1212.1447 (R. Burioni et al.)

Rare events and scaling properties in field-induced anomalous dynamics    [PDF]

R. Burioni, G. Gradenigo, A. Sarracino, A. Vezzani, A. Vulpiani

We prove that, in particular regimes of a broad class of continuous time random walks, a small external field can turn diffusion from standard into anomalous. We illustrate our findings in the trap model, a prototype of subdiffusion in disordered and glassy materials, and in the L\'evy walk process, which describes superdiffusion within inhomogeneous media. For both models, in the presence of an external field, rare events induce a singular behavior in the originally Gaussian displacements distribution, giving rise to power-law tails. Remarkably, in the subdiffusive trap model, the combined effect of highly fluctuating waiting times and of a drift yields a non-Gaussian distribution characterized by long spatial tails and strong anomalous superdiffusion.

View original: http://arxiv.org/abs/1212.1447