title: Fractional Langevin equation.
abstract: We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffusion exhibit the same power-law behavior. Here we show that their lowest moments are actually all identical, except the second moment of the velocity. This provides a simple criterion that enable us to distinguish these two non-Markovian processes.
authors.affiliation: Département de Physique Théorique, Université de Genève, 24 quai Ernest Ansermet, 1211 Genève 4, Switzerland.
authors.forename: E
authors.initials: E
authors.lastname: Lutz