Statistical scattering of waves in disordered waveguides: The limiting macroscopic statistics in the ballistic regime

TL;DR

This paper develops a perturbative analytical method to study the statistical properties of wave scattering in disordered ballistic waveguides, revealing the role of closed channels and providing results consistent with numerical simulations.

Contribution

It introduces a Born series-based perturbative approach valid in the ballistic regime, explicitly accounting for closed channels, and analytically characterizes wave scattering statistics in disordered waveguides.

Findings

Closed channels are relevant for amplitude expectations.

Intensities and conductance are insensitive to closed channels.

Analytical results agree with numerical simulations.

Abstract

In this work, we present a theoretical study of the statistical properties of wave scattering in a disordered ballistic waveguide of length L; we have called this system the "building block". The building block is interesting as a physical system because its statistical properties could be studied experimentally in the laboratory. In order to study the building block, as a physical system in itself, we have developed a perturbative method based on Born series. This method is valid only in the ballistic regime, when the length of the system L is smaller than the mean free path l, and in the short-wave-length approximation, when the the wave number k and the mean free path l satisfy kl >> 1. This method has allowed to find, analytically, the behavior of quantities of interest that we have not been able to find from the diffusion equation. In contrast with the diffusion equation method, which takes into account approximately the contribution of closed channels, this method takes them explicitly. In earlier works numerical evidence was found that the expectation values of some interesting quantities are insensitive to the number of closed channels that were used on the calculations; with this method, we could show that closed channels are relevant for the expectation values of amplitudes but irrelevant for the intensities and conductance expectation values. The results of this method show a good agreement with numerical simulations.