Experimental versus numerical eigenvalues of a Bunimovich stadium billiard: a comparison

Area of Science:

• Quantum Chaos
• Statistical Mechanics
• Microwave Physics

Background:

• Bunimovich stadium billiards exhibit complex dynamics.
• Eigenvalue statistics probe quantum chaos.
• Superconducting microwave resonators offer a platform for studying quantum chaotic systems.

Purpose of the Study:

• Compare statistical properties of eigenvalue sequences from a real system and an ideal model.
• Investigate the influence of mechanical imperfections on spectral fluctuations and length spectra.
• Analyze the impact of marginally stable 'bouncing ball' orbits.

Main Methods:

• Obtained eigenvalues from a superconducting microwave resonator (real system).
• Calculated eigenvalues numerically for an ideal Bunimovich stadium billiard.
• Analyzed spectral fluctuations and length spectra.

Main Results:

• Identified discrepancies between real and ideal systems due to mechanical imperfections.
• Demonstrated the influence of imperfections on spectral fluctuations and length spectra.
• Observed the effect of 'bouncing ball' orbits in different billiard geometries.

Conclusions:

• Mechanical imperfections significantly alter the statistical properties of eigenvalue sequences in real systems.
• The 'bouncing ball' orbits play a crucial role in the dynamics of stadium billiards.
• Discrepancies highlight the importance of considering system imperfections in quantum chaos studies.