Exclusion Process on two intersected lanes with constrained resources: Symmetry breaking and shock dynamics

TL;DR

This paper investigates the exclusion process on a network with intersected lanes and finite resources, revealing symmetry breaking, phase transitions, and shock dynamics through analytical and simulation methods.

Contribution

It introduces a novel model of intersected lanes with resource constraints and provides analytical insights into phase behavior and shock phenomena.

Findings

Symmetry breaking occurs beyond a critical particle number.

Multiple phase transitions are identified with increasing particles.

Shock dynamics depend on system phase and particle entry rate.

Abstract

We present a study of exclusion process on a peculiar topology of network with two intersected 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 the lanes interact only at the intersected site. The symmetry of system is maintained till number of particles do not exceed 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 infnite number of particles. The complexity of phase diagram shows a non-monotonic behaviour with increasing number of particles in the system. A bulk induced shock appears in a symmetric phase, whereas, a boundary induced shock is observed in symmetric as well as asymmetric phase. Monitoring the location of 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.