Channel cross-correlations in transport through complex media

TL;DR

This study measures and analyzes the cross-correlations of transmission channels in microwave cavities, revealing anti-phased behavior influenced by channel coupling strength and absorption, aligning with theoretical predictions.

Contribution

It provides experimental validation of channel cross-correlation behaviors in complex media and incorporates absorption effects into theoretical models.

Findings

Channel cross-correlations are anti-phased with coupling strength.

Absorption effects are crucial for matching theory and experiment.

Anti-correlation impacts universal conductance fluctuations.

Abstract

Measuring transmission between four antennas in microwave cavities, we investigate directly the channel cross-correlations $C$ of the cross sections $\sigma^{ab}$ from antenna at $\vec{r}_a$ to antenna $\vec{r}_b$. Specifically we look for the $C_\Sigma$ and $C_\Lambda$, where the only difference is that $C_\Lambda$ has none of the four channels in common, whereas $C_\Sigma$ has exactly one channel in common. We find experimentally that these two channel cross-correlations are anti-phased as a function of the channel coupling strength, as predicted by theory. This anti-correlation is essential to give the correct values for the universal conductance fluctuations. To obtain a good agreement between experiment and predictions from random matrix theory the effect of absorption had to be included.