Subdiffusive continuous time random walks and weak ergodicity breaking analyzed with the distribution of generalized diffusivities

Abstract

We propose a new tool for analyzing data from anomalous diffusion processes: The distribution of generalized diffusivities pα(D,τ) describes the fluctuations during the diffusion process around the generalized diffusion coefficient obtained from the mean squared displacement and its τ-dependence captures the non-trivial part of the process dynamics. We apply this tool to subdiffusive continuous time random walks which are known to show weak ergodicity breaking. We characterize how the distribution of generalized diffusivities obtained from an ensemble of trajectories differs from the distribution obtained as a time average from one single-particle trajectory and show how such an analysis leads to a deeper understanding of weak ergodicity breaking.