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arXiv · 1708.05553

"Sinc"-Noise for the KPZ Equation

Oliver Niggemann·Haye Hinrichsen
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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 $ξ$. 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 $ξ$ 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 ($\sim e^{-x^2/(2ξ^2)}$), 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 $ξ$ is finite.

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Oliver Niggemann, Haye Hinrichsen. 2017-08-18. "Sinc"-Noise for the KPZ Equation. https://doi.org/10.1103/physreve.97.062125

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