Mirror symmetry breakdown in the Kardar-Parisi-Zhang universality class

Area of Science:

• Statistical Physics
• Nonlinear Dynamics
• Condensed Matter Physics

Background:

• Kardar-Parisi-Zhang (KPZ) universality describes the dynamics of many systems with fluctuating interfaces.
• Fluctuation statistics in 1+1 dimensions are known to be sensitive to the system's initial state.
• The Baik-Rains distribution characterizes steady-state fluctuations in certain KPZ systems.

Purpose of the Study:

• To investigate the influence of initial states on fluctuation statistics within the KPZ universality class.
• To identify universal and scale-invariant patterns in conditioned fluctuation averages.
• To explore the transition in initial-state order parameter distributions and its relation to shock dynamics.

Main Methods:

• Large-scale Monte Carlo simulations of the totally asymmetric simple exclusion process (TASEP).
• Analysis of current/height fluctuation statistics in the steady-state regime.
• Investigation of conditioned probability distributions of initial-state order parameters.

Main Results:

• Averages over initial states exhibit universal and scale-invariant patterns when conditioned on fluctuations.
• A transition from unimodal to bimodal distribution of the initial-state order parameter was observed.
• Bimodality is linked to superdiffusive shock dynamics and breakdown of KPZ mirror symmetry for negative fluctuations.

Conclusions:

• The study establishes universality and scale invariance in conditioned fluctuation averages for KPZ systems.
• The observed bimodality in initial-state distributions provides insights into the underlying shock dynamics.
• These findings suggest potential for similar initial-state-fluctuation relationships in other universality classes.