Abstract
I discuss some new universal aspects of diffusion in classical deterministic and chaotic dynamical systems, especially in Hamiltonian systems. First ergodic (fully chaotic) systems are discussed, described by the random model and then the mixed type systems with a typical KAM scenario described by the generalized Poissonian model. A simple analytic power law model is worked out. Some generalizations by treating the correlations are presented, to describe the effects of stickyness in the dynamics, caused typically by the existence of cantori in the chaotic region, which lead to a modified random model (suppressed coefficient in the exponential law). Finally, I explain the relevance of these studies in the context of problems in stationary quantum chaos, namely the statistical properties of the energy spectra, especially in the classically mixed type systems, following the Principle of Uniform Semiclassical Condensation and in the context of the Berry-Robnik theory.
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