{
  "annotation_id": "7c90a7b7-1cfd-4bb9-9f4b-a99144b51c47",
  "date_created": "2026-03-02T18:02:20.582000Z",
  "date_modified": "2026-03-02T18:02:20.582000Z",
  "file_hash": "192b6da5bcc21b429c0d64943cb968c908d356ad68451d66bc1831ba5a323146",
  "private": false,
  "record": {
    "abstract": "We study approximations of billiard systems by lattice graphs. It is\ndemonstrated that under natural assumptions the graph wavefunctions approximate\nsolutions of the Schroedinger equation with energy rescaled by the billiard\ndimension. As an example, we analyze a Sinai billiard with attached leads. The\nresults illustrate emergence of global structures in large quantum graphs and\noffer interesting comparisons with patterns observed in complex networks of a\ndifferent nature.",
    "arxiv_id": "quant-ph/0508226",
    "authors": [
      "Pavel Exner",
      "Pavel Hejcik",
      "Petr Seba"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP"
    ],
    "doi": "10.1016/S0034-4877(06)80031-5",
    "journal_ref": "Rep. Math. Phys. 57 (2006), 445-455",
    "title": "Approximations by graphs and emergence of global structures",
    "url": "https://arxiv.org/abs/quant-ph/0508226"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a7ee8007-98d1-47bd-94ca-13a3d0be45c8",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}