Driven lattice gases with quenched disorder: exact results and different macroscopic regimes

Abstract

We study the effect of quenched spatial disorder on the current-carrying steady states of driven stochastic systems of particles interacting through hard-core exclusion. Two sorts of models are studied: disordered drop-push processes and their generalizations, and the disordered asymmetric simple exclusion process. Quenched disorder enters through spatially random microscopic transition probabilities and the drive is modeled by asymmetry in transition probabilities between sites. Exact steady-state measures are obtained for the drop-push and the generalized drop-push dynamics in d dimensions for arbitrary disorder. This allows us to compute closed form expressions for the steady-state current and site-dependent densities. The steady state of the asymmetric exclusion process with disordered bond strengths is studied in one dimension by numerical simulation and by a mean-field approximation that allows for density variations from site to site. In the totally asymmetric case, we present strong numerical evidence that the current is invariant under reflection. We show that disorder can induce phase separation into macroscopic regions of different densities. We propose approximations, supported by direct numerical simulations, to describe these phenomena and the phase diagram of the model in the current-density plane in terms of macroscopic parameters of the model. We also study the effect of making the direction of easy flow in each bond a random variable and find that the current decreases with system size in this case. We conclude that there are three distinct regimes in disordered driven diffusive systems in one dimension: a homogeneous regime in which the state of the system is characterized by a single macroscopic density and a nonzero current; a segregated-density regime, where the state of the system is characterized by two distinct phase-separated values of density and a nonzero current; a vanishing-current regime, where the state of the system is characterized by two distinct values of the density and the current decreases as the system size increases and vanishes in the thermodynamic limit. Using a mapping from lattice gases to interfaces, these regimes translate into distinct regimes of interface growth in the presence of columnar disorder.