Time evolution of the hydrogen-like Rydberg atom placed in homogeneous electric and magnetic fields with an arbitrary time dependence is considered. Within the manifold of the electron states with the same principal quantum number n, the problem is effectively reduced to the solution of two independent two-state problems. In particular, this reduction allows us to use in the analysis exactly solvable two-state models which are well known in the collision theory. As an example, we consider the case of perpendicular space-fixed fields; the magnetic field remains constant whereas the electric field strength varies linearly with time. The effective two-state problem corresponds to the well known Landau - Zener model. The simple formulae are obtained for the final population of Rydberg states. In the case of time-periodic fields the general properties of the quasienergy spectrum are established.

The double photoionization of He is investigated using the hyperspherical R matrix with semiclassical outgoing waves method. Triply, doubly, and singly differential, as well as fully integrated, cross sections are computed in a variety of geometrical and dynamical situations. The results are found to be in excellent agreement with absolute measurements both in shape and, more importantly, in magnitude. This demonstrates the robustness and accuracy of this ab initio method, which also provides a visualization of the formation of the various cross sections during the expansion of the system. This visualization reveals that, for very asymmetric energy sharings, the cross sections take their final form when the electrons are thousands of atomic units away from the ionic core, a distance where no other method is able to describe the double continuum wave function accurately.

The energy and angular distributions of photoelectrons (the double differential cross sections, DDCS) for attosecond-pulse induced photoemission from atoms in the presence of a strong laser field are theoretically considered. We suggest a comparatively simple computational method based on the strong field approximation for calculation of the DDCS of short pulse photoionization which explicitly includes competing processes of interference and dephasing of the electronic wave packets. The method can be useful for analysis of attosecond streaking experiments. It is tested by comparison with the exact quantum-mechanical computation based on a numerical solving of the time-dependent Schrödinger equation. An excellent agreement between the two computational methods is demonstrated in a wide range of the pulse durations.

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