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01/07/2019, 15:00 — 16:30 — Room P4.35, Mathematics Building

Martin Evans, *Edinburgh University*

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Open Boundary ASEP (I)

The asymmetric simple exclusion process (ASEP) has been studied in probability theory since Spitzer in 1970. Remarkably a version with open boundaries had already been introduced as a model for RNA translation in 1968. This “open ASEP” has since the 1990’s been widely studied in the theoretical physics community as a model of a nonequilibrium system, which sustains a stationary current. In these lectures I will introduce and motivate the model then present a construction — the matrix product ansatz — which yields the exact stationary state for all system sizes. I will derive the phase diagram and analyse the nonequilibrium phase transitions. Finally I will discuss how the approach generalises to multispecies systems.

In this first lecture I will introduce the motivations; correlation functions; mean-field theory and hydrodynamic limit; dynamical mean-field theory; domain wall theory.