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

Abstract

We study the perturbative corrections to the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) equation which arises in the weak coupling limit. The spin-boson model in the rotating wave approximation at zero temperature is considered. We show that the perturbative part of the density matrix satisfies the time-independent GKSL equation for arbitrary order of the perturbation theory (if all the moments of the reservoir correlation function are finite). But to reproduce the right asymptotic precision at long times, one should use an initial condition different from the one for exact dynamics. Moreover, we show that the initial condition for this master equation even fails to be a density matrix under certain resonance conditions.