2005/01/31 by Mendeli H. Vainstein, Ismael V. L. Costa, Rafael Morgado +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Anomalous diffusion #Computer science #Correlation function (quantum field theory) #Diffusion #Diffusion process #Exponential decay #Exponential function #Fractional Differential Equations Solutions #Function (biology) #Innovation diffusion #Langevin equation #Mathematical analysis #Mathematics #Noise (video) #Physics #Power law #Quantum mechanics #Relaxation (psychology) #Spectral density #Statistical physics #Statistics #cond-mat.dis-nn #stochastic dynamics and bifurcation
paper · pdf · doi:10.1209/epl/i2005-10455-9
published as Europhys. Lett., 73 (5), p. 726 (2006) · 6 pages, 2 figures
openalex publication_date 2006/01/17 · arxiv created 2006/05/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.