Abstract
A simple model, one spinS=1/2 interacting with an alternating transverse field and with a single mode of a boson field, treated as an open system, is rigorously investigated. An approach based on the Zubarev method is applied. An integro-differential equation for a mean value of the Zeeman operator is derived. Kernels of this equation are defined as solutions of some functional (integral) equations. A particular case, known as the Jaynes-Cummings model in quantum optics, is considered. The Markovian limit of the integro-differential equation for the Jaynes-Cummings model leads to a simple relaxation equation.
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