A mechanical model of normal and anomalous diffusion

Details A mechanical model of normal and anomalous diffusion A mechanical model of normal and anomalous diffusion

2002-02-14

arxiv.org/abs/nlin/0202029v1

Nonlinear Sciences

Chaotic Dynamics

16 pages, no figures

Scientific paper

10.1103/PhysRevE.67.011102

The overdamped dynamics of a charged particle driven by an uniform electric field through a random sequence of scatterers in one dimension is investigated. Analytic expressions of the mean velocity and of the velocity power spectrum are presented. These show that above a threshold value of the field normal diffusion is superimposed to ballistic motion. The diffusion constant can be given explicitly. At the threshold field the transition between conduction and localization is accompanied by an anomalous diffusion. Our results exemplify that, even in the absence of time-dependent stochastic forces, a purely mechanical model equipped with a quenched disorder can exhibit normal as well as anomalous diffusion, the latter emerging as a critical property.

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