2003/07/03 by Noëlle Pottier, Noelle Pottier, A. Mauger +1 · 3 citations
Materials Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Anomalous diffusion #Condensed matter physics #Correlation function (quantum field theory) #Diffusion #Displacement (psychology) #Exponent #Function (biology) #Geometry #Material Dynamics and Properties #Mathematics #Mean squared displacement #Molecular dynamics #Omega #Physics #Quantum mechanics #Square (algebra) #Thermodynamics #cond-mat.soft #cond-mat.stat-mech #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/j.physa.2003.10.034
published as Physica A 332, 15 (2004)
arxiv created 2003/07/03 · openalex publication_date 2003/11/07 · arxiv updated 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 T\rm eff.(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.