Dynamical aspects of spontaneous symmetry breaking in driven flow with exclusion

Abstract

We present a numerical study of a two-lane version of the stochastic non-equilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally-imposed particle injection ($\alpha$) and ejection ($\beta$) rates, spontaneous symmetry breaking can occur. We investigate the statistics and internal structure of the stochastically-induced transitions, or "flips", which occur between opposite broken-symmetry states as the system evolves in time. From the distribution of time intervals separating successive flips, we show that the evolution of the associated characteristic times against externally-imposed rates yields information regarding the proximity to a critical point in parameter space. On short time scales, we probe for the possible existence of precursor events to a flip between opposite broken-symmetry states. We study an adaptation of domain-wall theory to mimic the density reversal process associated with a flip.

arXiv comment9 pages, 10 figures (published version)

References in corpus (16)

• Traffic and Related Self-Driven Many-Particle Systems
• Statistical Physics of Vehicular Traffic and Some Related Systems
• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide
• Non-equilibrium statistical mechanics: From a paradigmatic model to biological transport
• Steady-state selection in driven diffusive systems with open boundaries
• Rotations and cessations of the large-scale circulation in turbulent Rayleigh-Benard convection
• Critical phenomena and universal dynamics in one-dimensional driven diffusive systems with two species of particles
• Flow reversal in a simple dynamical model of turbulence
• Signatures of critical full counting statistics in a quantum-dot chain
• Spontaneous symmetry breaking in a bridge model fed by junctions
• Dynamical origin of spontaneous symmetry breaking in a field-driven nonequilibrium system
• Rigorous results on spontaneous symmetry breaking in a one-dimensional driven particle system
• Magnetization reversal times in the 2D Ising model
• Spontaneous symmetry breaking in a two-lane model for bidirectional overtaking traffic
• On the effective velocity created by a point vortex in two-dimensional hydrodynamics
• Domain wall theory and non-stationarity in driven flow with exclusion