In the theory of disordered systems the spectral form factor S(tau), the Fourier transform of the two-level correlation function with respect to the difference of energies, is linear for tautau(c). Near zero and near tau(c) it exhibits oscillations which have been discussed in several recent papers. In problems of mesoscopic fluctuations and quantum chaos a comparison is often made with a random matrix theory. It turns out that, even in the simplest Gaussian unitary ensemble, these oscillations have not yet been studied there. For random matrices, the two-level correlation function rho(lambda(1),lambda(2)) exhibits several well-known universal properties in the large-N Limit. Its Fourier transform is linear as a consequence of the short-distance universality of rho(lambda(1),lambda(2)) However the crossover near zero and tau(c) requires one to study these correlations for finite N. For this purpose we use an exact contour-integral representation of the two-level correlation function which allows us to characterize these crossover oscillatory properties. This representation is then extended to the case in which the Hamiltonian is the sum of a deterministic part H-0 and of a Gaussian random potential V. Finally, we consider the extension to the time-dependent case.
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