A functional renormalization method for wave propagation in random media

TL;DR

This paper introduces a novel renormalization group approach using field theory to accurately determine wave propagation speed in media with random inhomogeneities, validated through dielectric constant calculations.

Contribution

It develops an exact renormalization group method for wave propagation in random media, applying field theory and testing with dielectric constant computations.

Findings

Renormalization group approach effectively models wave speed in random media

Simple approximation matches self-consistent two-loop dielectric constant calculation

Method provides a systematic way to evaluate effective wave properties

Abstract

We develop the exact renormalization group approach as a way to evaluate the effective speed of propagation of a scalar wave in a medium with random inhomogeneities. We use the Martin-Siggia-Rose formalism to translate the problem into a non equilibrium field theory one, and then consider a sequence of models with a progressively lower infrared cutoff; in the limit where the cutoff is removed we recover the problem of interest. As a test of the formalism, we compute the effective dielectric constant of an homogeneous medium interspersed with randomly located, interpenetrating bubbles. Already a simple approximation to the renormalization group equations turns out to be equivalent to a self-consistent two-loops evaluation of the effective dielectric constant.