Anomalous Diffusion in the Kicked Harper System

Abstract

Stochastic properties of Hamiltonian dynamical systems exhibit anomalous behaviour owing to intermittent processes between regular orbits and chaotic motion. In particular, the accelerator modes give rise to the anomalous enhancement of the diffusion process. In order to explore the effect of the accelerator modes on stochastic diffusion, the kicked Harper system is investigated in detail. It is found that the numerical observation of the diffusion coefficient manifests good agreement with the analytical expression obtained by the characteristic function method, except in the domains where the accelerator modes exist. It is interesting to notice that, unlike the case of the standard map, the multi-period multi-step accelerator modes are responsible for a profound effect of the enhancement of diffusion even in the domain of larger stochastic parameters.