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

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 12-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 nonequilibrium physics models.

Automated summary

The study of dynamical large deviations reveals a dynamical phase transition in two-dimensional random walk models, with insights provided by both numerical microscopic characterization and macroscopic fluctuation theory. The spectral analysis of the microscopic generator shows that this continuous phase transition involves spontaneous symmetry breaking, leading to the loss of reflection symmetry in the stationary solution. Such dynamical phase transitions, which do not depend on exclusion effects or interactions, may be observed in more complex nonequilibrium physics models.