Deterministic Exclusion Process with a Stochastic Defect: Matrix-Product Ground States

Abstract

We study a one-dimensional anisotropic exclusion model describing particles moving deterministically on a ring with a single defect across which they move with probability 0 < q < 1. We show that the stationary state of this model can be represented as a matrix-product state.

13 pages, LaTeX, including two postscript figures, minor mistakes have been corrected

References in corpus (6)

• Exact Solution of the Master Equation for the Asymmetric Exclusion Process
• Bose-Einstein Condensation In Disordered Exclusion Models and Relation to Traffic Flow
• Representations of the quadratic Algebra and Partially Asymmetric Diffusion with Open Boundaries
• On Matrix Product Ground States for Reaction-Diffusion Models
• Matrix Product Ground States for Asymmetric Exclusion Processes with Parallel Dynamics
• The asymmetric exclusion model with sequential update

Cited by in corpus (14)

• Exact solution of a partially asymmetric exclusion model using a deformed oscillator algebra
• Exact Steady States of Disordered Hopping Particle Models with Parallel and Ordered Sequential Dynamics
• Matrix Product Eigenstates for One-Dimensional Stochastic Models and Quantum Spin Chains
• Single-Bottleneck Approximation for Driven Lattice Gases with Disorder and Open Boundary Conditions
• An Exactly Solvable Two-Way Traffic Model With Ordered Sequential Update
• Defect-induced phase transition in the asymmetric simple exclusion process
• Exactly solvable statistical model for two-way traffic
• Exact stationary state for a deterministic high speed traffic model with open boundaries
• Multi-Species Asymmetric Exclusion Process in Ordered Sequential Update
• Interference of two co-directional exclusion processes in the presence of a static bottleneck: a biologically motivated model
• Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics
• On the phase transition in the sublattice TASEP with stochastic blockage
• Impurity-induced shocks in the asymmetric exclusion process with long-range hopping
• Analytical results for a coagulation/decoagulation model on an inhomogeneous lattice