{
  "id": "1207.6190",
  "version": "v2",
  "published": "2012-07-26T07:51:27.000Z",
  "updated": "2013-03-25T08:02:56.000Z",
  "title": "Fokker-Planck equation with memory: the crossover from ballistic to diffusive processes in many-particle systems and incompressible media",
  "authors": [
    "Valery Ilyin",
    "Itamar Procaccia",
    "Anatoly Zagorodny"
  ],
  "comment": "18 pages, 11 figures",
  "journal": "Condens. Matter Phys., 2013, vol. 16, No. 1, 13004:1-18",
  "doi": "10.5488/CMP.16.13004",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization of the Fokker-Planck equation. The necessary non-Markovian kinetic coefficients are determined by the observable quantities (mean- and mean square displacements). Solutions of the non-Markovian equation describing diffusive processes in the physical space are obtained. For long times, these solutions agree with the predictions of the continuous random walk theory; they are, however, much superior at shorter times when the effect of the ballistic behavior is crucial.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-03-25T08:02:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fokker-planck equation",
      "many-particle systems",
      "incompressible media",
      "equation describing diffusive processes",
      "ballistic behavior"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1207.6190I"
    }
  }
}