Perturbative treatment of inter-site couplings in the local description of open quantum networks

Трушечкин, А. С.; Волович, И. В.

doi:10.1209/0295-5075/113/30005

Cited by 137 publications

(137 citation statements)

References 27 publications

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“…The origin of these effects, as shown in [75], lies in the fact that the heat fluxes become of the same order of magnitude as the neglected nonlocal terms They thus suggest to use the GME to fix such thermodynamic anomalies. These findings generated a considerable stream of investigations on the comparison between global and LMEs [49,52,53,61,[76][77][78][79][80][81][82] as well as clever possible alternatives [83,84].Recent results indicate, however, that it is possible to construct a consistent thermodynamic framework for LMEs, resolving these seeming contradictions. First and foremost, it is important to mention that, unlike Redfield equations, LMEs are in Lindblad form and therefore generate completely positive trace preserving (CPTP) maps.…”

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confidence: 99%

Reconciliation of quantum local master equations with thermodynamics

et al. 2018

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The study of open quantum systems often relies on approximate master equations derived under the assumptions of weak coupling to the environment. However when the system is made of several interacting subsystems such a derivation is in many cases very hard. An alternative method, employed especially in the modeling of transport in mesoscopic systems, consists in using local master equations (LMEs) containing Lindblad operators acting locally only on the corresponding subsystem. It has been shown that this approach however generates inconsistencies with the laws of thermodynamics. In this paper we demonstrate that using a microscopic model of LMEs based on repeated collisions all thermodynamic inconsistencies can be resolved by correctly taking into account the breaking of global detailed balance related to the work cost of maintaining the collisions. We provide examples based on a chain of quantum harmonic oscillators whose ends are connected to thermal reservoirs at different temperatures. We prove that this system behaves precisely as a quantum heat engine or refrigerator, with properties that are fully consistent with basic thermodynamics. derivations are in general quite involved since they require knowledge of the full set of eigenvalues and eigenvectors of the system's Hamiltonian, something which quickly becomes prohibitive when the number of subsystems increases. Moreover, depending on the approximations employed, one may also arrive at equations which do not generate completely positive maps (the so-called Redfield equations [50]), or equations which contain unphysical heat currents [54]. For these reasons, microscopic derivations of master equations for systems connected to multiple environments still continues, nowadays, to be a topic of great interest.An alternative, more heuristic, approach consists in deriving a master equation for the individual subsystems, neglecting the interaction with the remaining subsystems. The resulting master equation will then contain only local jump operators describing exchanges between the environment E i and its corresponding subsystem S i . Such equations, which we shall henceforth refer to as LMEs (also frequently called boundarydriven master equations), are typically accurate when the dissipation rates are larger than the interaction between subsystems. Due to their computational simplicity, they have been extensively employed over the last two decades in the study of transport in non-equilibrium quantum systems [55][56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73].It turns out, however, that the nonlocal terms neglected in the LME may still lead to non-thermal steadystates [74] and play a significant role if the heat exchanges are small, even for weakly interacting parts. As a consequence, it has been found that LMEs may lead to apparent thermodynamic inconsistencies, as pointed out recently by Levy and Kosloff [75]. They have shown that the LME for two coupled quantum harmonic oscillators (QHO) may predict currents from a cold to a hot ther...

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confidence: 99%

Reconciliation of quantum local master equations with thermodynamics

et al. 2018

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“…Our model can also serve as an example to verify the consistent of local approach with the second law of thermodynamics, which was questioned recently [31,32,[35][36][37][38][39]. Here, we argue that the local approach is valid under the resonance between subsystems.…”

Section: Discussionmentioning

confidence: 65%

“…Our treatment of the master equation is a hybrid of the global and local approaches [31,32]. Namely, the two-qubit fridge is considered as a whole.…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium quantum absorption refrigerator

Zhang

2018

New J. Phys.

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We study a quantum absorption refrigerator, in which a target qubit is cooled by two machine qubits in a nonequilibrium steady-state. It is realized by a strong internal coupling in the two-qubit fridge and a vanishing tripartite interaction among the whole system. The coherence of a machine virtual qubit is investigated as quantumness of the fridge. A necessary condition for cooling shows that the quantum coherence is beneficial to the nonequilibrium fridge, while it is detrimental as far as the maximum coefficient of performance (COP) and the COP at maximum power are concerned. Here, the COP is defined only in terms of heat currents caused by the tripartite interaction, with the one maintaining the two-qubit nonequilibrium state being excluded. The later can be considered to have no direct involvement in extracting heat from the target, as it is not affected by the tripartite interaction.

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“…Alternatively, one can use a 'local' approach, where each generator  a acts non-trivially only on one part of the network s S Ì a , driving it towards thermal equilibrium while leaving its complement s ā unaffected. That is, Generators satisfyingequation (8) may either be derived microscopically using various approximations [19,24,47,49], or directly postulated on phenomenological grounds [63][64][65][66]. In the local approach, S r ¥ is not necessarily diagonal in the energy eigenbasis, and therefore provides a consistent model for the internal current dynamics as required by equation (3).…”

Section: Preliminariesmentioning

confidence: 99%

Non-additive dissipation in open quantum networks out of equilibrium

2018

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We theoretically study a simple non-equilibrium quantum network whose dynamics can be expressed and exactly solved in terms of a time-local master equation. Specifically, we consider a pair of coupled fermionic modes, each one locally exchanging energy and particles with an independent, macroscopic thermal reservoir. We show that the generator of the asymptotic master equation is not additive, i.e. it cannot be expressed as a sum of contributions describing the action of each reservoir alone. Instead, we identify an additional interference term that generates coherences in the energy eigenbasis, associated with the current of conserved particles flowing in the steady state. Notably, non-additivity arises even for wide-band reservoirs coupled arbitrarily weakly to the system. Our results shed light on the non-trivial interplay between multiple thermal noise sources in modular open quantum systems.

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Perturbative treatment of inter-site couplings in the local description of open quantum networks

Cited by 137 publications

References 27 publications

Reconciliation of quantum local master equations with thermodynamics

Reconciliation of quantum local master equations with thermodynamics

Nonequilibrium quantum absorption refrigerator

Non-additive dissipation in open quantum networks out of equilibrium

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