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

A method for investigating the motion of an electron of a classical hydrogenic atom in an oscillating electric field is presented which is asymptotically exact at high frequencies and provides a good approximation for medium and low frequencies. An adiabatic approximation is shown to accurately describe the approach of the stochastic ionizaton threshold field strength to the static field ionization threshold. A quantum mechanical description indicates that the ionization results from the great number of one-photon transitions in the strongly perturbed spectrum of the atom, leading to diffusion of the electron in energy space which is identical to the diffusion due to stochastic classical motion.