Central limit theorem for the wave transport in disordered waveguides: a perturbative approach

TL;DR

This paper develops a perturbative theoretical framework demonstrating that wave transport in disordered waveguides follows a generalized central limit theorem, with macroscopic statistics depending only on first and second moments of individual scatterers.

Contribution

It introduces a statistical approach that does not assume specific scattering distributions and applies to dense-weak-scattering and ballistic regimes.

Findings

Macroscopic wave transport statistics depend only on first and second moments of scatterers.

The approach is consistent with the optical theorem.

Results are valid in dense-weak-scattering and ballistic regimes.

Abstract

The statistical scattering properties of wave transport in disordered waveguides are derived perturbatively within the transition matrix formalism. The limiting macroscopic statistic of the wave transport, emerges as a consequence of a generalized central-limit-theorem: the expectation values of macroscopic observables depend only on the first and second moments of the reflection matrix of individual scatterers. This theoretical approach does not consider any statistical assumption on the scattering properties of the individual scatterers and it is fully consistent with the optical theorem. The results are found in the so called dense-weak-scattering limit and in the ballistic regime.