Minimum action method for the Kardar-Parisi-Zhang equation

TL;DR

This paper applies a minimum action numerical method to the 1D KPZ equation, revealing nucleation-driven transition scenarios consistent with weak noise analytical results, and briefly discusses 2D transitions.

Contribution

It introduces a numerical minimum action approach to analyze rare events in the KPZ equation, connecting large deviation theory with interface growth dynamics.

Findings

Transition driven by nucleation and propagation of facets in 1D

Consistent with analytical weak noise limit results

Brief discussion of 2D transition scenarios

Abstract

We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for a growing interface. In one dimension we find that the switching scenario is determined by the nucleation and subsequent propagation of facets or steps, corresponding to moving domain walls or growth modes in the underlying noise driven Burgers equation. The transition scenario is in accordance with recent analytical studies of the one dimensional Kardar-Parisi-Zhang equation in the asymptotic weak noise limit. We also briefly discuss transitions in two dimensions.