SPECTRAL PROPERTIES OF SYSTEMS WITH DYNAMIC LOCALIZATION .2. FINITE-SAMPLE APPROACH

We study correlations in the quasi-energy spectrum of the quantum kicked rotor restricted to a Hilbert space of finite dimension. The spectral correlations depend on the ratio gamma of the localization length to the basis size. We derive semiclassical expressions for the two-point cluster function which interpolate between COE behaviour for gamma --> infinity and Poissonian (lack of correlations) for gamma --> 0. We show how the diffusive nature of the classical dynamics finds its expression in the quantal spectral correlations.