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.
Categories: cond-mat.stat-mech