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ФИЗИКА ЭЛЕМЕНТАРНЫХ ЧАСТИЦ И АТОМНОГО ЯДРА

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

Alexander Evgen’evich Teretenkov

Published Sep 24, 2025• 0 citations
OpenAlex

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.

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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

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

Alexander Evgen’evich Teretenkov

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.

arXiv:2105.02443•Lobachevskii Journal of Mathematics•Oct 1, 2021•9 citations

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

Alexander Evgen’evich Teretenkov

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.

arXiv:2008.02820•Journal of Physics A Mathematical and Theoretical•May 17, 2021•26 citations

Описание динамики квантовых систем, взаимодействующих с лазерным излучением, методом функционала влияния

Александр Александрович Бирюков, Alexander Alexandrovich Biryukov, Марк Александрович Шлеенков +1 more

The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for single- and multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.

Вестник Самарского государственного технического университета Серия Физико-математические науки•Jan 1, 2013•0 citations

Time-Convolutionless Master Equations for Composite Open Quantum Systems

A. Yu. Karasev, Alexander Evgen’evich Teretenkov

Abstract In this work we consider the master equations for composite open quantum systems. We provide purely algebraic formulae for terms of perturbation series defining such equations. We also give conditions under which the Bogolubov–van Hove limit exists and discuss some corrections to this limit. We present an example to illustrate our results. In particular, this example shows, that inhomogeneous terms in time-convolutionless master equations can vanish after reservoir correlation time, but lead to renormalization of initial conditions at such a timescale.

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Algebraic aspects of the driven dynamics in the density operator and correlation functions calculation for multi-level open quantum systems

Nikolai N. Bogolubov, Andrey Vladimirovich Soldatov

Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can be simplified significantly if the free Hamiltonian driven dynamics of an arbitrary quantum multi-level system under the influence of the external driving fields as well as its Markovian and non-Markovian evolution, stipulated by the interaction with the environment, are described in terms of the SU(N) algebra representation. As a consequence, efficient numerical methods can be developed and employed to analyze these master equations for real problems in various fields of theoretical and applied physics. It was also shown that literally the same master equations hold not only for the reduced density operator but also for arbitrary nonequilibrium multi-time correlation functions as well under the only assumption that the system and the environment are uncorrelated at some initial moment of time. A calculational scheme was proposed to account for these lost correlations in a regular perturbative way, thus providing additional computable terms to the correspondent master equations for the correlation functions.

International Journal of Modern Physics B•Oct 13, 2017•0 citations
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.
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.
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 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.
The description of interacting multilevel quantum system and quantum electromagnetic field in terms of statistical density matrix is considered in path integral approach. The statistical operator and probability transitions of quantum system are represented as mean of electromagnetic field influence functional. The influence functionals are defined for specific models of electromagnetic field. The explicit form for single- and multimode electromagnetic field is concretized in cases when initial state of the field is represented by vacuum and pure coherent.
Abstract In this work we consider the master equations for composite open quantum systems. We provide purely algebraic formulae for terms of perturbation series defining such equations. We also give conditions under which the Bogolubov–van Hove limit exists and discuss some corrections to this limit. We present an example to illustrate our results. In particular, this example shows, that inhomogeneous terms in time-convolutionless master equations can vanish after reservoir correlation time, but lead to renormalization of initial conditions at such a timescale.
Exact and approximate master equations were derived by the projection operator method for the reduced statistical operator of a multi-level quantum system with finite number N of quantum eigenstates interacting with arbitrary external classical fields and dissipative environment simultaneously. It was shown that the structure of these equations can be simplified significantly if the free Hamiltonian driven dynamics of an arbitrary quantum multi-level system under the influence of the external driving fields as well as its Markovian and non-Markovian evolution, stipulated by the interaction with the environment, are described in terms of the SU(N) algebra representation. As a consequence, efficient numerical methods can be developed and employed to analyze these master equations for real problems in various fields of theoretical and applied physics. It was also shown that literally the same master equations hold not only for the reduced density operator but also for arbitrary nonequilibrium multi-time correlation functions as well under the only assumption that the system and the environment are uncorrelated at some initial moment of time. A calculational scheme was proposed to account for these lost correlations in a regular perturbative way, thus providing additional computable terms to the correspondent master equations for the correlation functions.