Probability Distribution for Coherent Transport of Random Waves

TL;DR

This paper develops a probability theory for coherent wave transport in linear media, revealing the transmissivity distribution's shape, bounds, and asymptotic behavior, and resolving a paradox related to eigenvalue and transmissivity distributions.

Contribution

It introduces a comprehensive probabilistic framework for wave transport, showing the transmissivity distribution as a B-spline and analyzing its asymptotic Gaussian behavior.

Findings

Transmissivity distribution is a B-spline with knots at transmission eigenvalues.

In the large n limit, the distribution converges to a Gaussian.

The Gaussian mean and variance depend on the eigenvalues' moments.

Abstract

We establish a comprehensive probability theory for coherent transport of random waves through arbitrary linear media. The transmissivity distribution for random coherent waves is a fundamental B-spline with knots at the transmission eigenvalues. We analyze the distribution's shape, bounds, moments, and asymptotic behaviors. In the large n limit, the distribution converges to a Gaussian whose mean and variance depend solely on those of the eigenvalues. This result resolves the apparent paradox between bimodal eigenvalue distribution and unimodal transmissivity distribution.