{
  "id": "cond-mat/0207047",
  "version": "v1",
  "published": "2002-07-02T04:39:54.000Z",
  "updated": "2002-07-02T04:39:54.000Z",
  "title": "Anomalous Behaviors in Fractional Fokker-Planck Equation",
  "authors": [
    "Kyungsik Kim",
    "Y. S. Kong"
  ],
  "comment": "10 pages, Latex",
  "journal": "J. Korean Phys. Soc. 40, 979 (2002)",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We introduce a fractional Fokker-Planck equation with a temporal power-law dependence on the drift force fields. For this case, the moments of the tracer from the force-force correlation in terms of the time-dependent drift force fields are discussed analytically. The long-time asymptotic behavior of the second moment is determined by the scaling exponent $\\xi$ imposed by the drift force fields. In the special case of the space scaling value $\\nu=1$ and the time scaling value $\\tau=1$, our result can be classified according to the temporal scaling of the mean second moment of the tracer for large $t$: $< \\bar{x^2(t)} >$ $\\propto$ $t$ with $\\xi={1/4}$ for normal diffusion, and $< \\bar{x^2(t)} >$ $\\propto$ $t^{\\eta}$ with $\\eta>1$ and $\\xi>{1/4}$ for superdiffusion.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-07-02T04:39:54.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional fokker-planck equation",
      "anomalous behaviors",
      "time-dependent drift force fields",
      "long-time asymptotic behavior",
      "mean second moment"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002cond.mat..7047K"
    }
  }
}