Fractional Langevin equation - art. no. 051106

We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to st udy both subdiffusion and superdiffusion of a free particle coupled to a fr actal heat bath. We further compare fractional Brownian motion with the fra ctal time process. The respective mean-square displacements of these two fo rms of anomalous diffusion exhibit the same power-law behavior. Here we sho w that their lowest moments are actually all identical, except the second m oment of the velocity. This provides a simple criterion that enable us to d istinguish these two non-Markovian processes.