Non-equilibrium processes: driven lattice gases, interface dynamics, and quenched disorder effects on density profiles and currents

摘要

Properties of the one-dimensional totally asymmetric simple exclusion process(TASEP), and their connection with the dynamical scaling of moving interfacesdescribed by a Kardar-Parisi-Zhang (KPZ) equation are investigated. Withperiodic boundary conditions, scaling of interface widths (the latter definedvia 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, resultsare as follows: (i) in the maximal-current phase, the exponents are the same asfor 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 atvariance with the Bethe ansatz prediction $z=0$; (iii) on the coexistence linebetween 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 relaxationtime, related to kinematic-wave propagation and having an effective exponent$z^\prime=1$, is shown to be the limiting slow process for the low densityphase, which accounts for the above-mentioned discrepancy with Bethe ansatzresults. 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 approachto steady-state properties of TASEP with quenched disorder, closed-formexpressions for the piecewise shape of averaged density profiles are given, aswell as rather restrictive bounds on currents. All these are substantiated innumerical simulations.