Stochastic dynamics of hydrogenic atoms in the microwave field: modelling by maps and quantum description

The motion of an electron of a classical hydrogenic atom in an oscillating electric field is studied theoretically. An analysis is provided, based on the iterative (mapping) forms of the classical equations of motion in perturbation theory and the adiabatic approximation. The method is asymptotically exact at high field frequencies and gives a good approximation for medium and low frequencies. The adiabatic approximation describes well the approach of the stochastic ionisation threshold field strength to the static field ionisation threshold. From the quantum mechanical point of view the ionisation is a result of the great number of one-photon transitions in the strongly perturbed spectrum of the atom. This results in the diffusion of the electron in energy space identical to the diffusion due to stochastic classical motion. The estimation of the mean time of diffusive ionisation is also given. (author)