Issue 44, 2014

Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

Abstract

Modern microscopic techniques following the stochastic motion of labelled tracer particles have uncovered significant deviations from the laws of Brownian motion in a variety of animate and inanimate systems. Such anomalous diffusion can have different physical origins, which can be identified from careful data analysis. In particular, single particle tracking provides the entire trajectory of the traced particle, which allows one to evaluate different observables to quantify the dynamics of the system under observation. We here provide an extensive overview over different popular anomalous diffusion models and their properties. We pay special attention to their ergodic properties, highlighting the fact that in several of these models the long time averaged mean squared displacement shows a distinct disparity to the regular, ensemble averaged mean squared displacement. In these cases, data obtained from time averages cannot be interpreted by the standard theoretical results for the ensemble averages. Here we therefore provide a comparison of the main properties of the time averaged mean squared displacement and its statistical behaviour in terms of the scatter of the amplitudes between the time averages obtained from different trajectories. We especially demonstrate how anomalous dynamics may be identified for systems, which, on first sight, appear to be Brownian. Moreover, we discuss the ergodicity breaking parameters for the different anomalous stochastic processes and showcase the physical origins for the various behaviours. This Perspective is intended as a guidebook for both experimentalists and theorists working on systems, which exhibit anomalous diffusion.

Graphical abstract: Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

Article information

Article type
Perspective
Submitted
04 Aug 2014
Accepted
19 Sep 2014
First published
22 Sep 2014
This article is Open Access
Creative Commons BY license

Phys. Chem. Chem. Phys., 2014,16, 24128-24164

Author version available

Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking

R. Metzler, J. Jeon, A. G. Cherstvy and E. Barkai, Phys. Chem. Chem. Phys., 2014, 16, 24128 DOI: 10.1039/C4CP03465A

This article is licensed under a Creative Commons Attribution 3.0 Unported Licence. You can use material from this article in other publications without requesting further permissions from the RSC, provided that the correct acknowledgement is given.

Read more about how to correctly acknowledge RSC content.

Social activity

Spotlight

Advertisements