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

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Abstract
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. This greatly facilitates the numerical investigation of stochasticity and the ionisation process and allows the approximate analytical estimation of the threshold field strengths for the onset of chaos and of the diffusion coefficient of the electron in energy space. 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.