  The non-Markovian master equation for open quantum systems is obtained by
generalization of the standard Zwanzig-Nakajima (ZN) projection technique. To
this end, a coupled chain of equations for the reduced density matrices of the
bath $\varrho_{B}(t)$ and of the system $\varrho_{S}(t)$ are written. Formal
solution of the equation for $\varrho_{B}(t)$ in the 2-nd approximation in
interaction yields a specific extra term, related to the intrinsic bath
dynamics. This term is nonlinear in the reduced density matrix
$\varrho_{S}(t)$, and vanishes in the Markovian limit. To verify the
consistence and robustness of our approach, we apply the generalized ZN
projection scheme to a simple dephasing model. We study the obtained kinetic
equation both in the Markovian approximation and beyond it (for the term
related to the intrinsic bath dynamics) and compare the results with the exact
ones.

Quantum Physics