Long-time Markovianity of multi-level systems in the rotating wave approximation

TL;DR

This paper analyzes the long-time Markovian behavior of multi-level quantum systems under the rotating wave approximation, extending previous models by including Hamiltonian dependence and perturbative corrections.

Contribution

It provides a generalized perturbation theory for multi-level systems, demonstrating their long-time Markovianity with Hamiltonian dependence considered.

Findings

Dynamics are long-time Markovian after bath correlation time

Non-Markovian effects are captured by initial condition and correlation function renormalization

Perturbative corrections extend previous spin-boson model results

Abstract

For the model of a multi-level system in the rotating wave approximation we obtain the corrections for a usual weak coupling limit dynamics by means of perturbation theory with Bogolubov-van Hove scaling. It generalizes our previous results on a spin-boson model in the rotating wave approximation. Additionally, in this work we take into account some dependence of the system Hamiltonian on the small parameter. We show that the dynamics is long-time Markovian, i.e. after the bath correlation time all the non-Markovianity could be captured by the renormalization of initial condition and correlation functions.