title: Temporal evolution of product shock measures in the totally asymmetric simple exclusion process with sublattice-parallel update.
abstract: It is known that when the steady state of a one-dimensional multispecies system, which evolves via a random-sequential updating mechanism, is written in terms of a linear combination of Bernoulli shock measures with random-walk dynamics, it can be equivalently expressed as a matrix-product state. In this case the quadratic algebra of the system always has a two-dimensional matrix representation. Our investigations show that this equivalence exists at least for the systems with deterministic sublattice-parallel update. In this paper we consider the totally asymmetric simple exclusion process on a finite lattice with open boundaries and sublattice-parallel update as an example.
authors.affiliation: Physics Department, Bu-Ali Sina University, 65174-4161 Hamedan, Iran. farhad@ipm.ir
authors.forename: F H
authors.initials: FH
authors.lastname: Jafarpour
authors.forename: S R
authors.initials: SR
authors.lastname: Masharian