Abstract

The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed in phase space, the spectral form factor K (tau) agrees with the GOE prediction of random-matrix theory up to second order included in the time tau measured in units of the Heisenberg time (leading off-diagonal approximation). Our approach is based on the mechanism of periodic-orbit correlations discovered recently by Sieber and Richter (2001 Phys. Scr. T 90 128). By reformulating the theory of these authors in phase space, their result on the free motion on a Riemann surface with constant negative curvature is extended to general Hamiltonian hyperbolic systems with two degrees of freedom.