Some new aspects of Lévy walks and flights: directed transport, manipulation through flights and population exchange

Lévy flights and walks have been shown to arise in a broad spectrum of areas, leading to anomalous diffusion. Here we investigate their central role in some dynamical phenomena encountered in Hamiltonian systems with a mixed phase space. In particular we discuss, within the continuous time random walk (CTRW) framework, the possibility to obtain currents in Hamiltonian systems and how to manipulate them, and the effect of population exchange between islands of stability. The latter can be viewed as the classical counterpart of chaos-assisted tunneling.