Driven lattice gases with quenched disorder: Exact results and different macroscopic regimes
Driven lattice gases with quenched disorder: Exact results and different macroscopic regimes
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DOI：
10.1103/physreve.58.1911
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发表时间：
1997-11
影响因子：
2.4
通讯作者：
G. Tripathy;M. Barma
中科院分区：
文献类型：
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作者：
G. Tripathy;M. Barma
我们研究了猝灭空间无序对通过硬核排斥相互作用的受驱动随机粒子系统载流稳态的影响。研究了两类模型：无序下推过程及其推广，无序非对称简单排斥过程。猝灭无序是通过空间随机的微观跃迁几率进入的，而驱动是通过位置间跃迁几率的不对称性来模拟的。对于任意无序，得到了d元维广义下推动力学和广义下推动力学的精确稳态度量。这使我们能够计算稳态电流和与位置相关的密度的闭合形式表达式。通过数值模拟和平均场近似，研究了具有无序键强度的非对称排斥过程的一维稳态。在完全不对称的情况下，我们给出了强的数值证据，证明了电流在反射下是不变的。我们发现，无序可以导致不同密度的宏观区域的相分离。我们提出了由直接数值模拟支持的近似来描述这些现象，并根据模型的宏观参数在电流密度平面上描述了模型的相图。我们还研究了将每个键中的易流动方向作为随机变量的影响，发现在这种情况下，电流随着系统的大小而减小。我们得出结论：在一维无序驱动扩散系统中存在三个不同的区域：均匀区域，其中系统的状态由单个宏观密度和非零电流来表征；分离密度区域，其中系统的状态由两个不同的相分离的密度和非零电流来表征；消失电流区域，其中系统的状态由两个截然不同的密度和非零电流来表征，其中系统的状态由两个不同的密度值来表征，并且电流随着系统规模的增大而减小，并且在热力学极限中消失。利用从晶格气体到界面的映射，在存在柱状无序的情况下，这些区域转化为不同的界面生长区域。
We study the effect of quenched spatial disorder on the current-carrying steady states of driven stochastic systems of particles interacting through hard-core exclusion. Two sorts of models are studied: disordered drop-push processes and their generalizations, and the disordered asymmetric simple exclusion process. Quenched disorder enters through spatially random microscopic transition probabilities and the drive is modeled by asymmetry in transition probabilities between sites. Exact steady-state measures are obtained for the drop-push and the generalized drop-push dynamics in $d$ dimensions for arbitrary disorder. This allows us to compute closed form expressions for the steady-state current and site-dependent densities. The steady state of the asymmetric exclusion process with disordered bond strengths is studied in one dimension by numerical simulation and by a mean-field approximation that allows for density variations from site to site. In the totally asymmetric case, we present strong numerical evidence that the current is invariant under reflection. We show that disorder can induce phase separation into macroscopic regions of different densities. We propose approximations, supported by direct numerical simulations, to describe these phenomena and the phase diagram of the model in the current-density plane in terms of macroscopic parameters of the model. We also study the effect of making the direction of easy flow in each bond a random variable and find that the current decreases with system size in this case. We conclude that there are three distinct regimes in disordered driven diffusive systems in one dimension: a homogeneous regime in which the state of the system is characterized by a single macroscopic density and a nonzero current; a segregated-density regime, where the state of the system is characterized by two distinct phase-separated values of density and a nonzero current; a vanishing-current regime, where the state of the system is characterized by two distinct values of the density and the current decreases as the system size increases and vanishes in the thermodynamic limit. Using a mapping from lattice gases to interfaces, these regimes translate into distinct regimes of interface growth in the presence of columnar disorder.