Non-Markovian Evolution of Multi-level System Interacting with Several Reservoirs. Exact and Approximate

Teretenkov, A. E.

doi:10.1134/s1995080219100263

Cited by 23 publications

(30 citation statements)

References 76 publications

(133 reference statements)

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“…In [10] we have considered the simplest model, namely, the spin-boson in the rotating wave approximation (RWA). Here we generalize the main results of [10] to the multi-level model considered in [12] and [13].…”

Section: Introductionmentioning

confidence: 58%

“…We consider the model of a multi-level system interacting with several reservoirs from [12]. So let us recall its definition and the main results which we use in this paper.…”

Section: Integro-differential Schroedinger Equationmentioning

confidence: 99%

“…Theorem 2. Let G(p) be twice continuously differentiable with respect to p. For fixed t > 0 at λ → 0 one has W λ (t) = e Lt r + O(λ 4 ), (12) where r and L are N × N matrices defined as…”

Section: Expansion With Bogolubov-van Hove Scalingmentioning

confidence: 99%

“…In Section 2 we recall the results from [12,13] in such a manner which is useful for the further parts of the article. In Section 3 we obtain the first asymptotic correction to the dynamics obtained in the Bogolubov-van Hove limit.…”

Section: Introductionmentioning

confidence: 99%

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

Teretenkov

2021

Preprint

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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.

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Section: Introductionmentioning

confidence: 58%

“…We consider the model of a multi-level system interacting with several reservoirs from [12]. So let us recall its definition and the main results which we use in this paper.…”

Section: Integro-differential Schroedinger Equationmentioning

confidence: 99%

Section: Expansion With Bogolubov-van Hove Scalingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Teretenkov

2021

Preprint

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“…This would imply that the solutions constructed are in a sense exhaustive for physically interesting initial states. One can also check the validity of assumptions (2.7) and (4.2) for exactly solvable models, for example, for models solvable by the pseudomode method [17,18,[41][42][43].…”

Section: Discussionmentioning

confidence: 99%

Derivation of the Redfield quantum master equation and corrections to it by the Bogoliubov method

Trushechkin

2021

Preprint

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Following the ideas N. N. Bogoliubov used to derive the classical and quantum nonlinear kinetic equations, we give an alternative derivation of the Redfield quantum linear master equation, which is widely used in the theory of open quantum systems, as well as higher-order corrections to it. This derivation naturally considers initially correlated system-reservoir states arising from the previous system-reservoir dynamics. It turns out that the Redfield equation does not require any modifications in this case. The expressions of higher-order corrections are simpler than those obtained by other methods.

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Quantum thermodynamics and open-systems modeling

Kosloff

2019

The Journal of Chemical Physics

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A comprehensive approach to modeling open quantum systems consistent with thermodynamics is presented. The theory of open quantum systems is employed to define system bath partitions. The Markovian master equation defines an isothermal partition between the system and bath. Two methods to derive the quantum master equation are described: the weak coupling limit and the repeated collision model. The role of the eigenoperators of the free system dynamics is highlighted, in particular, for driven systems. The thermodynamical relations are pointed out. Models that lead to loss of coherence, i.e., dephasing are described. The implication of the laws of thermodynamics to simulating transport and spectroscopy is described. The indications for self-averaging in large quantum systems and thus its importance in modeling are described. Basic modeling by the surrogate Hamiltonian is described, as well as thermal boundary conditions using the repeated collision model and their use in the stochastic surrogate Hamiltonian. The problem of modeling with explicitly time dependent driving is analyzed. Finally, the use of the stochastic surrogate Hamiltonian for modeling ultrafast spectroscopy and quantum control is reviewed.

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Non-Markovian Evolution of Multi-level System Interacting with Several Reservoirs. Exact and Approximate

Cited by 23 publications

References 76 publications

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

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

Derivation of the Redfield quantum master equation and corrections to it by the Bogoliubov method

Quantum thermodynamics and open-systems modeling

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