{
  "id": "cond-mat/0307139",
  "version": "v2",
  "published": "2003-07-07T13:33:35.000Z",
  "updated": "2004-03-04T19:17:58.000Z",
  "title": "Minimal Stochastic Model for Fermi's Acceleration",
  "authors": [
    "Freddy Bouchet",
    "Fabio Cecconi",
    "Angelo Vulpiani"
  ],
  "comment": "RevTeX4, 4 pages, 2 eps-figures (minor revision)",
  "journal": "Phys. Rev. Lett., vol.92, 040601 (2004)",
  "doi": "10.1103/PhysRevLett.92.040601",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn",
    "nlin.CD"
  ],
  "abstract": "We introduce a simple stochastic system able to generate anomalous diffusion both for position and velocity. The model represents a viable description of the Fermi's acceleration mechanism and it is amenable to analytical treatment through a linear Boltzmann equation. The asymptotic probability distribution functions (PDF) for velocity and position are explicitly derived. The diffusion process is highly non-Gaussian and the time growth of moments is characterized by only two exponents $\\nu_x$ and $\\nu_v$. The diffusion process is anomalous (non Gaussian) but with a defined scaling properties i.e. $P(|{\\bf x}|,t) = 1/t^{\\nu_x}F_x(|{\\bf x}|/t^{\\nu_x})$ and similarly for velocity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-03-04T19:17:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "minimal stochastic model",
      "diffusion process",
      "asymptotic probability distribution functions",
      "fermis acceleration mechanism",
      "simple stochastic system"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. Lett."
    },
    "note": {
      "typesetting": "RevTeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}