Europhys. Lett.
Volume 73, Number 5, March 2006
Page(s) 726 - 732
Section Condensed matter: structural, mechanical and thermal properties
Published online 18 January 2006
Europhys. Lett., 73 (5), pp. 726-732 (2006)
DOI: 10.1209/epl/i2005-10455-9

Non-exponential relaxation for anomalous diffusion

M. 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.

© EDP Sciences 2006