Non-equilibrium 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 (KPZ) 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 $z^{\prime }=1$, 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.

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Cited by in corpus (15)

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• Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes
• Generic nonequilibrium steady states in an exclusion process on an inhomogeneous ring
• Driven flow with exclusion and transport in graphene-like structures
• Energy Transport in an Ising Disordered Model
• Statistics of current activity fluctuations in asymmetric flow with exclusion
• Domain wall theory and non-stationarity in driven flow with exclusion
• Simulations of driven and reconstituting lattice gases
• Current-activity versus local-current fluctuations in driven flow with exclusion
• Dynamics of driven flow with exclusion in graphene-like structures
• Driven flow with exclusion and spin-dependent transport in graphenelike structures
• Universal properties of the Kardar-Parisi-Zhang equation with quenched columnar disorders
• FKPP fronts in quenched random media