{
  "annotation_id": "20de1cef-fcad-409b-9806-6a39c2807bbe",
  "date_created": "2026-03-02T18:01:53.060000Z",
  "date_modified": "2026-03-02T18:01:53.060000Z",
  "file_hash": "ddffd5b44dde9ce1d64bf2ae68c951147cda7f9fcc86d0a0edd6f051c7a3e61c",
  "private": false,
  "record": {
    "abstract": "We study the Landau-problem on the $\\theta$-deformed two-torus and use\nwell-known projective modules to obtain perturbed spectra. For a strong\nmagnetic field B the problem can be restricted to one particular Landau-level.\nFirst we represent generators of the algebra of the non-commutative torus as\nfinite dimensional matrices. A second approach leads to a reducible\nrepresentation with a $\\theta$-dependent center. For a simple periodic\npotential, the rational part of the Hofstadter-butterfly spectrum is obtained.",
    "arxiv_id": "quant-ph/0210042",
    "authors": [
      "H. Grosse",
      "M. Kornexl"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "journal_ref": "Lett.Math.Phys. 63 (2003) 73-83",
    "title": "The Landau-Problem on the \\theta-Deformed Two-Torus",
    "url": "https://arxiv.org/abs/quant-ph/0210042"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6da7f1bc-b02b-4533-9970-7494059571a6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}