Emergence of jams in the generalized totally asymmetric simple exclusion process

The generalized totally asymmetric exclusion process (TASEP) [J. Stat. Mech. (2012) P05014] 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.

Figure 1

ZRP-ASEP mapping.

Figure 2

The rescaled cumulants of total number of particle jumps ${\tilde{c}}_n$ vs $\theta$ in the transition regime $N\to \infty ,\lambda N^{-2}=\mathrm{const}$.

Figure 3

Universal cumulant ratio $R\left(\theta \right).$ The dashed line shows the limiting KPZ value $R\left(\infty \right).$