Missing level statistics in a dissipative microwave resonator with partially violated time-reversal invariance

TL;DR

This study experimentally investigates the fluctuation properties of a dissipative microwave resonator simulating a quantum billiard with partial time-reversal invariance violation, analyzing incomplete spectra using random-matrix theory.

Contribution

It introduces analytical expressions for spectral correlations in incomplete spectra with partial TIV, validated by experimental data.

Findings

Analytical formulas accurately describe spectral statistics with partial TIV.

Experimental spectra show consistency with random-matrix theory predictions.

Dissipation prevents complete resonance frequency identification, affecting spectral analysis.

Abstract

We report on the experimental investigation of the fluctuation properties in the resonance frequency spectra of a flat resonator simulating a dissipative quantum billiard subject to partial time-reversal invariance violation (TIV) which is induced by two magnetized ferrites. The cavity has the shape of a quarter bowtie billiard of which the corresponding classical dynamics is chaotic. Due to dissipation it is impossible to identify a complete list of resonance frequencies. Based on a random-matrix theory approach we derive analytical expressions for statistical measures of short- and long-range correlations in such incomplete spectra interpolating between the cases of preserved time-reversal invariance and complete TIV and demonstrate their applicability to the experimental spectra.