba9a94eff9ff83f653c55ec5274fc47fd7c43ef2",
  "private": false,
  "record": {
    "abstract": "We consider the Landau Hamiltonian $\\widehat H_B+V$ on $L^2({\\mathbb R}^2)$ with a periodic electric potential $V$. For every $m\\in {\\mathbb N}$ we prove that there exist nonconstant periodic electric potentials $V\\in C^{\\infty }({\\mathbb R}^2;{\\mathbb R})$ with zero mean values that analytically depend on a small parameter $\\varepsilon \\in {\\mathbb R}$ such that the Landau level $(2m+1)B$ is an eigenvalue of the Hamiltonian (of infinite multiplicity) where $B\u003e0$ is a strength of a homogeneous magnetic field.",
    "arxiv_id": "2601.07495",
    "authors": [
      "Leonid Danilov"
    ],
    "categories": [
      "math-ph",
      "math.MP",
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On eigenvalues of the Landau Hamiltonian with a periodic electric potential",
    "url": "https://arxiv.org/abs/2601.07495",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "9f06bd5e-bd3b-454b-b532-b3887f5ec2ff",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}