Deterministic diffusion and magnetotransport in periodically modulated magnetic fields

Matching of separatrix map and resonant dynamics, with application to global chaos onset between separatrices

We have developed a general method for the description of separatrix chaos, based on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of perturbation, the maximum width of the chaotic layer in energy may be much larger than it was assumed before. We use the above method to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered [S. M. Soskin, O. M. Yevtushenko, and R. Mannella, Phys. Rev. Lett. 90, 174101 (2003)]. The theory well agrees with simulations. We also discuss generalizations and applications. The method may be generalized for single-separatrix cases. The facilitation of global chaos onset may be relevant to a variety of systems, e.g., optical lattices, magnetic and semiconductor superlattices, meandering flows in the ocean, and spinning pendulums. Apart from dynamical transport, it may facilitate noise-induced transitions and the stochastic web formation.

Drastic facilitation of the onset of global chaos

We show that the onset of global chaos in a time periodically perturbed Hamiltonian system may occur at unusually small magnitudes of perturbation if the unperturbed system possesses more than one separatrix. The relevant scenario is the combination of the overlap in the phase space between resonances of the same order and their overlap in energy with chaotic layers associated with separatrices of the unperturbed system. We develop the asymptotic theory and verify it in simulations.