Exclusion process on two intersecting lanes with constrained resources: symmetry breaking and shock dynamics

Abstract

We present a study of the exclusion process on a peculiar topology of network with two intersecting lanes, competing for the particles in a reservoir with finite capacity. To provide a theoretical ground for our findings, we exploit mean-field approximation along with domain-wall theory. The stationary properties of the system, including phase transitions, density profiles, and position of the domain wall are derived analytically. Under the similar dynamical rules, the particles of both lanes interact only at the intersected site. The symmetry of the system is maintained until the number of particles do not exceed the total number of sites. However, beyond this, the symmetry breaking phenomenon occurs, resulting in the appearance of asymmetric phases and continues to persist even for an infinite number of particles. The complexity of the phase diagram shows a nonmonotonic behavior with an increasing number of particles in the system. A bulk induced shock appears in a symmetric phase, whereas, a boundary induced shock is observed in the symmetric as well as the asymmetric phase. Monitoring the location of localized shock with increasing entry of particles, we explain the possible phase transitions. The theoretical results are supported by extensive Monte Carlo simulations and explained using simple physical arguments.