Numerical Evidence for Stretched Exponential Relaxations in the Kardar-Parisi-Zhang Equation

TL;DR

This paper provides numerical evidence supporting the presence of stretched exponential decay in the dynamical structure factor of the 1+1 dimensional KPZ equation, confirming scaling behavior over extensive ranges.

Contribution

The study offers extensive numerical integration results and an analytic approximation for the long-time behavior of the KPZ equation's structure factor.

Findings

Confirmed scaling and stretched exponential decay in the structure factor

Provided an analytic expression closely matching numerical data

Validated long-time behavior predictions for the KPZ equation

Abstract

We present results from extensive numerical integration of the KPZ equation in $1 + 1$ dimensions aimed to check the long-time behavior of the dynamical structure factor of that system. Over a number of decades in the size of the structure factor we confirm scaling and stretched exponential decay. We also give an analytic expression that yields a very good approximation to the numerical data.