PERIODIC-ORBIT THEORY OF THE NUMBER VARIANCE SIGMA(2)(L) OF STRONGLY CHAOTIC SYSTEMS

We discuss the number variance Sigma(2)(L) and the spectral form facto r F(tau) of the energy levels of bound quantum systems whose classical counterparts are strongly chaotic. Exact periodic-orbit representatio ns of Sigma(2) (L) and F(tau) are derived which explain the breakdown of universality, i.e., the deviations from the predictions of random-m atrix theory. The relation of the exact spectral form factor F(tau) to the commonly used approximation K(tau) is clarified. As an illustrati on the periodic-orbit representations are tested in the case of a stro ngly chaotic system at low and high energies including very long-range correlations up to L = 700. Good agreement between ''experimental'' d ata and theory is obtained.