Renormalization Group Theory for Global Asymptotic Analysis

TL;DR

This paper demonstrates how renormalization group theory can unify and simplify the analysis of singular perturbation methods and amplitude equations in nonequilibrium systems, providing more effective approximation techniques.

Contribution

It introduces a unified RG framework for understanding and applying singular perturbation methods and amplitude equations in nonequilibrium phenomena.

Findings

RG theory can unify singular and reductive perturbation methods.

Renormalized perturbation approach simplifies analysis and improves approximations.

Amplitude equations are identified as RG equations.

Abstract

We show with several examples that renormalization group (RG) theory can be used to understand singular and reductive perturbation methods in a unified fashion. Amplitude equations describing slow motion dynamics in nonequilibrium phenomena are RG equations. The renormalized perturbation approach may be simpler to use than other approaches, because it does not require the use of asymptotic matching, and yields practically superior approximations.