Quantum Chaotic Scattering in Microwave Resonators

TL;DR

This study experimentally investigates quantum chaotic scattering using microwave resonators, measuring scattering amplitudes and comparing statistical fluctuations with random-matrix theory predictions, confirming the theory with high accuracy.

Contribution

First experimental validation of random-matrix theory predictions for quantum chaotic scattering in microwave resonators across various regimes.

Findings

Statistical measures of S-matrix fluctuations match theoretical predictions.

Goodness-of-fit tests confirm the accuracy of the random-matrix approach.

The data supports the universality of quantum chaotic scattering statistics.

Abstract

In a frequency range where a microwave resonator simulates a chaotic quantum billiard, we have measured moduli and phases of reflection and transmission amplitudes in the regimes of both isolated and of weakly overlapping resonances and for resonators with and without time-reversal invariance. Statistical measures for S-matrix fluctuations were determined from the data and compared with extant and/or newly derived theoretical results obtained from the random-matrix approach to quantum chaotic scattering. The latter contained a small number of fit parameters. The large data sets taken made it possible to test the theoretical expressions with unprecedented accuracy. The theory is confirmed by both, a goodness-of-fit-test and the agreement of predicted values for those statistical measures that were not used for the fits, with the data.