Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes

We develop the hydrodynamic theory for number conserving asymmetric exclusion processes with short-range random quenched disordered hopping rates, which is one-dimensional Kardar-Parisi- Zhang (KPZ) equation with quenched columnar disorder. We show that when the system is away from half-filling, the universal spatio-temporal scaling of the density fluctuations is indistinguishable from its pure counterpart, with the model belonging to the one-dimensional Kardar-Parisi-Zhang universality class. In contrast, close to half-filling, the quenched disorder is relevant, leading to a new universality class. We physically argue that the irrelevance of the quenched disorder when away from half-filling is a consequence of the averaging of the disorder by the propagating density fluctuations in the system. In contrast, close to half-filling the density fluctuations are overdamped, and as a result, are strongly influenced by the quenched disorder.