Drift, diffusion, and noise in hopping systems

We present recent advances on transport phenomena in periodic hopping systems. Making use of a Monte Carlo technique, we have adopted different models with increasing complexity. Drift, diffusion, and noise are investigated for structures with a large number of barriers, with particles correlated by the asymmetric simple exclusion process, and for superlattices under high electric fields. Within these approaches we have clarified some contradictory results on the interrelation between diffusion and noise in a closed and open chain of interacting hopping sites, and we have analyzed transport features in real superlattices. Here, signatures of classical versus quantum transport are emphasized.