{
  "annotation_id": "d94a4f2a-ad82-4260-a54c-77327a5b99c5",
  "date_created": "2026-03-02T18:02:47.709000Z",
  "date_modified": "2026-03-02T18:02:47.709000Z",
  "file_hash": "852be742ea0051725ce5a1ccc0029a635529c17fa4986327420ad4bd89d71114",
  "private": false,
  "record": {
    "abstract": "For a time-dependent $\\tau$-periodic harmonic oscillator of two linearly\nindependent homogeneous solutions of classical equation of motion which are\nbounded all over the time (stable), it is shown, there is a representation of\nstates cyclic up to multiplicative constants under $\\tau$-evolution or\n$2\\tau$-evolution depending on the model. The set of the wave functions is\ncomplete. Berry\u0027s phase which could depend on the choice of representation can\nbe defined under the $\\tau$- or $2\\tau$-evolution in this representation. If a\nhomogeneous solution diverges as the time goes to infinity, it is shown that,\nBerry\u0027s phase can not be defined in any representation considered. Berry\u0027s\nphase for the driven harmonic oscillator is also considered. For the cases\nwhere Berry\u0027s phase can be defined, the phase is given in terms of solutions of\nthe classical equation of motion.",
    "arxiv_id": "quant-ph/9907062",
    "authors": [
      "Dae-Yup Song"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.61.024102",
    "journal_ref": "Phys.Rev.A61:024102,2000",
    "title": "Periodic Hamiltonian and Berry\u0027s phase in harmonic oscillators",
    "url": "https://arxiv.org/abs/quant-ph/9907062"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "c7c46463-bc45-441f-9f67-9f529356cf8e",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}