The asymmetric exclusion model with sequential update

TL;DR

This paper provides an exact solution for the stationary state of an asymmetric exclusion model with sequential update, using a matrix-product formalism, and shows its equivalence to other update schemes.

Contribution

It introduces an exact matrix-product solution for the model with sequential update and demonstrates its equivalence to sublattice-parallel and random sequential updates.

Findings

Exact stationary state solution derived

Matrix algebra for sequential and sublattice-parallel updates are identical

Model maps onto previously studied random sequential case

Abstract

We present a solution for the stationary state of an asymmetric exclusion model with sequential update and open boundary conditions. We solve the model exactly for random hopping in both directions by applying a matrix-product formalism which was recently used to solve the model with sublattice-parallel update[1]. It is shown that the matrix-algebra describing the sequential update and sublattice-parallel update are identical and can be mapped onto the random sequential case treated by Derrida et al[2].