{
  "id": "1302.0456",
  "version": "v1",
  "published": "2013-02-03T04:58:16.000Z",
  "updated": "2013-02-03T04:58:16.000Z",
  "title": "Aharonov-Bohm effect and geometric phases -- Exact and approximate topology",
  "authors": [
    "Kazuo Fujikawa"
  ],
  "comment": "6 pages. Invited talk given at Tonomura FIRST International Symposium on Electron Microscopy and Gauge Fields, May 9-10, 2012, Tokyo, Japan",
  "categories": [
    "quant-ph",
    "cond-mat.str-el",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "By analyzing an exactly solvable model in the second quantized formulation which allows a unified treatment of adiabatic and non-adiabatic geometric phases, it is shown that the topology of the adiabatic Berry's phase, which is characterized by the singularity associated with possible level crossing, is trivial in a precise sense. This topology of the geometric phase is quite different from the topology of the Aharonov-Bohm effect, where the topology is specified by the external local gauge field and it is exact for the slow as well as for the fast motion of the electron.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-03T04:58:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "aharonov-bohm effect",
      "approximate topology",
      "external local gauge field",
      "non-adiabatic geometric phases",
      "adiabatic berrys phase"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 1219011,
      "adsabs": "2014imat.conf..130F"
    }
  }
}