$1/f^\alpha$ power spectrum in the Kardar-Parisi-Zhang universality class

TL;DR

This paper investigates the $1/f^eta$ power spectrum in the KPZ universality class, revealing universal features and connecting spectral exponents to the Baik-Rains distribution through experimental and numerical analysis.

Contribution

It introduces a detailed characterization of the $1/f^eta$ spectrum in the KPZ class and links spectral exponents to universal distribution functions.

Findings

The $1/f^eta$ spectrum is observed in KPZ interfaces.

Spectral exponents match predictions from the aging Wiener-Khinchin theorem.

The spectrum encodes the Baik-Rains universal variance.

Abstract

The power spectrum of interface fluctuations in the $(1+1)$-dimensional Kardar-Parisi-Zhang (KPZ) universality class is studied both experimentally and numerically. The $1/f^\alpha$-type spectrum is found and characterized through a set of "critical exponents" for the power spectrum. The recently formulated "aging Wiener-Khinchin theorem" accounts for the observed exponents. Interestingly, the $1/f^\alpha$ spectrum in the KPZ class turns out to contain information on a universal distribution function characterizing the asymptotic state of the KPZ interfaces, namely the Baik-Rains universal variance. It is indeed observed in the presented data, both experimental and numerical, and for both circular and flat interfaces, in the long time limit.