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Autocorrelation function of level velocities for ray-splitting billiards

Hlushchuk1, Kohler, Bauch

  • 1Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland and College of Science, Aleja Lotnikow 32/46, 02-668 Warszawa, Poland.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 25, 2000
PubMed
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This study investigates the autocorrelation function and generalized conductance in chaotic ray-splitting systems using microwave cavities and quantum calculations. Results align with random matrix theory predictions for quantum chaos.

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.

Related Experiment Videos

  • 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.