{
  "annotation_id": "2a66fc36-e261-473f-a36d-3d2926e96fc3",
  "date_created": "2026-03-02T18:01:14.470000Z",
  "date_modified": "2026-03-02T18:01:14.470000Z",
  "file_hash": "3bf839f33b08e218bebf33fa1aaae2944965d90c09b6bd288786c24ea59aa38e",
  "private": false,
  "record": {
    "abstract": "A hierarchical ordering is demonstrated for the periodic orbits in a strongly\ncoupled multidimensional Hamiltonian system, namely the hydrogen atom in\ncrossed electric and magnetic fields. It mirrors the hierarchy of broken\nresonant tori and thereby allows one to characterize the periodic orbits by a\nset of winding numbers. With this knowledge, we construct the action variables\nas functions of the frequency ratios and carry out a semiclassical torus\nquantization. The semiclassical energy levels thus obtained agree well with\nexact quantum calculations.",
    "arxiv_id": "physics/0610013",
    "authors": [
      "Stephan Gekle",
      "J\u00f6rg Main",
      "Thomas Bartsch",
      "T. Uzer"
    ],
    "categories": [
      "physics.atom-ph",
      "nlin.CD"
    ],
    "doi": "10.1103/PhysRevA.75.023406",
    "title": "Hydrogen atom in crossed electric and magnetic fields: Phase space   topology and torus quantization via periodic orbits",
    "url": "https://arxiv.org/abs/physics/0610013"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "6ca2a92f-4119-44f6-8dff-b74c783f7048",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}