  We propose an exactly soluble W*-dynamical system generated by repeated
harmonic perturbations of the one-mode quantum oscillator. In the present paper
we deal with the case of isolated system. Although dynamics is Hamiltonian and
quasi-free, it produces relaxation of initial state of the system to the steady
state in the large-time limit. The relaxation is accompanied by the entropy
production and we found explicitly the rate for it. Besides, we study evolution
of subsystems to elucidate their eventual correlations and convergence to
equilibrium state. Finally we prove a universality of the dynamics driven by
repeated harmonic perturbations in a certain short-time interaction limit.
