Invariance property of wave scattering through disordered media

TL;DR

This paper reveals a universal invariance property of wave scattering in disordered media, showing that mean trajectory length depends only on boundary geometry, not on the scattering details, extending beyond diffusion to various physical systems.

Contribution

It extends the invariance property of mean trajectory length from diffusive systems to wave scattering in diverse regimes, unifying observations across multiple scientific fields.

Findings

Invariance holds for wave scattering in resonant, ballistic, chaotic, and localized systems.

Mean trajectory length depends only on boundary geometry, not scattering details.

Potential for experimental validation using light in disordered media.

Abstract

A fundamental insight in the theory of diffusive random walks is that the mean length of trajectories traversing a finite open system is independent of the details of the diffusion process. Instead, the mean trajectory length depends only on the system's boundary geometry and is thus unaffected by the value of the mean free path. Here we show that this result is rooted on a much deeper level than that of a random walk, which allows us to extend the reach of this universal invariance property beyond the diffusion approximation. Specifically, we demonstrate that an equivalent invariance relation also holds for the scattering of waves in resonant structures as well as in ballistic, chaotic or in Anderson localized systems. Our work unifies a number of specific observations made in quite diverse fields of science ranging from the movement of ants to nuclear scattering theory. Potential experimental realizations using light fields in disordered media are discussed.