{
  "annotation_id": "f858095d-c2e2-4c3b-9cc3-0846cccb2470",
  "date_created": "2026-03-02T18:01:24.038000Z",
  "date_modified": "2026-03-02T18:01:24.038000Z",
  "file_hash": "e7f8ffaeba9091b7c34aca5b5d1fcdba03639303a931325905161f167b574b32",
  "private": false,
  "record": {
    "abstract": "A new algorithm for determining the eigenstates of n-dimensional billiards is\npresented. It is based on the application of the Cauchy theorem for the\ndetermination of the null space of the boundary overlap matrix. The method is\nfree from the limitations associated with the shape of the billiard and could\nbe applied even for nonconvex geometries where other algorithms face\ndifficulties. Moreover it does not suffer from the existence of eigenvalue\ndegeneracies which is another serious shortcoming of many methods. In the paper\nwe apply the algorithm to a few simple cases where the analytical solutions\nexist. Numerical solutions have been investigated for the case of annular\nbilliard.",
    "arxiv_id": "physics/9902057",
    "authors": [
      "Aurel Bulgac",
      "Piotr Magierski"
    ],
    "categories": [
      "physics.comp-ph",
      "chao-dyn",
      "cond-mat",
      "nlin.CD"
    ],
    "title": "Eigenstates for billiards of arbitrary shapes",
    "url": "https://arxiv.org/abs/physics/9902057"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8f805ec8-4fbc-40da-9fcb-a8d5a1894226",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}