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Anomalous diffusion of a particle in an aging medium

Author

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  • Pottier, Noëlle
  • Mauger, Alain

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 |ω|δ−1 at small frequencies, with 0<δ<2. The aging properties of the medium are encoded in a frequency-dependent effective temperature Teff.(ω). The latter is modelized by a function proportional to |ω|α at small frequencies, with α<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 δ as it would be the case in a thermal bath, but also to the exponent α characterizing the density of slow modes.

Suggested Citation

  • Pottier, Noëlle & Mauger, Alain, 2004. "Anomalous diffusion of a particle in an aging medium," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 15-28.
    • Handle: RePEc:eee:phsmap:v:332:y:2004:i:c:p:15-28
    DOI: 10.1016/j.physa.2003.10.034
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