Domain wall theory and non-stationarity in driven flow with exclusion

Abstract

We study the dynamical evolution toward steady state of the stochastic non-equilibrium model known as totally asymmetric simple exclusion process, in both uniform and non-uniform (staggered) one-dimensional systems with open boundaries. Domain-wall theory and numerical simulations are used and, where pertinent, their results are compared to existing mean-field predictions and exact solutions where available. For uniform chains we find that the inclusion of fluctuations inherent to the domain-wall formulation plays a crucial role in providing good agreement with simulations, which is severely lacking in the corresponding mean-field predictions. For alternating-bond chains the domain-wall predictions for the features of the phase diagram in the parameter space of injection and ejection rates turn out to be realized only in an incipient and quantitatively approximate way. Nevertheless, significant quantitative agreement can be found between several additional domain-wall theory predictions and numerics.

12 pages, 12 figures (published version)

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• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
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Cited by in corpus (3)

• Marching on a rugged landscape: Universality in disordered asymmetric exclusion processes
• Dynamical aspects of spontaneous symmetry breaking in driven flow with exclusion
• Driven flow with exclusion and spin-dependent transport in graphenelike structures