Emergence of jams in the generalized totally asymmetric simple exclusion process

TL;DR

This paper investigates the generalized TASEP with interactions that promote clustering, analyzing its large-time behavior, phase transitions, and current fluctuations, revealing a crossover from finite clusters to large-scale aggregation as interaction strength varies.

Contribution

It introduces a comprehensive analysis of the generalized TASEP, identifying a transition regime and deriving the large deviation function for particle current across different interaction strengths.

Findings

Finite correlation length and TASEP-like behavior at finite interaction parameter.

Growth of correlation length with system size indicating a transition regime.

Derived large deviation function interpolating between known models.

Abstract

The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech. P05014 (2012)] is an integrable generalization of the TASEP equipped with an interaction, which enhances the clustering of particles. The process interpolates between two extremal cases: the TASEP with parallel update and the process with all particles irreversibly merging into a single cluster moving as an isolated particle. We are interested in the large time behavior of this process on a ring in the whole range of the parameter $\lambda$ controlling the interaction. We study the stationary state correlations, the cluster size distribution and the large-time fluctuations of integrated particle current. When $\lambda$ is finite, we find the usual TASEP-like behavior: The correlation length is finite; there are only clusters of finite size in the stationary state and current fluctuations belong to the Kardar-Parisi-Zhang universality class. When $\lambda$ grows with the system size so does the correlation length. We find a nontrivial transition regime with clusters of all sizes on the lattice. We identify a crossover parameter and derive the large deviation function for particle current, which interpolates between the case considered by Derrida-Lebowitz and a single particle diffusion.