Temporal evolution of product shock measures in TASEP with sublattice-parallel update
arXiv:0902.4047 · doi:10.1103/PhysRevE.79.051124
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.
5 pages, reference added, minor revision
References in corpus (9)
- Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
- Time-dependent correlation functions in a one-dimensional asymmetric exclusion process
- Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
- Microscopic structure of travelling wave solutions in a class of stochastic interacting particle systems
- Matrix-Product States for a One-Dimensional Lattice Gas with Parallel Dynamics
- Derivation of a Matrix Product Representation for the Asymmetric Exclusion Process from Algebraic Bethe Ansatz
- Matrix Product Steady States as Superposition of Product Shock Measures in 1D Driven Systems
- Dyck Paths, Motzkin Paths and Traffic Jams
- The Grand-Canonical Asymmetric Exclusion Process and the One-Transit Walk
Cited by in corpus (5)
- A reverse duality for the ASEP with open boundaries
- On the phase transition in the sublattice TASEP with stochastic blockage
- Equivalence of a one-dimensional driven-diffusive system and an equilibrium two-dimensional walk model
- One-transit paths and steady-state of a non-equilibrium process in a discrete-time update
- Relaxation time in a non-conserving driven-diffusive system with parallel dynamics