Effective coupling for open billiards.
We derive an explicit expression for the coupling constants of individual eigenstates of a closed billiard that is opened by attaching a waveguide. The Wigner time delay and the resonance positions resulting from the coupling constants are compared to an exact numerical calculation. Deviations can be attributed to evanescent modes in the waveguide and to the finite number of eigenstates taken into account. The influence of the shape of the billiard and of the boundary conditions at the mouth of the waveguide are also discussed. Finally we show that the mean value of the dimensionless coupling constants tends to the critical value when the eigenstates of the billiard follow random-matrix theory.
Pichugin
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K
Institute of Physics, Czech Academy of Sciences, Cukrovarnicka 10, Prague, Czech Republic and Kirensky Institute of Physics, 660036 Krasnoyarsk, Russia.
Schanz
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H
Seba
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