Non-exponential relaxation for anomalous diffusion

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

Published 2005-01-21, updated 2006-05-04Version 2

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.