Exact Stationary State for an ASEP with Fully Parallel Dynamics
Jan de Gier (University of Utrecht), Bernard Nienhuis (University, of Amsterdam)
TL;DR
This paper derives the exact stationary state of an ASEP with fully parallel dynamics using the matrix product Ansatz, providing explicit correlation functions and the phase diagram.
Contribution
It introduces a simple derivation for the deterministic case and an explicit matrix algebra representation for the probabilistic case, advancing understanding of ASEP stationary states.
Findings
Exact stationary state derived for ASEP with fully parallel dynamics
Explicit correlation functions obtained
Exact phase diagram determined
Abstract
The exact stationary state of an asymmetric exclusion process with fully parallel dynamics is obtained using the matrix product Ansatz. We give a simple derivation for the deterministic case by a physical interpretation of the dimension of the matrices. We prove the stationarity via a cancellation mechanism and by making use of an explicit representation of the matrix algebra we easily find closed expressions for the correlation functions in the general probabalistic case. Asymptotic expressions, obtained by making use of earlier results, allow us to derive the exact phase diagram.
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