Ballistic flights and random diffusion as building blocks for Hamiltonian kinetics

We propose a kinetic approach to transport in Hamiltonian systems with a mixed phase space. The approach is based on the decomposition of the dynamical picture into two contributions: (a) ballistic flights, and (b) random diffusion. The kinetic scheme leads to a stochastic process with statistical properties which are similar to those produced by the original Hamiltonian. We show that our approach helps in obtaining an insight into several properties of Hamiltonian kinetics such as anomalous diffusion, chaos-assisted population exchange, and current rectification. In particular, the chaos-assisted exchange offers a classical counterpart for the recently reported chaos-assisted tunneling.