Dynamical Transition in the Open-boundary Totally Asymmetric Exclusion Process

Abstract

We revisit the totally asymmetric simple exclusion process with open boundaries (TASEP), focussing on the recent discovery by de Gier and Essler that the model has a dynamical transition along a nontrivial line in the phase diagram. This line coincides neither with any change in the steady-state properties of the TASEP, nor the corresponding line predicted by domain wall theory. We provide numerical evidence that the TASEP indeed has a dynamical transition along the de Gier-Essler line, finding that the most convincing evidence was obtained from Density Matrix Renormalisation Group (DMRG) calculations. By contrast, we find that the dynamical transition is rather hard to see in direct Monte Carlo simulations of the TASEP. We furthermore discuss in general terms scenarios that admit a distinction between static and dynamic phase behaviour.

27 pages, 18 figures. v2 to appear in J Phys A features minor corrections and better-quality figures

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• Simple Exclusion Processes with Local Resetting
• Dynamics of ribosomes in mRNA translation under steady and non-steady state conditions
• Cluster approximations for the TASEP: stationary state and dynamical transition
• Dynamical transition in the TASEP with Langmuir kinetics: mean-field theory
• Exact domain wall theory for deterministic TASEP with parallel update
• An exclusion process on a tree with constant aggregate hopping rate
• Asymptotics for the norm of Bethe eigenstates in the periodic totally asymmetric exclusion process
• Unbalanced Langmuir kinetics affects TASEP dynamical transitions: mean-field theory
• KPZ fluctuations in finite volume
• Totally asymmetric simple exclusion process with local resetting and open boundary conditions
• Dynamical transitions in a driven diffusive model with interactions