Spectral properties of systems with dynamical localization. II. Finite sample approach

Abstract

For pt.I see ibid., vol.4, p.59-84 (1991). The authors 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. They derive semiclassical expressions for the two-point cluster function which interpolate between COE behaviour for gamma to infinity and Poissonian (lack of correlations) for gamma to 0. They show how the diffusive nature of the classical dynamics finds its expression in the quantal spectral correlations.