Localized growth modes, dynamic textures, and upper critical dimension for the Kardar-Parisi-Zhang equation in the weak noise limit

TL;DR

This paper applies a nonperturbative weak noise approach to the KPZ equation, revealing a texture of localized growth modes and proposing that the upper critical dimension is four.

Contribution

It introduces a nonperturbative weak noise scheme to analyze the KPZ equation across all dimensions and conjectures the upper critical dimension based on Derrick's theorem.

Findings

Growth morphology characterized by localized modes

Upper critical dimension conjectured to be four

Texture of diffusive modes superimposed on growth modes

Abstract

A nonperturbative weak noise scheme is applied to the Kardar-Parisi-Zhang equation for a growing interface in all dimensions. It is shown that the growth morphology can be interpreted in terms of a dynamically evolving texture of localized growth modes with superimposed diffusive modes. Applying Derrick's theorem it is conjectured that the upper critical dimension is four.