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We study the perturbative corrections to the {Gorini-Kossakowski-Sudarshan-Lindblad equation which arises in the weakcoupling limit}. The spin-boson model in the rotating wave approximation atzero temperature is considered. We show that the perturbative part of thedensity matrix satisfies the time-independentGorini-Kossakowski-Sudarshan-Lindblad equation for arbitrary order of theperturbation theory (if all the moments of the reservoir correlation functionare finite). But to reproduce the right asymptotic precision at long times, oneshould use { an initial condition different} from the one for exact dynamics.Moreover, we show that the initial condition for this master equation evenfails to be a density matrix under certain resonance conditions.

Non-perturbative effects in corrections to quantum master equation arising in Bogolubov-van Hove limit