Analytical approach to the one-dimensional disordered exclusion process with open boundaries and random sequential dynamics

A one-dimensional disordered particle hopping rate asymmetric exclusion process (ASEP) with open boundaries and a random sequential dynamics is studied analytically. Combining the exact results of the steady states in the pure case with a perturbative mean field-like approach the broken particle-hole symmetry is highlighted and the phase diagram is studied in the parameter space (alpha,beta), where alpha and beta represent respectively the injection rate and the extraction rate of particles. The model displays, as in the pure case, high-density, low-density and maximum-current phases. All critical lines are determined analytically showing that the high-density low-density first order phase transition occurs at alpha not equal beta. We show that the maximum-current phase extends its stability region as the disorder is increased and the usual 1/root l-decay of the density profile in this phase is universal. Assuming that some exact results for the disordered model on a ring hold for a system with open boundaries, we derive some analytical results for platoon phase transition within the low-density phase and we give an analytical expression of its corresponding critical injection rate alpha*. As it was observed numerically (Bengrine et al. J. Phys. A: Math. Gen. 32:2527, [1999]), we show that the quenched disorder induces a cusp in the current-density relation at maximum flow in a certain region of parameter space and determine the analytical expression of its slope. The results of numerical simulations we develop agree with the analytical ones.