1 Semi - classical calculations of the two - point correlation form factor for diffractive systems

The computation of the two-point correlation form factor K(τ) is performed for a rectangular billiard with a small size impurity inside for both periodic or Dirichlet boundary conditions. It is demonstrated that all terms of perturbation expansion of this form factor in powers of τ can be computed directly from a semiclassical trace formula. The main part of the calculation is the summation of non-diagonal terms in the cross product of classical orbits. When the diffraction coefficient for the scattering on the impurity is a constant our results coincide with the expansion of exact expressions obtained in Ref. [1] by a different method.