First experimental test of a trace formula for billiard systems showing mixed dynamics

Area of Science:

• Quantum Mechanics and Classical Dynamics
• Condensed Matter Physics
• Mathematical Physics

Background:

• Trace formulas connect quantum system properties (density of states) to classical periodic orbits.
• Existing formulas like Berry-Tabor (regular) and Gutzwiller (chaotic) describe limiting cases.
• Superconducting billiards with mixed dynamics present a challenge for current semiclassical descriptions.

Purpose of the Study:

• To develop a generalized trace formula applicable to superconducting billiards with mixed dynamics.
• To provide a unified semiclassical description bridging regular, chaotic, and mixed quantum behaviors.
• To interpolate between established Berry-Tabor and Gutzwiller trace formulas.

Main Methods:

• Application of a generalized trace formula derived by Ullmo et al. to experimental microwave spectra.
• Analysis of semiclassical description for superconducting billiards exhibiting mixed classical dynamics.
• Comparison with limiting cases of fully regular and fully chaotic systems.

Main Results:

• Successful semiclassical description of microwave spectra from superconducting Limaçon billiards.
• Demonstration that the generalized trace formula accurately models mixed dynamics.
• The formula serves as a continuous interpolation between Berry-Tabor and Gutzwiller formulas.

Conclusions:

• The generalized trace formula provides a unified framework for understanding quantum dynamics in systems with mixed classical behavior.
• This work extends semiclassical methods to complex systems, offering insights into the quantum-classical correspondence.
• The findings are crucial for analyzing spectral properties in superconducting quantum billiards.