{
  "id": "0804.3362",
  "version": "v1",
  "published": "2008-04-21T17:18:26.000Z",
  "updated": "2008-04-21T17:18:26.000Z",
  "title": "q-Gaussians in the porous-medium equation: stability and time evolution",
  "authors": [
    "Veit Schwämmle",
    "Fernando D. Nobre",
    "Constantino Tsallis"
  ],
  "comment": "20 pages, 6 figures",
  "doi": "10.1140/epjb/e2008-00451-y",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "The stability of $q$-Gaussian distributions as particular solutions of the linear diffusion equation and its generalized nonlinear form, $\\pderiv{P(x,t)}{t} = D \\pderiv{^2 [P(x,t)]^{2-q}}{x^2}$, the \\emph{porous-medium equation}, is investigated through both numerical and analytical approaches. It is shown that an \\emph{initial} $q$-Gaussian, characterized by an index $q_i$, approaches the \\emph{final}, asymptotic solution, characterized by an index $q$, in such a way that the relaxation rule for the kurtosis evolves in time according to a $q$-exponential, with a \\emph{relaxation} index $q_{\\rm rel} \\equiv q_{\\rm rel}(q)$. In some cases, particularly when one attempts to transform an infinite-variance distribution ($q_i \\ge 5/3$) into a finite-variance one ($q<5/3$), the relaxation towards the asymptotic solution may occur very slowly in time. This fact might shed some light on the slow relaxation, for some long-range-interacting many-body Hamiltonian systems, from long-standing quasi-stationary states to the ultimate thermal equilibrium state.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-21T17:18:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.40.Fb",
      "05.20.-y",
      "05.40.Jc"
    ],
    "keywords": [
      "time evolution",
      "porous-medium equation",
      "ultimate thermal equilibrium state",
      "asymptotic solution",
      "q-gaussians"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "European Physical Journal B",
      "year": 2008,
      "month": "Dec",
      "volume": 66,
      "number": 4,
      "pages": 537
    },
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008EPJB...66..537S"
    }
  }
}