Aspects of two-level systems under external time-dependent fields

The dynamics of two-level systems in time-dependent backgrounds is under consideration. We present some new exact solutions in special backgrounds decaying in time. On the other hand, following ideas of Feynman et al, we discuss in detail the possibility of reducing the quantum dynamics to a classical Hamiltonian system. This, in particular, opens the possibility of directly applying powerful methods of classical mechanics (e.g. KAM methods) to study the quantum system. Following such an approach, we draw conclusions of relevance for 'quantum chaos' when the external background is periodic or quasi-periodic in time. (author)