Defect versus defect: stationary states of single file marching in periodic landscapes with road blocks

Abstract

Totally asymmetric simple exclusion process (TASEP) sets the paradigm for one-dimensional driven single file motion. We study a periodic TASEP with two ``road blocks'' or defects of different kinds, one point and another extended, across which particle flows are inhibited. We show how the interplay between particle number conservation and competition between the defects lead to inhomogeneous steady states with localised domain walls (LDW). The LDW locations jump discontinuously, indicating a discontinuous transition between these LDW states, as the system passes from being controlled by one defect to the other. When the defects are ``competing'', instead of an LDW a pair of delocalised domain walls appear, none of which can penetrate the extended defect. A minimum current principle can be used to identify the dominant defect that controls the domain wall formations. Our results should be important in diverse systems, ranging from protein synthesis by ribosomes in biological cells to urban traffic networks.