Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents

Abstract

The study of dynamical large deviations allows for a characterization of stationary states of lattice gas models out of equilibrium conditioned on averages of dynamical observables. The application of this framework to the two-dimensional random walk conditioned on partial currents reveals the existence of a dynamical phase transition between delocalized band dynamics and localized vortex dynamics. We present a numerical microscopic characterization of the phases involved, and provide analytical insight based on the macroscopic fluctuation theory. A spectral analysis of the microscopic generator shows that the continuous phase transition is accompanied by spontaneous ${\mathbb{Z}}_2$-symmetry breaking whereby the stationary solution loses the reflection symmetry of the generator. Dynamical phase transitions similar to this one, which do not rely on exclusion effects or interactions, are likely to be observed in more complex non-equilibrium physics models.

13 pages, 6 figures

References in corpus (17)

• Many body localization and thermalization in quantum statistical mechanics
• The large deviation approach to statistical mechanics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Fluctuation theorems for stochastic dynamics
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• A fluidized granular medium as an instance of the Fluctuation Theorem
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Construction of a Coordinate Bethe Ansatz for the asymmetric simple exclusion process with open boundaries
• Dynamical symmetry breaking and phase transitions in driven diffusive systems
• A minimal model of dynamical phase transition
• Symmetries in Fluctuations Far from Equilibrium
• Multiple phases in stochastic dynamics: geometry and probabilities
• Phase transitions in large deviations of reset processes
• Vortices in the two-dimensional Simple Exclusion Process
• Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod
• Thermodynamic formalism for dissipative quantum walks