Microwave study of quantum n-disk scattering

TL;DR

This study uses microwave cavities to experimentally investigate quantum scattering in chaotic n-disk systems, confirming semiclassical predictions and revealing detailed resonance and autocorrelation behaviors.

Contribution

It provides a wave-mechanical implementation of quantum n-disk scattering and compares experimental results with semiclassical theory, highlighting non-universal oscillations at intermediate energies.

Findings

Good agreement between measured and semiclassical resonance spectra.

Extraction of escape rates from autocorrelation functions matches classical predictions.

Detection of non-universal oscillations indicating periodic orbit effects.

Abstract

We describe a wave-mechanical implementation of classically chaotic n-disk scattering based on thin 2-D microwave cavities. Two, three, and four-disk scattering are investigated in detail. The experiments, which are able to probe the stationary Green's function of the system, yield both frequencies and widths of the low-lying quantum resonances. The observed spectra are found to be in good agreement with calculations based on semiclassical periodic orbit theory. Wave-vector autocorrelation functions are analyzed for various scattering geometries, the small wave-vector behavior allowing one to extract the escape rate from the quantum repeller. Quantitative agreement is found with the value predicted from classical scattering theory. For intermediate energies, non-universal oscillations are detected in the autocorrelation function, reflecting the presence of periodic orbits.