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

TL;DR

This paper investigates non-perturbative effects in quantum master equations derived from the weak coupling limit, revealing conditions under which initial states and resonance affect the accuracy and physical validity of the equations.

Contribution

It demonstrates that the perturbative corrections satisfy the GKSL equation at all orders and identifies the necessity of modified initial conditions for correct long-term behavior.

Findings

Perturbative density matrix obeys GKSL equation at all orders.

Correct asymptotic behavior requires different initial conditions.

Initial conditions may fail to be valid density matrices under resonance.

Abstract

We study the perturbative corrections to the { Gorini-Kossakowski-Sudarshan-Lindblad 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 Gorini-Kossakowski-Sudarshan-Lindblad 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.