Non-exponential relaxation for anomalous diffusion

Abstract

We study the relaxation process in normal and anomalous diffusion regimes for\nsystems described by a generalized Langevin equation (GLE). We demonstrate the\nexistence of a very general correlation function which describes the relaxation\nphenomena. Such function is even; therefore, it cannot be an exponential or a\nstretched exponential. However, for a proper choice of the parameters, those\nfunctions can be reproduced within certain intervals with good precision. We\nalso show the passage from the non-Markovian to the Markovian behaviour in the\nnormal diffusion regime. For times longer than the relaxation time, the\ncorrelation function for anomalous diffusion becomes a power law for broad-band\nnoise.\n