Non-anomalous diffusion is not always Gaussian

Abstract

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 do not imply an exact scaling property of the probability density.

RevTeX-4, 9 pages, 11 eps-figures

References in corpus (6)

• Anomalous transport in the crowded world of biological cells
• On the strong anomalous diffusion
• Multiscaling in Infinite Dimensional Collision Processes
• Levy flights from a continuous-time process
• Simple stochastic models showing strong anomalous diffusion
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• Field-induced superdiffusion and dynamical heterogeneity
• Models of infiltration into homogeneous and fractal porous media with localized sources
• Taming Lévy flights in confined crowded geometries
• Reaction fronts in persistent random walks with demographic stochasticity
• Reconstruction of substrate's diffusion landscape by the wavelet analysis of single particle diffusion tracks