Classical and quantum dynamics in high-frequency fields

The authors analyse the effect of a high-frequency harmonic field on a one-dimensional system whose natural frequency is a decreasing function of the classical action. The show that for weak to moderate fields the classical and quantal excitation mechanisms are quite different: the quantal motion is dominated by relatively few 'quasiresonant' states so it cannot follow the diffusive or chaotic classical motion. They approximate the motion near the initial state by a standard map and show that the system is characterised by an effective Planck constant which needs to be very small for classical dynamics to be valid. They apply this analysis to the one-dimensional hydrogen atom and compare calculations performed using a full basis and the quasiresonant basis and show that there is good agreement.