Accuracy and efficiency of reduced stochastic models for chaotic Hamiltonian systems with time-scale separation

Abstract

The study of the long time behavior of systems with time-scale separation is considerably facilitated if the fast degrees of freedom can be eliminated without affecting the slow dynamics. We investigate a technique in which the fluctuations due to a fast chaotic subsystem are replaced by a suitable stochastic process so that a Fokker-Planck equation for the slow variables results. The accuracy and efficiency of this technique is verified by the detailed numerical investigation of several coupled systems. The asymptotic behavior as well as transients turn out to be well modeled by the reduced dynamics. We concentrate on low-dimensional problems and cover different types of coupling schemes as well as different chaotic subsystems. As a physical application we discuss the classical dynamics of a hydrogen atom in a strong magnetic field.