{
  "annotation_id": "e698676b-b66c-4b12-92ca-a909c3868380",
  "date_created": "2026-03-02T18:01:42.419000Z",
  "date_modified": "2026-03-02T18:01:42.419000Z",
  "file_hash": "96ea19800074cddcf25c4a723329801df9532cccd702d6b46075eca5b4782bf0",
  "private": false,
  "record": {
    "abstract": "This article deals with non-adiabatic processes (i.e. processes excluded by\nthe adiabatic theorem) from the geometrical (group-theoretical) point of view.\nAn approximated formula for the probabilities of the non-adiabatic transitions\nis derived in the adiabatic regime for the case when the parameter-dependent\nHamiltonian represents a smooth curve in the Lie algebra and the quantal\ndynamics is determined by the corresponding Lie group evolution operator. We\ntreat the spin precession in a time-dependent magnetic field and the\nover-barrier reflection problem in a uniform way using the first-order\ndynamical equations on SU(2) and $SU(1.1)$ group manifolds correspondingly.\n  A comparison with analytic solutions for simple solvable models is provided.",
    "arxiv_id": "quant-ph/0011121",
    "authors": [
      "M. S. Marinov",
      "E. Strahov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/34/8/317",
    "title": "A geometrical approach to non-adiabatic transitions in quantum theory:   applications to NMR, over-barrier reflection and parametric excitation of   quantum oscillator",
    "url": "https://arxiv.org/abs/quant-ph/0011121"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "7a0dfa0d-c2e6-492f-87a5-b085421e4a07",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}