Determinant solution for the Totally Asymmetric Exclusion Process with parallel update

TL;DR

This paper derives an exact determinant solution for the totally asymmetric exclusion process with parallel update in discrete time, using Bethe ansatz and combinatorial methods.

Contribution

It provides a novel determinant formula for the non-stationary solution of the process, extending analytical tools for discrete-time exclusion models.

Findings

Determinant form of the non-stationary solution derived

Bethe ansatz applied to discrete-time parallel update model

Alternative combinatorial derivation of the solution

Abstract

We consider the totally asymmetric exclusion process in discrete time with the parallel update. Constructing an appropriate transformation of the evolution operator, we reduce the problem to that solvable by the Bethe ansatz. The non-stationary solution of the master equation for the infinite 1D lattice is obtained in a determinant form. Using a modified combinatorial treatment of the Bethe ansatz, we give an alternative derivation of the resulting determinant expression.