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The non-Markovian master equation for open quantum systems is obtained bygeneralization of the standard Zwanzig-Nakajima (ZN) projection technique. Tothis end, a coupled chain of equations for the reduced density matrices of thebath $\varrho_{B}(t)$ and of the system $\varrho_{S}(t)$ are written. Formalsolution of the equation for $\varrho_{B}(t)$ in the 2-nd approximation ininteraction yields a specific extra term, related to the intrinsic bathdynamics. This term is nonlinear in the reduced density matrix$\varrho_{S}(t)$, and vanishes in the Markovian limit. To verify theconsistence and robustness of our approach, we apply the generalized ZNprojection scheme to a simple dephasing model. We study the obtained kineticequation both in the Markovian approximation and beyond it (for the termrelated to the intrinsic bath dynamics) and compare the results with the exactones.

Decoherence in open quantum systems: influence of the intrinsic bath dynamics