Geodesic
Non-Markov theory of sudden modulation
Teoretičeskaâ i matematičeskaâ fizika, Tome 66 (1986) no. 2, pp. 253-263 
A. I. Burshtein; A. A. Zharikov; S. I. Temkin. Non-Markov theory of sudden modulation. Teoretičeskaâ i matematičeskaâ fizika, Tome 66 (1986) no. 2, pp. 253-263. http://geodesic.mathdoc.fr/item/TMF_1986_66_2_a9/
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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.

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