A Huygens principle for diffusion and anomalous diffusion in spatially extended systems

Abstract

We present a universal view on diffusive behaviour in chaotic spatially extended systems for anisotropic and isotropic media. For anisotropic systems, strong chaos leads to diffusive behaviour (Brownian motion with drift) and weak chaos leads to superdiffusive behaviour (Lévy processes with drift). For isotropic systems, the drift term vanishes and strong chaos again leads to Brownian motion. We establish the existence of a nonlinear Huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behaviour in odd space dimensions.

Supplementary information (referred to in paper) can be found on authors' websites and on the journal website. The title has been changed and labelling updated in accordance with regulations of the journal Proc. Natl. Acad. Sci. USA (2013)

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