Chaotic Scattering in the Regime of Weakly Overlapping Resonances

TL;DR

This study investigates microwave scattering in a resonator simulating a chaotic quantum system, analyzing scattering matrix distributions and autocorrelation functions with random-matrix theory, revealing frequency-dependent agreement.

Contribution

It provides experimental measurements of microwave scattering in a chaotic resonator and compares the results with random-matrix theory predictions across different frequency regimes.

Findings

Good agreement with theory below 10.1 GHz

Distribution of scattering matrix elements is non-Gaussian

Autocorrelation function fits well with theoretical models below 10.1 GHz

Abstract

We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the resonator simulates a chaotic quantum system. The distribution of the elements of the scattering matrix S is not Gaussian. The Fourier coefficients of S are used for a best fit of the autocorrelation function if S to a theoretical expression based on random--matrix theory. We find very good agreement below but not above 10.1 GHz.