Weak disorder in periodic potentials: anomalous transport and diffusion

Abstract

Particles driven through a periodic potential by an external constant force are known to exhibit a pronounced peak of the diffusion around the critical deterministic force that defines the transition between locked and running states. It has recently been shown both experimentally and numerically that this peak is greatly enhanced if some amount of spatial disorder is superimposed on the periodic potential. Here, we show that this enhancement is a fingerprint of a broad phenomenology that goes well beyond a simple augmentation. For some values of the model parameters, including the characteristic distances associated with the periodic and random components of the potential, the magnitude of the external force, and the temperature, the system can exhibit a rich variety of regimes from normal diffusion to superdiffusion, subdiffusion and even subtransport.