Statistical analysis of level-spacing ratios in pseudointegrable systems: Semi-Poisson insight and beyond

Area of Science:

• Quantum mechanics
• Statistical physics
• Condensed matter physics

Background:

• Quantum systems can exhibit complex statistical properties.
• Pseudointegrable systems present unique spectral characteristics.
• Understanding spectral statistics is key to classifying quantum system behavior.

Purpose of the Study:

• To investigate the statistical properties of a quantum system in the pseudointegrable regime.
• To experimentally simulate and theoretically analyze a two-dimensional quantum billiard with a point-like perturbation.
• To characterize the system's behavior using gap ratios and probability distributions.

Main Methods:

• Experimental simulation of a quantum billiard using a flat rectangular resonator with wire antennas.
• Analysis of scattering spectra and energy level gap ratios.
• Theoretical derivation of higher-order nonoverlapping probability distributions.

Main Results:

• The system exhibits semi-Poisson behavior in the 8-16 GHz frequency range.
• The probability distribution parameter ξ was found to be 0.97±0.03.
• Scale-dependent convergence of spectral statistics towards Random Matrix Theory ensembles was observed.

Conclusions:

• The experimental and numerical results confirm the pseudointegrability of the studied system.
• The semi-Poisson ensemble demonstrates scale-dependent properties, approaching Gaussian orthogonal ensemble for k=2.
• Spectral statistics can mimic chaos-like features in nonchaotic systems, highlighting the importance of scale-dependent analysis.