Nonlinearities in Conservative Growth Equations

TL;DR

This paper uses the dynamic renormalization group method to classify nonlinearities in conservative growth equations, revealing only two universality classes and providing geometric insights.

Contribution

It explicitly computes correlation functions to classify nonlinearities and extends the analysis to higher orders with a geometric interpretation.

Findings

Nonlinearities fall into two classes: Edwards-Wilkinson and Lai-Das Sarma.

Explicit computation of two and three point functions at first order.

Generalization to higher order nonlinearities with geometric interpretation.

Abstract

Using the dynamic renormalization group (DRG) technique, we analyze general nonlinearities in a conservative nonlinear growth equation with non-conserved gaussian white noise. We show that they fall in two classes only: the Edwards-Wilkinson and Lai-Das Sarma types, by explicitly computing the associated amputated two and three point functions at the first order in perturbation parameter(s). We further generalize this analysis to higher order nonlinearities and also suggest a physically meaningful geometric interpretation of the same.