Dynamics at barriers in bidirectional two-lane exclusion processes

Abstract

A two-lane exclusion process is studied where particles move in the two lanes in oppositedirections and are able to change lanes. The focus is on the steady state behavior insituations where a positive current is constrained to an extended subsystem (either byappropriate boundary conditions or by the embedding environment) where, in theabsence of the constraint, the current would be negative. We have found twoqualitatively different kinds of steady states and formulated the conditions for them interms of the transition rates. In the first type of steady state, a localized clusterof particles forms with an anti-shock located in the subsystem and the currentvanishes exponentially with the extension of the subsystem. This behavior isanalogous to that of the one-lane partially asymmetric simple exclusion process, andcan be realized e.g. when the local drive is induced by making the jump rates intwo lanes unequal. In the second type of steady state, which is realized e.g. if thelocal drive is induced purely by the bias in the lane change rates, and whichthus has no counterpart in the one-lane model, a delocalized cluster of particlesforms which performs a diffusive motion as a whole and, as a consequence, thecurrent vanishes inversely proportionally to the extension of the subsystem. Themodel is also studied in the presence of quenched disorder, where, in the case ofdelocalization, phenomenological considerations predict anomalously slow, logarithmicdecay of the current with the system size in contrast with the usual power law.