A Dynamics Driven by Repeated Harmonic Perturbations

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.