paper

Simple stochastic models showing strong anomalous diffusion

arXiv:cond-mat/0004070 · doi:10.1007/s100510070032

Abstract

We show that {\it strong} anomalous diffusion, i.e. $\mean{|x(t)|^q} \sim t^{q ν(q)}$ where is a nonlinear function of , 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^ν, 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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