Characteristic Sign Renewals of Kardar-Parisi-Zhang Fluctuations

TL;DR

This paper investigates the sign dynamics of KPZ fluctuations, revealing unexpected links to renewal processes, ergodicity breaking, and differences between interface geometries, through experimental and numerical analysis.

Contribution

It uncovers a novel ergodicity breaking phenomenon in KPZ fluctuations and establishes surprising correlations with renewal processes, highlighting differences in long-time averages and interface geometries.

Findings

KPZ sign fluctuations show renewal process-like recurrence times.

Long-time averages of KPZ signs have broad, nontrivial distributions.

Differences observed between circular and flat KPZ interfaces.

Abstract

Tracking the sign of fluctuations governed by the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class, we show, both experimentally and numerically, that its evolution has an unexpected link to a simple stochastic model called the renewal process, studied in the context of aging and ergodicity breaking. Although KPZ and the renewal process are fundamentally different in many aspects, we find remarkable agreement in some of the time correlation properties, such as the recurrence time distributions and the persistence probability, while the two systems can be different in other properties. Moreover, we find inequivalence between long-time and ensemble averages in the fraction of time occupied by a specific sign of the KPZ-class fluctuations. The distribution of its long-time average converges to nontrivial broad functions, which are found to differ significantly from that of the renewal process, but instead be characteristic of KPZ. Thus, we obtain a new type of ergodicity breaking for such systems with many-body interactions. Our analysis also detects qualitative differences in time-correlation properties of circular and flat KPZ-class interfaces, which were suggested from previous experiments and simulations but still remain theoretically unexplained.