Non-exponential relaxation for anomalous diffusion

Vainstein, Mendeli H.; Costa, Ismael V. L.; Morgado, Rafael; Oliveira, Fernando A.

Non-exponential relaxation for anomalous diffusion

Authors

Vainstein, Mendeli H.

Costa, Ismael V. L.

Morgado, Rafael

Oliveira, Fernando A.

Description

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.
6 pages, 2 figures