Power Spectrum of Discrete and Finite Series of Levels in Chaotic Resonators with and without Partially Violated Time-Reversal Invariance - The Case of Missing Levels

M. Białousa, B. Dietzb, L. Sirkoa aInstitute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warszawa, Poland bLanzhou Center for Theoretical Physics and the Gansu Provincial Key Laboratory of Theoretical Physics, Lanzhou University, Lanzhou, Gansu 730000, China

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We report on experimental investigation of the power spectrum of discrete and finite series of levels in quantum billiards with chaotic classical dynamics and, respectively, with preserved and partially violated time-reversal (T) invariance. In the experiment a flat microwave resonator with the shape of a two-dimensional quarter bow-tie billiard was used. The partial T-invariance violation was induced by two embedded ferrites that were magnetized by an external magnetic field. Due to the openness and internal dissipation of the resonator and ferrites, one typically has to cope with incomplete sequences of resonance frequencies. We employ missing-level statistics to investigate the fluctuation properties in the spectra in terms of statistical measures such as the nearest-neighbor spacing distribution and the power spectrum. We confirm experimentally that the power spectrum can be directly used to evaluate the number of missing levels for both types of systems.

DOI:10.12693/APhysPolA.140.545 topics: wave chaos, microwave billiards, time-reversal invariance violation, chaotic scattering