Scaling and phase transitions in one-dimensional nonequilibrium driven systems

Abstract

We investigate scaling and phase transitions in 1D driven lattice gas models, related to Kardar-Parisi-Zhang (KPZ) surface dynamics. The results of three studies are presented. In the first one, we generalize the asymmetric diffusion-reaction process A + A → A by adding a mass-conserving coalescence feature. This leads to novel scaling behavior, which we explain analytically and confirm numerically. In the second and third studies, we focus on the scaling properties of dynamic phase transitions in driven flow, like queues behind obstacles, in the context of the asymmetric simple exclusion process (ASEP). First, we collapse the entire queue onto a single special site, the so-called parking garage, where the road starts and terminates. This new variant of the ASEP exhibits a dynamic analogue of Bose condensation, in terms of macroscopic occupancy of the garage. Next, we consider the ASEP with open and periodic boundary conditions with a special bond, where particles can pass with reduced or enhanced probability. Below a critical reduced passage probability, a macroscopic queue emerges behind the slow bond. We establish numerically the existence of a queuing transition. Novel power-law shaped density profiles also emerge below and above the critical point. This project was triggered by our collaboration with an experimental group studying faceting in slow combustion of paper induced by a columnar defect. An exact mapping exists between the ASEP and KPZ type surface growth processes.