Perturbative and non-perturbative phenomena in Bogolubov - van Hove approach

We consider the dynamics of the reduced density matrix for spin-boson model in the rotating wave approximation with the reservoir at zero temperature. We show that if one considers the perturbation theory with Bogolubov-van Hove scaling, then the dynamics of the perturbative part of the reduced density matrix is described by the Gorini – Kossakowski – Sudarshan – Lindblad equation with constant coefficients in the case, when the reservoir correlation function has finite moments of arbitrary order. We also show that the initial condition for the exact reduced density matrix and for its perturbative part generally do not coincide.