Diffusion of Monochromatic Classical Waves

TL;DR

This paper investigates how monochromatic classical waves diffuse in disordered acoustic media across 1D, 2D, and 3D systems, deriving key properties and highlighting differences in diffusion behavior between dimensions.

Contribution

It provides a detailed theoretical framework for wave diffusion in disordered media using scattering theory and the ladder approximation, including new insights into 2D diffusion characteristics.

Findings

Derived expressions for energy flux, density, and intensity in various dimensions.

Identified the transition from ballistic to diffusive wave propagation.

Revealed unique diffusion features in 2D compared to 3D, such as flux dependence on mean free path.

Abstract

We study the diffusion of monochromatic classical waves in a disordered acoustic medium by scattering theory. In order to avoid artifacts associated with mathematical point scatterers, we model the randomness by small but finite insertions. We derive expressions for the configuration-averaged energy flux, energy density, and intensity for one, two and three dimensional (1D, 2D and 3D) systems with an embedded monochromatic source using the ladder approximation to the Bethe-Salpeter equation. We study the transition from ballistic to diffusive wave propagation and obtain results for the frequency-dependence of the medium properties such as mean free path and diffusion coefficient as a function of the scattering parameters. We discover characteristic differences of the diffusion in 2D as compared to the conventional 3D case, such as an explicit dependence of the energy flux on the mean free path and quite different expressions for the effective transport velocity.