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.

arXiv comment13 pages, 6 figures

References in corpus (55)

• Many body localization and thermalization in quantum statistical mechanics
• The large deviation approach to statistical mechanics
• Dynamical Ensembles in Nonequilibrium Statistical Mechanics
• A Gallavotti-Cohen Type Symmetry in the Large Deviation Functional for Stochastic Dynamics
• Fluctuation theorem for stochastic dynamics
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Macroscopic fluctuation theory
• The Fluctuation Theorem as a Gibbs Property
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Spectral theory of Liouvillians for dissipative phase transitions
• Fluctuation theorems for stochastic dynamics
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Current fluctuations in non-equilibrium diffusive systems: an additivity principle
• Thermodynamic formalism for systems with Markov dynamics
• Nonequilibrium Markov processes conditioned on large deviations
• Thermodynamics of Quantum Jump Trajectories
• Macroscopic current fluctuations in stochastic lattice gases
• Large deviations and ensembles of trajectories in stochastic models
• Distribution of current in non-equilibrium diffusive systems and phase transitions
• Towards a theory of metastability in open quantum dynamics
• Nonequilibrium microcanonical and canonical ensembles and their equivalence
• Localization of maximal entropy random walk
• Non equilibrium current fluctuations in stochastic lattice gases
• A fluidized granular medium as an instance of the Fluctuation Theorem
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• Spontaneous Symmetry Breaking at the Fluctuating Level
• 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
• Making rare events typical in Markovian open quantum systems
• A minimal model of dynamical phase transition
• Symmetries in Fluctuations Far from Equilibrium
• Current large deviations for Asymmetric Exclusion Processes with open boundaries
• Dynamical phase transition for current statistics in a simple driven diffusive system
• Multiple phases in stochastic dynamics: geometry and probabilities
• Open Quantum Walks on Graphs
• Using matrix product states to study the dynamical large deviations of kinetically constrained models
• Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains
• Generic Dynamical Phase Transition in One-Dimensional Bulk-Driven Lattice Gases with Exclusion
• Phase transitions in large deviations of reset processes
• Building continuous time crystals from rare events
• Exact symmetries in the velocity fluctuations of a hot Brownian swimmer
• Order and symmetry-breaking in the fluctuations of driven systems
• Sampling rare events across dynamical phase transitions
• Vortices in the two-dimensional Simple Exclusion Process
• Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod
• Large deviations of random walks on random graphs
• Thermodynamic formalism for dissipative quantum walks
• Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz
• Fluctuation relations for anisotropic systems
• Glassy dynamics due to a trajectory phase transition in dissipative Rydberg gases
• Weak additivity principle for current statistics in d-dimensions
• Generalized optimal paths and weight distributions revealed through the large deviations of random walks on networks
• Dynamical criticality in open systems: non-perturbative physics, microscopic origin and direct observation
• Dynamical phase coexistence in the Fredrickson-Andersen model
• Current loops and fluctuations in the zero-range process on a diamond lattice

Cited by in corpus (6)

• Spectral signatures of symmetry-breaking dynamical phase transitions
• Finding the effective dynamics to make rare events typical in chaotic maps
• Delocalization-localization dynamical phase transition of random walks on graphs
• Large deviation and anomalous fluctuations scaling in degree assortativity on configuration networks
• Understanding random-walk dynamical phase coexistence through waiting times
• Making rare events typical in $d$-dimensional chaotic maps