"Sinc"-Noise for the KPZ Equation

TL;DR

This paper investigates how spatially correlated 'sinc'-profile noise affects the KPZ equation, revealing that large-scale behavior aligns with the standard KPZ fixed point regardless of finite correlation length.

Contribution

It demonstrates through field-theoretic techniques that the KPZ equation's large-scale behavior is universal for finite correlation length noise, extending previous Gaussian noise results.

Findings

Large-scale KPZ behavior is unaffected by finite 'sinc'-noise correlation length.

The system behaves as if driven by white noise at large scales.

Results support universality of KPZ dynamics with respect to noise structure.

Abstract

In this paper we study the one-dimensional Kardar-Parisi-Zhang equation (KPZ) with correlated noise by field-theoretic dynamic renormalization group techniques (DRG). We focus on spatially correlated noise where the correlations are characterized by a "sinc"-profile in Fourier-space with a certain correlation length $\xi$. The influence of this correlation length on the dynamics of the KPZ equation is analyzed. It is found that its large-scale behavior is controlled by the "standard" KPZ fixed point, i.e. in this limit the KPZ system forced by "sinc"-noise with arbitrarily large but finite correlation length $\xi$ behaves as if it were excited with pure white noise. A similar result has been found by Mathey et al. [Phys.Rev.E 95, 032117] in 2017 for a spatial noise correlation of Gaussian type ($\sim e^{-x^2/(2\xi^2)}$), using a different method. These two findings together suggest that the KPZ dynamics is universal with respect to the exact noise structure, provided the noise correlation length $\xi$ is finite.