CLASSICAL DIFFUSION, ANDERSON LOCALIZATION, AND SPECTRAL STATISTICS IN BILLIARD CHAINS

We study spectral properties of quasi-one-dimensional extended systems that show deterministic diffusion on the classical level and Anderson localization in the quantal description. Using semi-classical argumen ts we relate universal aspects of the spectral fluctuations to feature s of the set of classical periodic orbits, expressed in terms of the p robability to perform periodic motion, which are likewise universal. T his allows us to derive an analytical expression for the spectral form factor which reflects the diffusive nature of the corresponding class ical dynamics. It defines a novel spectral universality class which co vers the transition between GOE statistics in the limit of a small rat io of the system size to the localization length, corresponding to the ballistic regime of disordered systems, to Poissonian level fluctuati ons in the opposite limit. Our semi-classical predictions are illustra ted and confirmed by a numerical investigation of aperiodic chains of chaotic billiards.