Correlation-Picture Approach to Open-Quantum-System Dynamics

Alipour, S.; Rezakhani, A. T.; Babu, Aravind P.; Mølmer, Klaus; Möttönen, Mikko; Ala-Nissilä, Tapio

doi:10.1103/physrevx.10.041024

Cited by 43 publications

(49 citation statements)

References 48 publications

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“…This is typically a stricter requirement than the weak-coupling assumption in the BM approximation, and consequently, the Redfield equation may in many cases provide a more accurate model although not guaranteeing complete positivity. We note that recently this shortcoming has been remedied by the derivation of a Lindblad-like master equation based on expansion in terms of the correlation between the bath and the system instead of the coupling strength [61].…”

Section: Introduction To the Models Usedmentioning

confidence: 99%

Validity of Born-Markov master equations for single- and two-qubit systems

et al. 2021

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Section: Introduction To the Models Usedmentioning

confidence: 99%

Validity of Born-Markov master equations for single- and two-qubit systems

et al. 2021

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“…Thus, Eqs. ( 48) and (49) give us the exact reduced dynamics, at any time t and for any initial global state ρ SE .…”

Section: A Exactly Solvable Dephasing Modelmentioning

confidence: 99%

“…Perturbative techniques represent a general strategy yielding an explicit characterization of the open-system dynamics that is approximate but that can be applied in principle to any model and is linked directly to the microscopic features defining the system-environment interaction. As relevant examples we mention the secondorder expansion in the coupling constant of the propagator expressed in the Bargmann coherent-state basis [48], the expansion building on the system-environment correlations and leading to coupled reduced system and environmental integro-differential equations [49], and the perturbative method tailored to the correlations built up by the previous system-environment interaction [50]. Furthermore, a systematic perturbative approach can be obtained by means of a cumulant expansion [51,52] defined via projection operators, which single out the part of the global unitary dynamics that is relevant for the evolution of the open system.…”

Section: Introductionmentioning

confidence: 99%

Adapted projection operator technique for the treatment of initial correlations

et al. 2021

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Standard theoretical descriptions of the dynamics of open quantum systems rely on the assumption that the correlations with the environment can be neglected at some reference (initial) time. While being reasonable in specific instances, such as when the coupling between the system and the environment is weak or when the interaction starts at a distinguished time, the use of initially uncorrelated states is questionable if one wants to deal with general models, taking into account the mutual influence that the open-system and environmental evolutions perform on each other. Here we introduce a perturbative method that can be applied to any microscopic modeling of the system-environment interaction, including fully general initial correlations. Extending the standard technique based on projection operators that single out the relevant part of the global dynamics, we define a family of projections adapted to a convenient decomposition of the initial state, which involves a convex mixture of product operators with proper environmental states. This leads us to characterize the open-system dynamics via an uncoupled system of differential equations, which are homogeneous and whose number is limited by the dimensionality of the open system, for any kind of initial correlations. Our method is further illustrated by means of two case studies, for which it reproduces the expected dynamical behavior in the long-time regime more consistently than the standard projection technique.

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“…We prove that within the standard Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) dynamics universal local-energy preservation leads in general to correlation-energy preservation (for universal extensions of the GKLS dynamics see Ref. [7]). However, we also show that it is possible to find special initial states that allow dynamics to preserve local subsystem energies while correlation-related energy is exchanged between the system and the environment.…”

mentioning

confidence: 94%

“…A direct approach for explicitly considering correlation has been introduced in Ref. [7,8]. The effect of correlation in the thermodynamic arrow of time has been studied in literature and it has been shown that correlation can lead to reversal of the direction of heat flow from cold to hot [9][10][11].…”

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Correlation-Enabled Energy Exchange in Quantum Systems without External Driving

Pyhäranta,

Alipour,

Rezakhani

et al. 2021

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We study the role of correlation in mechanisms of energy exchange between an interacting bipartite quantum system and its environment by decomposing the energy of the system to local and correlation-related contributions. When the system Hamiltonian is time-independent, no external work is performed. In this case, energy exchange between the system and its environment occurs only due to the change in the state of the system. We investigate possibility of a special case where the energy exchange with the environment occurs exclusively due to changes in the correlation between the constituent parts of the bipartite system, while their local energies remain constant. We find sufficient conditions for preserving local energies. It is proven that under these conditions and within the Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) dynamics this scenario is not possible for all initial states of the bipartite system. Nevertheless, it is still possible to find special initial states for which the local energies remain unchanged during the associated evolution and the whole energy exchange is only due to the change in the correlation energy. We illustrate our results with an example.

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Correlation-Picture Approach to Open-Quantum-System Dynamics

Cited by 43 publications

References 48 publications

Validity of Born-Markov master equations for single- and two-qubit systems

Validity of Born-Markov master equations for single- and two-qubit systems

Adapted projection operator technique for the treatment of initial correlations

Correlation-Enabled Energy Exchange in Quantum Systems without External Driving

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