Effective Coupling for Open Billiards

Details Effective Coupling for Open Billiards Effective Coupling for Open Billiards

2001-04-09

arxiv.org/abs/nlin/0104023v1

Phys. Rev. E 64 (2001) 056227

Nonlinear Sciences

Chaotic Dynamics

Scientific paper

10.1103/PhysRevE.64.056227

We derive an explicit expression for the coupling constants of individual eigenstates of a closed billiard which 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.

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