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Fractional Langevin equation

E. Lutz
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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 sub- 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 which enables to distinguish these two non-Markovian processes.

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E. Lutz. 2001-03-06. Fractional Langevin equation. https://doi.org/10.1103/physreve.64.051106

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