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

Area of Science:

• Statistical Mechanics
• Non-equilibrium Physics
• Dynamical Systems

Background:

• Dynamical large deviations characterize non-equilibrium systems.
• Lattice gas models are studied out of equilibrium.
• Conditioning on dynamical observables provides insights.

Purpose of the Study:

• To investigate dynamical phase transitions in a 2D random walk model.
• To characterize stationary states conditioned on partial currents.
• To explore the underlying symmetry breaking mechanisms.

Main Methods:

• Application of dynamical large deviations framework.
• Numerical microscopic characterization of emergent phases.
• Analytical insights from macroscopic fluctuation theory.
• Spectral analysis of the microscopic generator.

Main Results:

• A dynamical phase transition was identified between delocalized band and localized vortex dynamics.
• The transition is continuous and accompanied by spontaneous Z_{2}-symmetry breaking.
• The stationary solution loses reflection symmetry, indicating a fundamental change in dynamics.
• The observed transition does not rely on exclusion or interaction effects.

Conclusions:

• Dynamical phase transitions are a key feature of non-equilibrium systems.
• The 2D random walk model provides a simplified yet insightful platform for studying these phenomena.
• Symmetry breaking is a crucial aspect of these transitions.
• Similar dynamical phase transitions are expected in more complex non-equilibrium models.