MPA for TASEP with a generalized update on a ring

TL;DR

This paper applies the Matrix Product Ansatz to analyze a generalized TASEP model on a ring with two hopping probabilities, deriving exact finite-size expressions for key quantities and exploring particle correlations in various regimes.

Contribution

It introduces a two-dimensional matrix-product representation for a generalized TASEP with two parameters, providing exact finite-size formulas and analyzing correlation behaviors.

Findings

Derived exact finite-size partition function and current.

Obtained explicit pair correlation function expressions.

Analyzed correlation behavior in different regimes, including aggregation limit.

Abstract

We apply the Matrix Product Ansatz to study the Totally Asymmetric Simple Exclusion Process on a ring with a generalized discrete-time dynamics depending on two hopping probabilities, $p$ and $\tilde{p}$. The model contains as special cases the TASEP with parallel update, when $\tilde{p} =0$, and with sequential backward-ordered update, when $\tilde{p} =p$. We construct a two-dimensional matrix-product representation and use it to obtain exact finite-size expressions for the partition function, the current of particles and the two-point correlation function. Our main new result is the derivation of the finite-size pair correlation function. Its behavior is analyzed in different regimes of effective attraction and repulsion between the particles, depending on whether $\tilde{p} >p$ or $\tilde{p} < p$. In particular, we explicitly obtain an analytic expression for the pair correlation function in the limit of irreversible aggregation $\tilde{p}\rightarrow 1$, when the stationary configurations contain just one cluster.