Green functions for the TASEP with sublattice parallel update

TL;DR

This paper derives exact Green functions for a discrete-time TASEP with sublattice parallel update, showing its equivalence to a known TASEP variant and providing determinant formulas for various initial and final states.

Contribution

It introduces a novel approach to compute Green functions for the TASEP with sublattice parallel update by mapping it to a backward-ordered sequential update model.

Findings

Green functions are obtained exactly in determinant form.

The model is shown to be equivalent to TASEP with backward-ordered sequential update.

Results apply to different initial and final particle configurations.

Abstract

We consider the totally asymmetric simple exclusion process (TASEP) in discrete time with the sublattice parallel dynamics describing particles moving to the right on the one-dimensional infinite chain with equal hoping probabilities. Using sequentially two mappings, we show that the model is equivalent to the TASEP with the backward-ordered sequential update in the case when particles start and finish their motion not simultaneously. The Green functions are obtained exactly in a determinant form for different initial and final conditions.