Non-exponential relaxation for anomalous diffusion

Details Non-exponential relaxation for anomalous diffusion Non-exponential relaxation for anomalous diffusion

2005-01-21

arxiv.org/abs/cond-mat/0501522v2

Europhys. Lett., 73 (5), p. 726 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

6 pages, 2 figures

Scientific paper

10.1209/epl/i2005-10455-9

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 broad-band noise.

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