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We consider dynamical semigroups with unbounded Kossakowski-Lindblad-Daviesgenerators which are related to evolution of an open system with a tunedrepeated harmonic perturbation. Our main result is the proof of existence ofuniquely determined minimal trace-preserving strongly continuous dynamicalsemigroups on the space of density matrices. The corresponding dual W*-dynamical system is shown to be unital quasi-free and completely positiveautomorphisms of the CCR-algebra. We also comment on the action of dynamicalsemigroups on quasi-free states.

Dynamical Semigroups for Unbounded Repeated Perturbation of Open System