Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA.
Phys Rev E. 2019 Aug;100(2-1):022101. doi: 10.1103/PhysRevE.100.022101.
The open asymmetric simple exclusion process (ASEP) has emerged as a paradigmatic model of nonequilibrium behavior, in part due to its complex dynamical behavior and wide physical applicability as a model of driven diffusion. We compare the dynamical phase behavior of the one-dimensional (1D) ASEP and the multi-lane ASEP, a previously unstudied extension of the 1D model that may be thought of as a finite-width strip of the fully two-dimensional (2D) system. Our characterization employs large deviation theory (LDT), matrix product states (MPS), and the density matrix renormalization group (DMRG) algorithm, to compute the current cumulant generating function and its derivatives, which serve as dynamical order parameters. We use this measure to show that when particles cannot exit or enter the lattice vertically, the phase behavior of the multi-lane ASEP mimics that of its 1D counterpart, exhibiting the macroscopic and microscopic signatures of the maximal current, shock, and high-density-low-density coexistence phases. Conversely, when particles are allowed to freely enter and exit the lattice, no such transition is observed. This contrast emphasizes the complex interplay between latitudinal and longitudinal hopping rates and the effect of current biasing. Our results support the potential of tensor networks as a framework to understand classical nonequilibrium statistical mechanics.
开放式不对称简单排斥过程（ASEP）已成为非平衡行为的典范模型，部分原因是其复杂的动力学行为和广泛的物理适用性，可作为驱动扩散的模型。我们比较了一维（1D）ASEP 和多通道 ASEP 的动力学相行为，多通道 ASEP 是 1D 模型的一个以前未研究的扩展，可被视为完全二维（2D）系统的有限宽度带。我们的表征方法采用大偏差理论（LDT）、矩阵乘积态（MPS）和密度矩阵重整化群（DMRG）算法，来计算电流累积生成函数及其导数，它们作为动力学序参量。我们使用这个度量来表明，当粒子不能垂直地进出格子时，多通道 ASEP 的相行为模拟其 1D 对应物，表现出最大电流、冲击和高密度-低密度共存相的宏观和微观特征。相反，当粒子被允许自由地进出格子时，不会观察到这种转变。这种对比强调了横向和纵向跳跃率之间的复杂相互作用以及电流偏置的影响。我们的结果支持张量网络作为理解经典非平衡统计力学的框架的潜力。
