{
  "annotation_id": "c9eddfd1-ca95-4806-8d20-9c09e5b01ae9",
  "date_created": "2026-03-02T18:02:48.183000Z",
  "date_modified": "2026-03-02T18:02:48.183000Z",
  "file_hash": "5ef98c45e4dd3c076a4a7ec070f7c0adeecd7ceeae18cb273f59093fd2508842",
  "private": false,
  "record": {
    "abstract": "Geometric phases of simple harmonic oscillator system are studied. Complete\nsets of \"eigenfunctions\" are constructed, which depend on the way of choosing\nclassical solutions. For an eigenfunction, two different motions of the\nprobability distribution function (pulsation of the width and oscillation of\nthe center) contribute to the geometric phase which can be given in terms of\nthe parameters of classical solutions. The geometric phase for a general wave\nfunction is also given. If a wave function has a parity under the inversion of\nspace coordinate, then the geometric phase can be defined under the evolution\nof half of the period of classical motions. For the driven case, geometric\nphases are given in terms of Fourier coefficients of the external force. The\noscillator systems whose classical equation of motion is Mathieu\u0027s equation are\nperturbatively studied, and the first term of nonvanishing geometric phase is\ncalculated.",
    "arxiv_id": "quant-ph/9911030",
    "authors": [
      "JeongHyeong Park",
      "Dae-Yup Song"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Geometric phases in the simple harmonic and perturbative Mathieu\u0027s   oscillator systems",
    "url": "https://arxiv.org/abs/quant-ph/9911030"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f998158a-126b-420f-a714-0158ded26ad9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}