Anomalous diffusion of a particle in an aging medium

Pottier, N.; Mauger, A.

doi:10.1016/j.physa.2003.10.034

Cited by 25 publications

(18 citation statements)

References 12 publications

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“…Those yield α = 1 + ν, for −1 < ν < 0. The GLE formalism allows ν to assume the values in the range [21,23,32] −1 < ν < 1, which encompass both subdiffusion and superdiffusion. There is a great advantage in our formulation, since the noise density of states exists not only in systems governed by a GLE, but in most physical systems.…”

Section: Discussionmentioning

confidence: 99%

Non-exponential relaxation for anomalous diffusion

et al. 2006

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We study the relaxation process in normal and anomalous diffusion regimes for systems described by a generalized Langevin equation (GLE). We demonstrate the existence of a very general correlation function which describes the relaxation phenomena. Such function is even; therefore, it cannot be an exponential or a stretched exponential. However, for a proper choice of the parameters, those functions can be reproduced within certain intervals with good precision. We also show the passage from the non-Markovian to the Markovian behaviour in the normal diffusion regime. For times longer than the relaxation time, the correlation function for anomalous diffusion becomes a power law for broadband noise.

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Section: Discussionmentioning

confidence: 99%

Non-exponential relaxation for anomalous diffusion

et al. 2006

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“…For an out of equilibrium bath as characterized by an effective temperature T eff. (ω), we showed in [11] that, if the latter can be modelized by an inverse power-law of ω at small ω, the diffusion exponent depends on both exponents associated with ℜe µ(ω) and T eff. (ω).…”

Section: Introductionmentioning

confidence: 91%

Out of equilibrium generalized Stokes–Einstein relation: determination of the effective temperature of an aging medium

Pottier

2005

Physica A: Statistical Mechanics and its Applications

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We analyze in details how the anomalous drift and diffusion properties of a particle evolving in an aging medium can be interpreted in terms of an effective temperature of the medium. From an experimental point of view, independent measurements of the mean-square displacement and of the mobility of a particle immersed in an aging medium such as a colloidal glass give access to an out of equilibrium generalized Stokes-Einstein relation, from which the effective temperature of the medium can eventually be deduced. We illustrate the procedure on a simple model with power-law behaviours. PACS:05.40.-a Fluctuation phenomena, random processes, noise and Brownian motion 02.50.Ey Stochastic processes

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“…This situation arises if one considers the diffusion of a Brownian particle in a complex medium (e.g. a glass, or granular matter) [35][36][37]. In this case the medium, which acts as a thermal bath with respect to the Brownian particle, is itself out of equilibrium.…”

Section: A Connection Between the Two?mentioning

confidence: 99%