Abstract
In order to describe the evolution of a quantum system that iscoupled to a reservoir, a non-phenomenological Kraus map isconstructed. At time zero, system and reservoir are notentangled. In the perturbative series for the density operator ofthe system all reservoir correlation functions are factorisedinto products of pair-correlation functions. This allows for aresummation of the perturbative series up to infinite order. Thedensity operator can be expressed in terms of an auxiliary systemoperator that satisfies an analytically tractable integralequation. Hence, the difficulties caused by integral kernels ofNakajima-Zwanzig type are circumvented. Assuming an interactionbetween system and reservoir of the Jaynes-Cummings form, oneshows that the Kraus map is capable of generating Rabioscillations of a two-level atom. If the reservoir is acontinuum, the Kraus map reproduces the Wigner-Weisskopf theoryof spontaneous emission.
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