Dynamic instability transitions in 1D driven diffusive flow with non-local hopping

Marcel den Nijs
University of Washington

One-dimensional directed driven stochastic flow with competing non-local and local hopping events has an instability threshold from a populated phase into an empty-road (ER) phase. We implement this in the context of the asymmetric exclusion process. The non-local skids promote strong clustering in the stationary populated phase. Such clusters drive the dynamic phase transition and determine its scaling properties. We numerically establish that the instability transition into the ER phase is second-order in the regime where the entry point reservoir controls the current and first-order in the regime where the bulk is in control. The first-order transition originates from a turn-about of the cluster drift velocity. At the critical line, the current remains analytic, the road density vanishes linearly, and fluctuations scale as uncorrelated noise. A self-consistent cluster dynamics analysis explains why these scaling properties remain that simple.  [Work done with Meesoon Ha and Hyunggyu Park.]