Semiclassical calculations of the two-point correlation form factor for diffractive systems

Abstract

The computation of the two-point correlation form factor K(τ) isperformed for a rectangular billiard with a small-size impurity inside forboth periodic or Dirichlet boundary conditions. It is demonstrated that allterms of perturbation expansion of this form factor in powers of τ canbe computed directly from a semiclassical trace formula. The main part of thecalculation is the summation of nondiagonal terms in the cross product ofclassical orbits. When the diffraction coefficient for the scattering on theimpurity is a constant our results coincide with the expansion of exactexpressions obtained earlier by a different method.