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

TL;DR

This paper investigates how mirror symmetry breaks down in the KPZ universality class, revealing a transition from unimodal to bimodal distributions in initial state fluctuations linked to shock dynamics.

Contribution

It uncovers the breakdown of mirror symmetry in KPZ fluctuations and demonstrates universality and scale invariance through large-scale simulations of TASEP.

Findings

Bimodality occurs for negative fluctuations due to shock dynamics

Mirror symmetry breakdown is linked to super-diffusive shocks

Universality confirmed via Monte Carlo simulations

Abstract

The current/height fluctuation statistics of Kardar-Parisi-Zhang (KPZ) universality in 1+1 dimensions are sensitive to the initial state. We find that the averages over the initial states exhibit universal and scale-invariant patterns when conditioning on fluctuations. To establish universality of our findings we demonstrate scale invariance at different times and heights using large-scale Monte-Carlo simulations of the totally asymmetric simple exclusion process (TASEP) which belongs to the KPZ universality class. Here we focus on current/height fluctuations in the steady state regime described by the Baik-Rains distribution. The conditioned probability distribution of an initial state order parameter shows a transition from uni- to bimodal. Bimodality occurs for negative current/height fluctuations that are dominated by super-diffusive shock dynamics. It is caused by two possible point-symmetric shock profiles and the KPZ mirror symmetry breakdown. Similar surprising relations between initial states and fluctuations might exist in other universality classes as well.