Anomalous diffusion of a particle in an aging medium

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 $T_{eff.}(\omega )$. 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.

References in corpus (2)

• Aging properties of an anomalously diffusing particle
• Experimental study of the Fluctuation-Dissipation-Relation during an aging process

Cited by in corpus (8)

• Slow dynamics in glassy soft matter
• Probing an nonequilibrium Einstein relation in an aging colloidal glass
• Fluctuation theorem for non-equilibrium relaxational systems driven by external forces
• Intermediate dynamics between Newton and Langevin
• Non-exponential relaxation for anomalous diffusion
• On the Fluctuation-Dissipation Relation in non-equilibrium and non-Hamiltonian systems
• Out of equilibrium generalized Stokes-Einstein relation: determination of the effective temperature of an aging medium
• Brownian motion and anomalous diffusion revisited via a fractional Langevin equation