Deformations and dilations of chaotic billiards: dissipation rate, and quasiorthogonality of the boundary wave functions

@article{Barnett2000DeformationsAD,
  title={Deformations and dilations of chaotic billiards: dissipation rate, and quasiorthogonality of the boundary wave functions},
  author={Barnett and Cohen and Heller},
  journal={Physical review letters},
  year={2000},
  volume={85 7},
  pages={
          1412-5
        }
}
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… Expand
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