DIFFUSION OF TRAJECTORIES IN A SIMPLE HAMILTONIAN SYSTEM WITH SLOW PERIODIC FORCING

The dynamics of phase-space trajectories in a sinusoidal potential with slowly modulated amplitude is considered. It is shown that trapping and detrapping of trajectories in the potential causes diffusion of the adiabatic invariant. An approximate diffusion coefficient is calculated and is shown to scale as epsilon-3, where epsilon << 1 is the modulation frequency. Numerical simulations are used to test the analytic results, showing that phase correlations significantly affect the magnitude and shape of the diffusion coefficient, although they do not alter its scaling with epsilon.