{
  "id": "1504.06382",
  "version": "v1",
  "published": "2015-04-24T03:19:58.000Z",
  "updated": "2015-04-24T03:19:58.000Z",
  "title": "The precise time-dependent solution of the Fokker-Planck equation with anomalous diffusion",
  "authors": [
    "Guo Ran",
    "Du Jiulin"
  ],
  "comment": "12 pages,6 figures",
  "doi": "10.1016/j.aop.2015.04.019",
  "categories": [
    "cond-mat.stat-mech",
    "physics.chem-ph"
  ],
  "abstract": "We study the time behavior of the Fokker-Planck equation in Zwanzig rule (the backward-Ito rule) based on the Langevin equation of Brownian motion with an anomalous diffusion in a complex medium. The diffusion coefficient is a function in momentum space and follows a generalized fluctuation-dissipation relation. We obtain the precise time-dependent analytical solution of the Fokker-Planck equation and at long time the solution approaches to a stationary power-law distribution in nonextensive statistics. As a test, numerically we have demonstrated the accuracy and validity of the time-dependent solution.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-24T03:19:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fokker-planck equation",
      "precise time-dependent solution",
      "anomalous diffusion",
      "stationary power-law distribution",
      "precise time-dependent analytical solution"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150406382G"
    }
  }
}