We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the Levy 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 CTRW, 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.
Rare events and scaling properties in field-induced anomalous dynamics / Burioni, Raffaella; G., Gradenigo; A., Sarracino; Vezzani, Alessandro; A., Vulpiani. - In: JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT. - ISSN 1742-5468. - 13:(2013), pp. P09022-P09032. [10.1088/1742-5468/2013/09/P09022]
Rare events and scaling properties in field-induced anomalous dynamics
BURIONI, Raffaella;VEZZANI, Alessandro;
2013-01-01
Abstract
We show that, in a broad class of continuous time random walks (CTRW), a small external field can turn diffusion from standard into anomalous. We illustrate our findings in a CTRW with trapping, a prototype of subdiffusion in disordered and glassy materials, and in the Levy 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 CTRW, 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.