Scaling properties and anomalous transport of particles inside the stochastic layer

Abstract

Particle motion in a two-wave field is considered as a model for studying the kinetic (transport) properties inside the stochastic layer. The existence of an exact renormalization invariance of the separatrix with respect to the perturbation parameter and the approximate renormalization invariance for the exact equation of motion near a saddle point is shown. High accuracy symplectic integration is used to obtain the distribution function, its moments, and transport exponents. Scaling properties and anomalous transport have been found. It is shown that, depending on the parameters of the system, there is a possibility of modifying the fine (islands) structure of the stochastic layer, which leads to variations of the transport properties from the anomalous to the normal (Gaussian) ones.