Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2105.02443 · Lobachevskii Journal of Mathematics

Long-time Markovianity of Multi-level Systems in the Rotating Wave Approximation

Alexander Evgen’evich Teretenkov

Published Oct 1, 2021• 9 citations
arXivHTMLPDF

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.

DOI
10.1134/s1995080221100218

Related papers

Long-Time Behavior of Multi-Level Open Systems Interacting with Non-Vacuum Reservoirs

Alexander Evgen’evich Teretenkov

Abstract The model of multi-level open quantum system interacting with a non-vacuum reservoir in the rotating wave approximation is considered. We provide an exact integral representation for the reduced density matrix of the system. For identical uncorrelated reservoirs in diagonal states we have obtained the first perturbative correction for such dynamics in the Bogolubov–van Hove limit. We have shown that after initial state renormalization it can be completely described in terms of finite-dimensional semigroup. The method we provide can also be applied to the further orders of perturbation theory with Bogolubov–van Hove scaling.

arXiv:2410.05505•Physics of Particles and Nuclei•Aug 1, 2025•1 citation

Effects of the rotating-wave and secular approximations on non-Markovianity

H. Mäkelä, Mikko Möttönen

We study the effect of the rotating-wave approximation (RWA) and the secular approximation (SA) on the non-Markovian behavior in the spin-boson model at zero temperature. We find that both the RWA and SA lead to a dramatic reduction in the observed non-Markovianity. In general, non-Markovian dynamics is observed for the whole relaxation time of the system, whereas the RWA and SA lead to such dynamics only on the short time scale of the environmental correlation time. Thus, the RWA and SA are not necessarily justified in the studies of non-Markovianity, although they can estimate the state of the system precisely. Furthermore, we derive an accurate analytical expression for the non-Markovianity measure without the RWA or SA. This expression yields important insight into the physics of the problem.

arXiv:1306.6301•Physical Review A•Nov 13, 2013•41 citations

Поведение на больших временах многоуровневых открытых систем, взаимодействующих с невакуумными резервуарами

Alexander Evgen’evich Teretenkov

The model of multi-level open quantum system interacting with a non-vacuum reservoir in the rotating wave approximation is considered. We provide an exact integral representation for the reduced density matrix of the system. For identical uncorrelated reservoirs in diagonal states we have obtained the first perturbative correction for such dynamics in the Bogolubov – van Hove limit. We have shown that after initial state renormalization it can be completely described in terms of finite-dimensional semigroup. The method we provide can also be applied to the further orders of perturbation theory with Bogolubov – van Hove scaling.

ФИЗИКА ЭЛЕМЕНТАРНЫХ ЧАСТИЦ И АТОМНОГО ЯДРА•Sep 24, 2025•0 citations

Comparison between non-Markovian dynamics with and without rotating wave approximation

Ning Tang, Tian-Tian Xu, Hao‐Sheng Zeng

In the limit of weak coupling between a system and its reservoir, we derive the time-convolutionless (TCL) non-Markovian master equation for a two-level system interacting with a zero-temperature structured environment with no rotating wave approximation (NRWA). By comparing the dynamics with RWA, we demonstrate the impact of RWA on the system dynamics, as well as the effects of non-Markovianity on the preservation of atomic coherence, squeezing, and entanglement.

Chinese Physics B•Mar 1, 2013•14 citations

Integral Representation of Finite Temperature Non-Markovian Evolution of Some Systems in Rotating Wave Approximation

Alexander Evgen’evich Teretenkov

We introduce the Friedrichs model at the finite temperature which is one- and zero-particle restriction of the spin-boson model in the rotating wave approximation and obtain the population of the excited state for this model. We also consider the oscillator interacting with bosonic thermal bath in the rotating wave approximation and obtain dynamics of the mean excitation number for this oscillator. Both solutions are expressed in terms of integrals of zero-temperature solutions with correspondent correlation functions.

arXiv:2003.13993•Lobachevskii Journal of Mathematics•Dec 1, 2020•3 citations

Comparison between non-Markovian dynamics with and without rotating wave approximation

唐宁, 徐甜甜, 曾浩生

In the limit of weak coupling between a system and its reservoir,we derive the time-convolutionless(TCL) nonMarkovian master equation for a two-level system interacting with a zero-temperature structured environment with no rotating wave approximation(NRWA).By comparing the dynamics with RWA,we demonstrate the impact of RWA on the system dynamics,as well as the effects of non-Markovianity on the preservation of atomic coherence,squeezing,and entanglement.

中国物理B：英文版•Jan 1, 2013•0 citations
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.
Abstract The model of multi-level open quantum system interacting with a non-vacuum reservoir in the rotating wave approximation is considered. We provide an exact integral representation for the reduced density matrix of the system. For identical uncorrelated reservoirs in diagonal states we have obtained the first perturbative correction for such dynamics in the Bogolubov–van Hove limit. We have shown that after initial state renormalization it can be completely described in terms of finite-dimensional semigroup. The method we provide can also be applied to the further orders of perturbation theory with Bogolubov–van Hove scaling.
We study the effect of the rotating-wave approximation (RWA) and the secular approximation (SA) on the non-Markovian behavior in the spin-boson model at zero temperature. We find that both the RWA and SA lead to a dramatic reduction in the observed non-Markovianity. In general, non-Markovian dynamics is observed for the whole relaxation time of the system, whereas the RWA and SA lead to such dynamics only on the short time scale of the environmental correlation time. Thus, the RWA and SA are not necessarily justified in the studies of non-Markovianity, although they can estimate the state of the system precisely. Furthermore, we derive an accurate analytical expression for the non-Markovianity measure without the RWA or SA. This expression yields important insight into the physics of the problem.
The model of multi-level open quantum system interacting with a non-vacuum reservoir in the rotating wave approximation is considered. We provide an exact integral representation for the reduced density matrix of the system. For identical uncorrelated reservoirs in diagonal states we have obtained the first perturbative correction for such dynamics in the Bogolubov – van Hove limit. We have shown that after initial state renormalization it can be completely described in terms of finite-dimensional semigroup. The method we provide can also be applied to the further orders of perturbation theory with Bogolubov – van Hove scaling.
We introduce the Friedrichs model at the finite temperature which is one- and zero-particle restriction of the spin-boson model in the rotating wave approximation and obtain the population of the excited state for this model. We also consider the oscillator interacting with bosonic thermal bath in the rotating wave approximation and obtain dynamics of the mean excitation number for this oscillator. Both solutions are expressed in terms of integrals of zero-temperature solutions with correspondent correlation functions.