Nonuniform asymmetric exclusion process: Stationary densities and domain walls

TL;DR

This paper analyzes the stationary density profiles and phase transitions in a spatially inhomogeneous TASEP with open boundaries, revealing discontinuities and domain wall behaviors influenced by nonuniform hopping rates.

Contribution

It provides a detailed calculation of steady state densities and phase diagrams for inhomogeneous TASEP, highlighting the effects of spatial nonuniformity on phase structure and domain walls.

Findings

Discontinuous density profiles in the maximal current phase.

Universal topology of phase diagrams.

Dependence of domain wall envelopes on hopping rate inhomogeneity.

Abstract

We explore the stationary densities in totally asymmetric exclusion processes (TASEP) with open boundary conditions and spatially inhomogeneous hopping rates. We calculate the steady state density profiles that characterise the associated phases. We show that in the contrast to the low and high density phases, the stationary density profile in the maximal current phase can be discontinuous, even when the space-dependent hopping rate is continuous. The phase diagrams in the plane of the control parameters show universal topology. The associated phase transitions are explored. We further investigate the domain walls, which are delocalised and calculate their envelops, which reveal their dependence on the spatial nonuniformity of the hopping rates.