Ergodicity breaking and localization

Abstract

We study the joint action of the non-Poisson renewal events (NPR) yielding Continuous-time random walk (CTRW) with index α<1 and two different generators of Hurst coefficient H≠0.5, one generating fractional Brownian motion (FBM) and another scaled Brownian motion (SBM). We discuss the ergodicity breaking emerging from these joint actions and we find that in both cases the adoption of time averages leads to localization. In the case of the joint action of NPR and SBM, localization occurs when SBM would produce subdiffusion. The joint action of NPR and FBM, on the contrary, may lead to localization when FBM is a source of superdiffusion. The joint action of NPR and FBM is equivalent to extending the CTRW to the case where the jumps of the runner are correlated and we argue that the the memory-induced localization requires a refinement of the theoretical perspective about determinism and randomness.