In this paper we study the one-dimensional Kardar-Parisi-Zhang (KPZ) equation with correlated noise by field-theoretic dynamic renormalization-group techniques. 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 by pure white noise. A similar result has been found by Mathey et al. [S. Mathey et al., Phys. Rev. E 95, 032117 (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.

• Received 23 August 2017
• Revised 21 December 2017

DOI:https://doi.org/10.1103/PhysRevE.97.062125