GUTZWILLERS TRACE FORMULA AND SPECTRAL STATISTICS - BEYOND THE DIAGONAL APPROXIMATION

We calculate the 2-point spectral correlation function for classically chaotic systems in the semiclassical limit using Gutzwiller's trace f ormula. The off-diagonal contributions from pairs of nonidentical peri odic orbits are evaluated by relating them to the diagonal terms. The behavior we find is similar to that recently discovered to hold for di sordered systems using nonperturbative supersymmetric methods. Our ana lysis generalizes immediately to include parametric statistics and hig her-order correlations and to the study of the semiclassical distribut ion of matrix elements.