HEX-TASEP: dynamics of pinned domains for TASEP transport on a periodic lattice ofhexagonal topology

Abstract

We investigate a totally asymmetric simple exclusion process (TASEP) on a periodichexagonal lattice with a single unit cell. We first explain the resulting stationarydensity profiles and the resulting fundamental current–density relation in terms ofmean-field arguments. For intermediate overall densities, transport through one of thesegments saturates in a maximum current phase, whereas the others developdomain walls of fixed height but fluctuating position. Via kinetic Monte Carlosimulations we focus on and fully characterize their non-equilibrium and stochasticphenomenology. We invoke a picture of anticorrelated domain wall dynamics, which wevisualize as a diffusing obstruction of constant size (‘jam’). The role of the boundaryconditions is discussed by comparing the periodic lattice carrying a fixed number ofparticles to a system coupled to reservoirs at open boundaries which is periodiconly on average. We highlight the differences in their dynamics based on a novelvisualization of domain wall motion at an intermediate ‘mesoscopic’ timescale.