de Queiroz S L A, Stinchcombe R B
Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21941-972 Rio de Janeiro RJ, Brazil.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Sep;78(3 Pt 1):031106. doi: 10.1103/PhysRevE.78.031106. Epub 2008 Sep 4.
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.
研究了一维完全非对称简单排斥过程（TASEP）的性质，以及它们与由 Kardar-Parisi-Zhang 方程描述的移动界面的动态标度之间的联系。在周期边界条件下，界面宽度的标度（后者通过离散占据数到高度的映射定义）给出指数α = 0.500(5)，z = 1.52(3)，β = 0.33(1)。在开放边界条件下，结果如下：(i) 在最大电流相，指数与周期情况相同，并且与最近的 Bethe 假设结果一致；(ii) 在低密度相，可以在相当程度上发现曲线塌缩，α = 0.497(3)，z = 1.20(5)，β = 0.41(2)，这显然与 Bethe 假设预测 z = 0 不一致；(iii) 在低密度和高密度相之间的共存线上，α = 0.99(1)，z = 2.10(5)，β = 0.47(2)，与 Bethe 假设预测 z = 2 相对较好地一致。从平均场连续体公式出发，一个与运动波传播相关且有效指数 z′ = 1 的特征弛豫时间，被证明是低密度相的极限慢过程，这解释了与 Bethe 假设结果的上述差异。对于具有淬火键无序的 TASEP，界面宽度标度给出α = 1.05(5)，z = 1.7(1)，β = 0.62(7)。从对具有淬火无序的 TASEP 的稳态性质的直接解析方法出发，给出了平均密度分布的分段形状的封闭形式表达式，以及对电流的相当严格的界限。所有这些在数值模拟中都得到了证实。
