{
  "id": "cond-mat/0306601",
  "version": "v1",
  "published": "2003-06-24T12:41:47.000Z",
  "updated": "2003-06-24T12:41:47.000Z",
  "title": "Lévy flights in a steep potential well",
  "authors": [
    "Aleksei V. Chechkin",
    "Vsevolod Yu. Gonchar",
    "Joseph Klafter",
    "Ralf Metzler",
    "Leonid V. Tanatarov"
  ],
  "comment": "13 pages in RevTeX4, numerous gif figures",
  "doi": "10.1023/B:JOSS.0000028067.63365.04",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Lévy flights in steeper than harmonic potentials have been shown to exhibit finite variance and a critical time at which a bifurcation from an initial mono-modal to a terminal bimodal distribution occurs (Chechkin et al., Phys. Rev. E {\\bf 67}, 010102(R) (2003)). In this paper, we present a detailed study of Lévy flights in potentials of the type U(x)∝|x|^c with c>2. Apart from the bifurcation into bimodality, we find the interesting result that for c>4 a trimodal transient exists due to the temporal overlap between the decay of the central peak around the initial $\\delta$-condition and the building up of the two emerging side-peaks, which are characteristic for the stationary state. Thus, for certain system parameters there exists a transient tri-modal distribution of the Lévy flight. These properties of LFs in external potentials of the power-law type can be represented by certain phase diagrams. We also present details about the proof of multi-modality and the numerical procedures to establish the probability distribution of the process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-06-24T12:41:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lévy flights",
      "steep potential",
      "terminal bimodal distribution occurs",
      "transient tri-modal distribution",
      "bifurcation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "RevTeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}