{
  "id": "cond-mat/0307306",
  "version": "v1",
  "published": "2003-07-14T12:04:39.000Z",
  "updated": "2003-07-14T12:04:39.000Z",
  "title": "Dilatation symmetry of the Fokker-Planck equation and anomalous diffusion",
  "authors": [
    "Sumiyoshi Abe"
  ],
  "comment": "15 pages, no figures, discussions expanded",
  "doi": "10.1103/PhysRevE.69.016102",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Based on the canonical formalism, the dilatation symmetry is implemented to the Fokker-Planck equation for the Wigner distribution function that describes atomic motion in an optical lattice. This reveals the symmetry principle underlying the recent result obtained by Lutz [Phys. Rev. A 67, 051402(R) (2003)] on the connection between anomalous transport in the optical lattice and Tsallis statistics in the high-energy regime.Lutz's discussion is generalized to the nonstationary case, and the condition, under which the solution distribution decays as a power law, is derived.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-07-14T12:04:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fokker-planck equation",
      "dilatation symmetry",
      "anomalous diffusion",
      "solution distribution decays",
      "wigner distribution function"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}