An efficient method for scattering problems in open billiards: Theory   and applications
  We present an efficient method to solve scattering problems in two-dimensional open billiards with two leads and a complicated scattering region. The basic idea is to transform the scattering region to a rectangle, which will lead to complicated dynamics in the interior, but simple boundary conditions. The method can be specialized to closed billiards, and it allows the treatment of interacting particles in the billiard. We apply this method to quantum echoes measured recently in a microwave cavity, and indicate, how it can be used for interacting particles. 
Gursoy B. Akguc, Thomas H. Seligman