Spontaneous symmetry breaking on a mutiple-channel hollow cylinder

Abstract

This Letter investigates coupled asymmetric exclusion processes with two types of particles on multiple parallel channels of a hollow cylinder. The model is inspired by the structure of microtubules, along which motor proteins such as kinesins and dyneins move in opposite directions. Interactions between two-species particles are assumed to take place only on the left and right boundaries where a rule of narrow entrances is applied. Narrow entrances mean that a particle cannot enter the system if either of two nearest-neighbor sites on the neighboring channels is occupied by a particle of the other species. This rule is similar to, but different from, that in [E. Pronina, A.B. Kolomeisky, J. Phys. A 40 (2007) 2275] since the narrow entrance rule in our model involves two neighbors. The phase diagram of our model is studied theoretically and via Monte Carlo simulations. The spontaneous symmetry breaking (SSB) is observed in the system. There are four possible phases in the system and with SSB occurring in two of them: high/low density and asymmetric low/low density. Bulk density and particle currents are also computed. Theoretical calculations deviate from Monte Carlo simulation results due to the neglecting of correlations in particles dynamics in mean-field analysis.