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Non-exponential relaxation for anomalous diffusion

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

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.

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Mendeli H. Vainstein, Ismael V. L. Costa, Rafael Morgado, Fernando A. Oliveira. 2006-05-04. Non-exponential relaxation for anomalous diffusion. https://doi.org/10.1209/epl%2Fi2005-10455-9

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