Dynamics of curved interfaces

TL;DR

This paper investigates stochastic growth on curved interfaces using PDEs derived from planar equations, revealing unique fluctuation behaviors, loss of correlations over time, and metric-dependent effects, with implications for nonuniversal propagation regimes.

Contribution

It introduces a framework for analyzing stochastic growth on curved geometries by deriving equations from planar models, highlighting new fluctuation dynamics and metric influences.

Findings

Loss of correlation through time in curved interface models

Distinct behavior of average fluctuations compared to planar cases

Propagation of correlations becomes nonuniversal in curved geometries

Abstract

Stochastic growth phenomena on curved interfaces are studied by means of stochastic partial differential equations. These are derived as counterparts of linear planar equations on a curved geometry after a reparametrization invariance principle has been applied. We examine differences and similarities with the classical planar equations. Some characteristic features are the loss of correlation through time and a particular behaviour of the average fluctuations. Dependence on the metric is also explored. The diffusive model that propagates correlations ballistically in the planar situation is particularly interesting, as this propagation becomes nonuniversal in the new regime.