Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents
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Gutiérrez, R., & Pérez-Espigares, C. (2021). Dynamical phase transition to localized states in the two-dimensional random walk conditioned on partial currents. Physical Review E, 104(4), 044134. [https://doi.org/10.1103/PhysRevE.104.044134]
SponsorshipEuropean Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Cofund Programme 754446; Project of I+D+i PID2020-113681GB-I00; FEDER "A way to make Europe"; ENEA, Italy; Italian research programme; European research programme
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 Z2-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.