Patterns in the Kardar-Parisi-Zhang equation

TL;DR

This paper reviews a weak noise approach to the KPZ equation, revealing a many-body picture of interface growth, scaling behavior, and the existence of an upper critical dimension.

Contribution

It introduces a weak noise framework for analyzing the KPZ equation, offering new insights into interface growth mechanisms and critical dimensions.

Findings

Weak noise approach models interface growth as a network of localized modes.

Scaling in 1D linked to a gapless domain wall mode.

Provides an argument for the upper critical dimension of KPZ.

Abstract

We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang equation for the kinetic growth of an interface in higher dimensions. The weak noise approach provides a many body picture of a growing interface in terms of a network of localized growth modes. Scaling in 1d is associated with a gapless domain wall mode. The method also provides an independent argument for the existence of an upper critical dimension.