Non-exponential relaxation for anomalous diffusionM. H. Vainstein, I. V. L. Costa, R. Morgado and F. A. Oliveira
International Center of Condensed Matter Physics and Institute of Physics University of Brasília - CP 04513 70919-970 Brasília-DF, Brazil
received 10 November 2005; accepted in final form 10 January 2006
published online 18 January 2006
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.
67.40.Fd - Dynamics of relaxation phenomena.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
02.50.Ey - Stochastic processes.
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