{
  "annotation_id": "9fbf4f30-c717-413c-9f78-5f768214d787",
  "date_created": "2026-03-02T18:02:13.453000Z",
  "date_modified": "2026-03-02T18:02:13.453000Z",
  "file_hash": "4a4beaa0bc8dfa70e9b39f5ef88e6dc25c032c0a9521459c6939587c72bc4561",
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  "record": {
    "abstract": "By using a second quantized formulation of level crossing, which does not\nassume adiabatic approximation, a convenient formula for geometric terms\nincluding off-diagonal terms is derived. The analysis of geometric phases is\nreduced to a simple diagonalization of the Hamiltonian in the present\nformulation. If one diagonalizes the geometric terms in the infinitesimal\nneighborhood of level crossing, the geometric phases become trivial for any\nfinite time interval $T$. The topological interpretation of Berry\u0027s phase such\nas the topological proof of phase-change rule thus fails in the practical\nBorn-Oppenheimer approximation, where a large but finite ratio of two time\nscales is involved.",
    "arxiv_id": "quant-ph/0411006",
    "authors": [
      "Kazuo Fujikawa"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1142/S0217732305016579",
    "journal_ref": "Mod.Phys.Lett. A20 (2005) 335-344",
    "title": "Topological properties of Berry\u0027s phase",
    "url": "https://arxiv.org/abs/quant-ph/0411006"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8580e039-f824-423e-81d0-25830d976d1d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}