"Sinc"-Noise for the KPZ Equation

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.