Statistics of the Mesoscopic Field

TL;DR

This paper demonstrates that the mesoscopic microwave field in quasi-1D dielectric samples behaves as a Gaussian random process, with its distribution and correlations described by the total transmission statistics.

Contribution

It provides a statistical description of the mesoscopic field, linking Gaussian process behavior to transmission distributions in diffusive and localized regimes.

Findings

Field normalized by sqrt of average flux is Gaussian

Field distribution is a mixture of Gaussians weighted by transmission

Correlation function factorizes into Gaussian correlator and transmission square root

Abstract

We find in measurements of microwave transmission through quasi-1D dielectric samples for both diffusive and localized waves that the field normalized by the square root of the spatially averaged flux in a given sample configuration is a Gaussian random process with position, polarization, frequency, and time. As a result, the probability distribution of the field in the random ensemble is a mixture of Gaussian functions weighted by the distribution of total transmission, while its correlation function is a product of correlators of the Gaussian field and the square root of the total transmission.