Non-Markov theory of sudden modulation

Kinetic equations are obtained for the averaged evolution operator of a quantum system whose Hamiltonian depends on a parameter that varies randomly in the time. It is assumed that the fluctuations of the parameter occur instantaneously, i.e., during the time of a “jump” that is appreciably shorter than the mean interval between jumps, when the parameter keeps a constant value. For an arbitrary distribution with respect to the times between jumps, the “noise” effect that modulates parametrically the system is not a Markov process. Nevertheless, one can find for the response of the system closed integrodifferential equations that contain as a special case the well-known results of the theory of sudden modulation for a homogeneous (Poisson) sequence of jumps in time. As an application, the reasons for oscillating behavior of the correlation functions of the dynamical variables in a dense medium are investigated.