{
  "id": "cond-mat/0307078",
  "version": "v1",
  "published": "2003-07-03T15:01:28.000Z",
  "updated": "2003-07-03T15:01:28.000Z",
  "title": "Anomalous diffusion of a particle in an aging medium",
  "authors": [
    "Noelle Pottier",
    "Alain Mauger"
  ],
  "journal": "Physica A 332, 15 (2004)",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "We report new results about the anomalous diffusion of a particle in an aging medium. For each given age, the quasi-stationary particle velocity is governed by a generalized Langevin equation with a frequency-dependent friction coefficient proportional to $|\\omega|^{\\delta-1}$ at small frequencies, with $0<\\delta<2$. The aging properties of the medium are encoded in a frequency dependent effective temperature $T_{\\rm eff.}(\\omega)$. The latter is modelized by a function proportional to $|\\omega|^\\alpha$ at small frequencies, with $\\alpha<0$, thus allowing for the medium to have a density of slow modes proportionally larger than in a thermal bath. Using asymptotic Fourier analysis, we obtain the behaviour at large times of the velocity correlation function and of the mean square displacement. As a result, the anomalous diffusion exponent in the aging medium appears to be linked, not only to $\\delta$ as it would be the case in a thermal bath, but also to the exponent $\\alpha$ characterizing the density of slow modes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-07-03T15:01:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "anomalous diffusion",
      "thermal bath",
      "frequency-dependent friction coefficient proportional",
      "small frequencies",
      "mean square displacement"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}