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

TL;DR

This paper introduces a one-dimensional exclusion model with a stochastic defect, demonstrating that its stationary state can be exactly represented using a matrix-product state, bridging deterministic and stochastic dynamics.

Contribution

It presents a novel matrix-product representation for the stationary state of a deterministic exclusion process with a stochastic defect, extending analytical tools in nonequilibrium statistical mechanics.

Findings

Stationary state expressed as a matrix-product state

Model combines deterministic movement with stochastic defect behavior

Provides analytical framework for similar exclusion processes

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.