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Effective coupling for open billiards.

K Pichugin1, H Schanz, P Seba

  • 1Institute of Physics, Czech Academy of Sciences, Cukrovarnicka 10, Prague, Czech Republic and Kirensky Institute of Physics, 660036 Krasnoyarsk, Russia.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
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We derived coupling constants for open billiards, comparing Wigner time delay and resonance positions to numerical calculations. Deviations highlight evanescent modes and finite eigenstates, with implications for billiard shape and boundary conditions.

Area of Science:

  • Quantum mechanics
  • Mesoscopic physics
  • Waveguide theory

Background:

  • Understanding quantum systems requires analyzing how closed systems interact with their environment.
  • Billiard models are crucial for studying wave phenomena in confined spaces.
  • Waveguides provide a means to couple quantum systems and probe their properties.

Purpose of the Study:

  • To derive an explicit expression for coupling constants in open billiards.
  • To compare theoretical predictions of Wigner time delay and resonance positions with numerical calculations.
  • To investigate the influence of billiard shape and waveguide boundary conditions on coupling constants.

Main Methods:

  • Derivation of an explicit expression for coupling constants.
  • Comparison of theoretical results with exact numerical calculations.

Related Experiment Videos

  • Analysis of Wigner time delay and resonance positions.

    • Main Results:

    • An explicit formula for coupling constants was derived.
    • Deviations from numerical calculations were attributed to evanescent modes and finite eigenstates.
    • The impact of billiard geometry and waveguide mouth boundary conditions was analyzed.
    • The mean value of dimensionless coupling constants approaches a critical value for random-matrix-theory-like eigenstates.

    Conclusions:

    • The derived expression provides insights into the coupling dynamics of open billiards.
    • Evanescent modes and the number of considered eigenstates are significant factors affecting accuracy.
    • Billiard shape and boundary conditions play a role in system behavior.
    • The study connects coupling constants to random-matrix theory predictions under specific conditions.