ANOMALOUS DIFFUSION IN THE KICKED HARPER SYSTEM

Abstract

Stochastic property of the Hamiltonian dynamical systems exhibits anomalous behavior 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, which could be attributed to temporal fractal property. In order to explore the effect of the accelerator modes on the stochastic diffusion, the kicked Harper system is investigated in detail. It is found that the numerical observation of the diffusion coefficient shows 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 note that, unlike the case of the standard map, the multi-period, multi-step accelerator modes are responsible for much of the profound effect of the enhancement of diffusion even in the domain of larger stochastic parameters.