DC currents in Hamiltonian systems by Lévy flights

We study the mechanism leading to directed transport in the stochastic layer of AC-driven Hamiltonian systems. We show that current rectification is obtained by breaking the symmetry of Lévy flights in ballistic channels which exist due to resonance islands with nonzero winding numbers. In the framework of the continuous time random walk (CTRW) approach, we construct a generalized asymmetric flights model and derive an expression for the current in terms of the characteristics of the relevant ballistic channels. We find very good agreement between the results of direct integration of the dynamical equations and the CTRW formulation.