Why spontaneous symmetry breaking disappears in a bridge system with PDE-friendly boundaries

TL;DR

This paper investigates a driven diffusive system with two particle types and boundary reservoirs, demonstrating that spontaneous symmetry breaking does not occur due to boundary effects, supported by theoretical analysis and Monte Carlo simulations.

Contribution

The study introduces projection measures for boundary reservoirs and shows the absence of spontaneous symmetry breaking in this PDE-friendly boundary system.

Findings

Spontaneous symmetry breaking is absent in the system.

Stationary states are approached via shock reflections.

Monte Carlo simulations confirm theoretical predictions.

Abstract

We consider a driven diffusive system with two types of particles, A and B, coupled at the ends to reservoirs with fixed particle densities. To define stochastic dynamics that correspond to boundary reservoirs we introduce projection measures. The stationary state is shown to be approached dynamically through an infinite reflection of shocks from the boundaries. We argue that spontaneous symmetry breaking observed in similar systems is due to placing effective impurities at the boundaries and therefore does not occur in our system. Monte-Carlo simulations confirm our results.