2021/03/16 by Akriti Jindal, Arvind Kumar Gupta
Mathematics · Physics and Astronomy · #Asymmetric simple exclusion process #Boundary (topology) #Classical mechanics #Complex Network Analysis Techniques #Condensed matter physics #Domain (mathematical analysis) #Geometry #Mathematical analysis #Mathematics #Monte Carlo method #Phase (matter) #Phase diagram #Phase transition #Physics #Position (finance) #Quantum mechanics #Shock (circulatory) #Statistical physics #Stochastic processes and statistical mechanics #Symmetry (geometry) #Symmetry breaking #Theoretical and Computational Physics #Topology (electrical circuits) #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.104.014138
published as Phys. Rev. E 104, 014138 (2021)
arxiv created 2021/03/16 · openalex publication_date 2021/07/27 · arxiv updated 2021/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.