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Название: Virtues and Limitations of Markovian Master Equations with a Time-Dependent Generator
Авторы: van Wonderen A.J., Lendi K.
Journal of Statistical Physics, Vol. 100, Nos. 3/4, 2000. p. 633-658.
A Markovian master equation with time-dependent generator is constructed that respects basic constraints of quantum mechanics, in particular the von Neumann conditions. For the case of a two-level system, Bloch equations with time-dependent parameters are obtained. Necessary conditions on the latter are formulated. By employing a time-local counterpart of the Nakajima-Zwanzig equation, we establish a relation with unitary dynamics. We also discuss the relation with the weak-coupling limit. On the basis of a uniqueness theorem, a standard form for the generator of time-local master equations is proposed. The Jaynes-Cummings model with atomic damping is solved. The solution explicitly demonstrates that reduced dynamics can be described by time-local master equations only on a finite time interval. This limitation is caused by divergencies in the generator. A limit of maximum entropy is presented that corroborates the foregoing statements. A second limiting case demonstrates that divergencies may even occur for small perturbations of the weak-coupling regime.