Periodic{orbit Theory of the Number Variance of Strongly Chaotic Systems

We discuss the number variance 2 (L) and the spectral form factor F() of the energy levels of bound quantum systems whose classical counterparts are strongly chaotic. Exact periodic{orbit representations of 2 (L) and F() are derived which explain the breakdown of universality, i. e., the deviations from the predictions of random{matrix theory. The relation of the exact spectral form factor F() to the commonly used approximation K() is clariied. As an illustration the periodic{orbit representations are tested in the case of a strongly chaotic system at low and high energies including very long{range correlations up to L = 700. Good agreement between \experimental" data and theory is obtained.