{
  "id": "1106.0458",
  "version": "v2",
  "published": "2011-06-02T15:58:09.000Z",
  "updated": "2011-12-14T15:54:43.000Z",
  "title": "Approach to equilibrium of diffusion in a logarithmic potential",
  "authors": [
    "Ori Hirschberg",
    "David Mukamel",
    "Gunter M. Schütz"
  ],
  "comment": "4 pages, 3 figures; Published version",
  "journal": "Phys. Rev. E 84, 041111 (2011)",
  "doi": "10.1103/PhysRevE.84.041111",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x ~ t^(1/2)) and a subdiffusive (x ~ t^{\\gamma} with a given {\\gamma} < 1/2) length scale, respectively, (ii) the overall scaling function is selected by the initial condition, and (iii) depending on the tail of the initial condition, the scaling exponent which characterizes the scaling function is found to exhibit a transition from a continuously varying to a fixed value.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-14T15:54:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.-a",
      "05.10.Gg"
    ],
    "keywords": [
      "equilibrium",
      "late-time distribution function",
      "one-dimensional logarithmic potential",
      "arbitrary initial conditions",
      "length scale"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Physical Review E",
      "year": 2011,
      "month": "Oct",
      "volume": 84,
      "number": 4,
      "pages": "041111"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011PhRvE..84d1111H"
    }
  }
}