Trace formula for chaotic dielectric resonators tested with microwave experiments

TL;DR

This study experimentally tests a semiclassical trace formula for chaotic dielectric resonators using microwave measurements, finding qualitative agreement and highlighting areas for theoretical refinement.

Contribution

First experimental validation of the semiclassical trace formula for chaotic dielectric resonators with microwave resonator data.

Findings

Good qualitative agreement between experiment and trace formula

Deviations due to missing resonances and need for higher-order corrections

Curvature correction improves the match but further work needed

Abstract

We measured the resonance spectra of two stadium-shaped dielectric microwave resonators and tested a semiclassical trace formula for chaotic dielectric resonators proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)]. We found good qualitative agreement between the experimental data and the predictions of the trace formula. Deviations could be attributed to missing resonances in the measured spectra in accordance with previous experiments [Phys. Rev. E 81, 066215 (2010)]. The investigation of the numerical length spectrum showed good qualitative and reasonable quantitative agreement with the trace formula. It demonstrated, however, the need for higher-order corrections of the trace formula. The application of a curvature correction to the Fresnel reflection coefficients entering the trace formula yielded better agreement, but deviations remained, indicating the necessity of further investigations.