Nonequilibrium processes: Driven lattice gases, interface dynamics, and quenched-disorder effects on density profiles and currents

Abstract

Properties of the one-dimensional totally asymmetric simple exclusion process (TASEP), and their connection with the dynamical scaling of moving interfaces described by a Kardar-Parisi-Zhang equation are investigated. With periodic boundary conditions, scaling of interface widths (the latter defined via a discrete occupation-number-to-height mapping), gives the exponents alpha=0.500(5) , z=1.52(3) , beta=0.33(1) . With open boundaries, results are as follows: (i) in the maximal-current phase, the exponents are the same as for the periodic case, and in agreement with recent Bethe ansatz results; (ii) in the low-density phase, curve collapse can be found to a rather good extent, with alpha=0.497(3) , z=1.20(5) , beta=0.41(2) , which is apparently at variance with the Bethe ansatz prediction z=0 ; (iii) on the coexistence line between low- and high-density phases, alpha=0.99(1) , z=2.10(5) , beta=0.47(2) , in relatively good agreement with the Bethe ansatz prediction z=2 . From a mean-field continuum formulation, a characteristic relaxation time, related to kinematic-wave propagation and having an effective exponent z;{'}=1 , is shown to be the limiting slow process for the low-density phase, which accounts for the above mentioned discrepancy with Bethe ansatz results. For TASEP with quenched bond disorder, interface width scaling gives alpha=1.05(5) , z=1.7(1) , beta=0.62(7) . From a direct analytic approach to steady-state properties of TASEP with quenched disorder, closed-form expressions for the piecewise shape of averaged density profiles are given, as well as rather restrictive bounds on currents. All these are substantiated in numerical simulations.