Crossover from Growing to Stationary Interfaces in the Kardar-Parisi-Zhang Class

TL;DR

This paper investigates the transition of (1+1)-dimensional KPZ class interfaces from growth to stationarity, revealing universal functions that describe this process through simulations and experiments.

Contribution

It introduces universal functions governing the transition from growing to stationary interfaces in the KPZ class, supported by simulations and experimental data.

Findings

Universal functions connect growth and stationary regimes.

Interfaces approach stationarity over time in experiments and simulations.

Transition dynamics are characterized by specific distribution and correlation functions.

Abstract

This Letter reports on how the interfaces in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) class undergo, in the course of time, a transition from the flat, growing regime to the stationary one. Simulations of the polynuclear growth model and experiments on turbulent liquid crystal reveal universal functions of the KPZ class governing this transition, which connect the distribution and correlation functions for the growing and stationary regimes. This in particular shows how interfaces realized in experiments and simulations actually approach the stationary regime, which is never attained unless a stationary interface is artificially given as an initial condition.