Markovian dynamics under weak periodic coupling.

We examine a completely positive and trace preserving evolution of finite dimensional open quantum system, coupled to large environment via periodically modulated interaction Hamiltonian. We derive a corresponding Markovian Master Equation under usual assumption of weak coupling using the projection operator techniques, in two opposite regimes of very small and very large modulation frequency. Special attention is granted to the case of uniformly (globally) modulated interaction, where some general results concerning the Floquet normal form of a solution and its asymptotic stability are also addressed.