Emergence of jams in the generalized totally asymmetric simple exclusion process

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.

arXiv comment19 pages, 3 figures, final revised version, appendix with explicit calculations added, comments on physical meaning of the results added, references updated, mistypes corrected

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Cited by in corpus (11)

• Exact short-time height distribution in 1D KPZ equation and edge fermions at high temperature
• The inverse scattering of the Zakharov-Shabat system solves the weak noise theory of the Kardar-Parisi-Zhang equation
• Generalizations of TASEP in discrete and continuous inhomogeneous space
• KPZ fluctuations in finite volume
• One-dimensional irreversible aggregation with TASEP dynamics
• A model of irreversible jam formation in dense traffic
• Time-headway distribution for periodic totally asymmetric exclusion process with various updates
• One-dimensional discrete aggregation-fragmentation model
• Current statistics in the q-boson zero range process
• Nonstationary generalized TASEP in KPZ and jamming regimes
• The q-Hahn PushTASEP