Autocorrelation function of level velocities for ray-splitting billiards

Area of Science:

• Physics
• Quantum Chaos
• Wave Phenomena

Background:

• Classical and quantum chaos are fundamental concepts in physics.
• Ray-splitting systems exhibit complex dynamics relevant to wave propagation.
• Autocorrelation functions and conductance are key observables in characterizing chaotic systems.

Purpose of the Study:

• To experimentally and theoretically investigate the autocorrelation function of level velocities and generalized conductance.
• To simulate a Sinai ray-splitting billiard using a microwave cavity.
• To compare experimental and numerical findings with predictions from random matrix theory.

Main Methods:

• Experimental simulation using a thin microwave rectangular cavity with a quarter-circle Teflon insert.
• Theoretical parameter-dependent quantum calculations of eigenenergies for an annular ray-splitting billiard.
• Comparison of experimental and numerical results with Gaussian orthogonal ensemble predictions.

Main Results:

• Experimental and theoretical data for the autocorrelation function c(x) and generalized conductance C(0) were obtained.
• The study provides insights into the behavior of chaotic ray-splitting systems.
• Results demonstrate consistency with theoretical models based on random matrix theory.

Conclusions:

• The study successfully characterized the autocorrelation function and generalized conductance in a simulated Sinai ray-splitting billiard.
• Experimental and theoretical findings support the applicability of random matrix theory to such systems.
• This research contributes to the understanding of quantum chaos in complex billiards.