Deformations and dilations of chaotic billiards: dissipation rate, and quasiorthogonality of the boundary wave functions
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))/Planck's over 2pi 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 such as omega(2), whereas for generic deformations it goes to a constant. Such special cases lead to quasiorthogonality of the eigenstates on the boundary.
Barnett
A
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Cohen
D
Heller
EJ