{
  "annotation_id": "488224dc-a551-4c62-bc9a-334dee1656b2",
  "date_created": "2026-03-02T18:01:45.955000Z",
  "date_modified": "2026-03-02T18:01:45.955000Z",
  "file_hash": "3e14201e4b1c30b2a4af299b77eb717d647c953ad5b9076350892b02ac886c20",
  "private": false,
  "record": {
    "abstract": "In this paper we continue to develop our approach to the chaoticity\nproperties of the quantum Hamiltonian systems. Our earlier suggested chaoticity\ncriterion characterizes the initial symmetry breaking and the destruction of\nthe corresponding integrals of motion in a perturbed system, which causes the\nsystem\u0027s chaotisation. Transition from regularity to chaos in quantum systems\noccurs at a certain critical value of the perturbation parameter. In our\nprevious papers we had to diagonalize the perturbed system\u0027s Hamiltonian matrix\nin order to estimate this parameter. In the present paper we demonstrate that\nthe critical perturbation parameter for the transition from regularity to chaos\ncan be estimated in the framework of the first order perturbation theory. The\nvalues of thus obtained critical parameter are in good agreement with the\nresults of our previous precise calculations for Hennon-Heiles Hamiltonian and\ndiamagnetic Kepler problem.",
    "arxiv_id": "quant-ph/0105082",
    "authors": [
      "V. E. Bunakov",
      "I. B. Ivanov",
      "R. B. Panin"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "The critical perturbation parameter estimate for the transition from   regularity to chaos in quantum systems",
    "url": "https://arxiv.org/abs/quant-ph/0105082"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a24a73b5-9689-4c19-b5c6-651968a08299",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}