Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

Details Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

2000-03-08

arxiv.org/abs/nlin/0003018v2

Phys. Rev. Lett. 85, 1412 (2000)

Nonlinear Sciences

Chaotic Dynamics

4 pages, 3 figures

Scientific paper

10.1103/PhysRevLett.85.1412

We consider chaotic billiards in d dimensions, and study the matrix elements M_{nm} corresponding to general deformations of the boundary. We analyze the dependence of |M_{nm}|^2 on \omega = (E_n-E_m)/\hbar using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency \omega. We show that for dilations and translations of the boundary, |M_{nm}|^2 vanishes like \omega^4 as \omega -> 0, for rotations like \omega^2, whereas for generic deformations it goes to a constant. Such special cases lead to quasi-orthogonality of the eigenstates on the boundary.

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