The renormalization group and fractional Brownian motion

Details The renormalization group and fractional Brownian motion The renormalization group and fractional Brownian motion

2002-06-06

arxiv.org/abs/cond-mat/0206083v1

Phys.Lett. A296 (2002) 272

Physics

Condensed Matter

Statistical Mechanics

14 pages (REVTeX4), no figures

Scientific paper

10.1016/S0375-9601(02)00290-6

We find that in generic field theories the combined effect of fluctuations and interactions leads to a probability distribution function which describes fractional Brownian Motion (fBM) and ``complex behavior''. To show this we use the Renormalization Group as a tool to improve perturbative calculations, and check that beyond the classical regime of the field theory (i. e., when no fluctuations are present) the non--linearities drive the probability distribution function of the system away from classical Brownian Motion and into a regime which to the lowest order is that of fBM. Our results can be applied to systems away from equilibrium and to dynamical critical phenomena. We illustrate our results with two selected examples: a particle in a heat bath, and the KPZ equation.

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