Non-perturbative calculation of the probability distribution of plane-wave transmission through a disordered waveguide

TL;DR

This paper develops a non-perturbative random-matrix theory to analyze the probability distribution of wave transmission through disordered waveguides, revealing a crossover from diffusive to localized regimes and contrasting behavior in chaotic cavities.

Contribution

It introduces a non-perturbative approach to calculate transmission distributions in disordered waveguides, highlighting a crossover from Gaussian to lognormal statistics.

Findings

Identifies a crossover from Gaussian to lognormal transmission statistics.

Shows different crossover behavior in chaotic cavities.

Provides a non-perturbative framework for wave transmission analysis.

Abstract

A non-perturbative random-matrix theory is applied to the transmission of a monochromatic scalar wave through a disordered waveguide. The probability distributions of the transmittances T_{mn} and T_n=\sum_m T_{mn} of an incident mode n are calculated in the thick-waveguide limit, for broken time-reversal symmetry. A crossover occurs from Rayleigh or Gaussian statistics in the diffusive regime to lognormal statistics in the localized regime. A qualitatively different crossover occurs if the disordered region is replaced by a chaotic cavity. ***Submitted to Physical Review E.***