Quantum Billiards with Surface Scattering: Ballistic Sigma-Model   Approach
  Statistical properties of energy levels and eigenfunctions in a ballistic system with diffusive surface scattering are investigated. The two-level correlation function, the level number variance, the correlation function of wavefunction intensities, and the inverse participation ratio are calculated. 
Ya. M. Blanter, A. D. Mirlin, and B. A. Muzykantskii