https://doi.org/10.1140/epjb/e2014-40956-0
Regular Article
Non-anomalous diffusion is not always Gaussian
1 Dipartimento di Fisica Università di
Roma “Sapienza”, P.le A. Moro
2, 00185
Roma,
Italy
2 CNR-Istituto dei Sistemi Complessi
(ISC), UOS “Sapienza”, P.le A. Moro 2, 00185
Roma,
Italy
a
e-mail: fabio.cecconi@roma1.infn.it
Received:
25
October
2013
Received in final form:
20
March
2014
Published online:
1
May
2014
Through the analysis of unbiased random walks on fractal trees and continuous time random walks, we show that even if a process is characterized by a mean square displacement (MSD) growing linearly with time (standard behaviour) its diffusion properties can be not trivial. In particular, we show that the following scenarios are consistent with a linear increase of MSD with time: (i) the high-order moments, ⟨x(t)q⟩ for q > 2 and the probability density of the process exhibit multiscaling; (ii) the random walk on certain fractal graphs, with non integer spectral dimension, can display a fully standard diffusion; (iii) positive order moments satisfying standard scaling does not imply an exact scaling property of the probability density.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2014