Brownian particles in a periodic potential corrugated by disorder: Anomalous diffusion and ergodicity breaking

Abstract

We present the anomalous diffusion and ergodicity breaking surviving in a finite time scale, as an overdamped Brownian particle in one-dimensional potentials, consisting of periodic and random components. By virtue of numerical simulations, we demonstrate the non-ergodic superdiffusion, non-ergodic subdiffusion, and non-ergodic uncertain diffusion, which are identified by the observable quantities (the mean squared displacement and ergodicity breaking parameter) averaged over quenched disorder and noise realizations in this system. Moreover, the analytical expression of ergodicity recovery time below and above which the system, respectively, exhibits non-ergodic and ergodic behaviors approximatively, is obtained. These results may be beneficial in further understanding the biological processes, such as an ergodic and a non-ergodic process coexisting in the plasma membrane and the subdivision of larger molecules or tracers in living cells.