Signatures of classical diffusion in quantum fluctuations of two-dimensional chaotic systems

We consider a two-dimensional (2D) generalization of the standard kicked rotor and show that it is an excellent model for the study of universal features of 2D quantum systems with underlying diffusive classical dynamics. First we analyze the distribution of wave-function intensities and compare them with the predictions derived in the framework of diffusive disordered samples. Next, we turn the closed system into an open one by constructing a scattering matrix. The distribution of the resonance widths P(Gamma) and Wigner delay times (tau(W)) are investigated. The forms of these distributions are obtained for different symmetry classes and the traces of classical diffusive dynamics are identified. Our theoretical arguments are supported by extensive numerical calculations.