Simple stochastic models showing strong anomalous diffusion

Details Simple stochastic models showing strong anomalous diffusion Simple stochastic models showing strong anomalous diffusion

2000-04-05

arxiv.org/abs/cond-mat/0004070v2

Physics

Condensed Matter

Statistical Mechanics

Final version

Scientific paper

10.1007/s100510070032

We show that {\it strong} anomalous diffusion, i.e. $\mean{|x(t)|^q} \sim t^{q \nu(q)}$ where $q \nu(q)$ is a nonlinear function of $q$, is a generic phenomenon within a class of generalized continuous-time random walks. For such class of systems it is possible to compute analytically nu(2n) where n is an integer number. The presence of strong anomalous diffusion implies that the data collapse of the probability density function P(x,t)=t^{-nu}F(x/t^nu) cannot hold, a part (sometimes) in the limit of very small x/t^\nu, now nu=lim_{q to 0} nu(q). Moreover the comparison with previous numerical results shows that the shape of F(x/t^nu) is not universal, i.e., one can have systems with the same nu but different F.

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