Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth

TL;DR

This paper analytically computes the skewness of height distribution in the (1+1)-dimensional KPZ growth model using dynamic renormalization-group methods, providing results consistent with numerical and experimental data.

Contribution

It applies the dynamic renormalization-group approach without rescaling to derive the skewness in the KPZ equation, offering an analytical estimate.

Findings

Skewness value S=0.3237 obtained analytically.

Results align with numerical and experimental estimates.

Method demonstrates the effectiveness of the diagrammatic approach in KPZ analysis.

Abstract

We use the $(1+1)$-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J.~Sci.\ Comput.~{\bf 1}, 3 (1986)]. Hence we calculate the second and third order moments of height distribution using the diagrammatic method in the large scale and long time limits. The moments so calculated lead to the value $S=0.3237$ for the skewness. This value is comparable with numerical and experimental estimates.