Exact domain wall theory for deterministic TASEP with parallel update

Abstract

Domain wall theory (DWT) has proved to be a powerful tool for the analysis of one-dimensional transport processes. A simple version of it was found very accurate for the Totally Asymmetric Simple Exclusion Process (TASEP) with random sequential update. However, a general implementation of DWT is still missing in the case of updates with less fluctuations, which are often more relevant for applications. Here we develop an exact DWT for TASEP with parallel update and deterministic (p=1) bulk motion. Remarkably, the dynamics of this system can be described by the motion of a domain wall not only on the coarse-grained level but also exactly on the microscopic scale for arbitrary system size. All properties of this TASEP, time-dependent and stationary, are shown to follow from the solution of a bivariate master equation whose variables are not only the position but also the velocity of the domain wall. In the continuum limit this exactly soluble model then allows us to perform a first principle derivation of a Fokker-Planck equation for the position of the wall. The diffusion constant appearing in this equation differs from the one obtained with the traditional `simple' DWT.

5 pages, 4 figures

References in corpus (6)

• Bethe Ansatz Solution of the Asymmetric Exclusion Process with Open Boundaries
• The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Exclusion Processes with Internal States
• Dynamic correlation functions and Boltzmann Langevin approach for driven one dimensional lattice gas
• Domain wall delocalization, dynamics and fluctuations in an exclusion process with two internal states

Cited by in corpus (5)

• Intracellular transport driven by cytoskeletal motors: General mechanisms and defects
• On-site residence time in a driven diffusive system: violation and recovery of mean-field
• Exclusion in a priority queue
• Self-duality and shock dynamics in the $n$-component priority ASEP
• Phase coexistence phenomena in an extreme case of the misanthrope process with open boundaries