Fractional kinetics emerging from ergodicity breaking in random media
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We present a modelling approach for diffusion in a complex medium characterized by a random lengthscale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single particle tracking experiments in living cells, such as ergodicity breaking, p- variation and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the lengthscale, a single parameter controls the ergodic- to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from non-fractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.