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

Abstract

We study the perturbative corrections to the weak coupling limit type Gorini-Kossakowski-Sudarshan-Lindblad equation for the reduced density matrix of an open system. For the spin-boson model in the rotating wave approximation at zero temperature we show that the perturbative part of the density matrix satisfies the time-independent Gorini-Kossakowski-Sudarshan-Lindblad equation for arbitrary order of the perturbation theory if all the moments of the reservoir correlation function are finite. But the initial condition for perturbative part of the density matrix does not only differ from that for the whole density matrix, but also fails to be a density matrix under certain resonance conditions