Non-equilibrium processes: driven lattice gases, interface dynamics, and quenched disorder effects on density profiles and currents
| dc.creator | de Queiroz, S. L. A. | |
| dc.creator | Stinchcombe, R. B. | |
| dc.date | 2008-06-20 | |
| dc.date | 2008-09-04 | |
| dc.date.accessioned | 2026-07-07T10:00:11Z | |
| dc.date.available | 2026-07-07T10:00:11Z | |
| dc.description | 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 $α=0.500(5)$, $z=1.52(3)$, $β=0.33(1)$. 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 $α=0.497(3)$, $z=1.20(5)$, $β=0.41(2)$, which is apparently at variance with the Bethe ansatz prediction $z=0$; (iii) on the coexistence line between low- and high- density phases, $α=0.99(1)$, $z=2.10(5)$, $β=0.47(2)$, 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 $α=1.05(5)$, $z=1.7(1)$, $β=0.62(7)$. 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. | |
| dc.identifier | https://arxiv.org/abs/0806.3439 | |
| dc.identifier | http://arxiv.org/abs/0806.3439 | |
| dc.identifier | Physical Review E 78, 031106 (2008) | |
| dc.identifier | doi:10.1103/PhysRevE.78.031106 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168263 | |
| dc.subject | Statistical Mechanics | |
| dc.title | Non-equilibrium processes: driven lattice gases, interface dynamics, and quenched disorder effects on density profiles and currents | |
| dc.type | text |