Performance of an irreversible quantum Carnot engine with spin 1∕2

Wu, Feng; Chen, Lingen; Wu, Shuang; Sun, Fengrui; Chen, Wu

doi:10.1063/1.2200693

Cited by 60 publications

(24 citation statements)

References 45 publications

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“…(23) MME obtained from standard microscopic models. Substituting (23) in (22), we get our final result (see Fig. 1 for a plot):…”

Section: ρ(T) = L T [ρ(T)]mentioning

confidence: 99%

“…Finitetime quantum thermodynamics [15][16][17] and Brownian quantum engines [18,19] were studied using the formalism of open quantum systems. In particular single-qubit heat engines subject to Markovian dissipation were considered in [20][21][22][23]. The impact of the bath spectral density on the efficiency of quantum engines was also noticed in the context of autonomous heat pumps [24,25] and single-qubit minimal machines [26].…”

Section: ρ(T) = L T [ρ(T)]mentioning

confidence: 99%

See 1 more Smart Citation

Slow Dynamics and Thermodynamics of Open Quantum Systems

2017

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We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We apply this technique to the analysis of finite-time isothermal processes in which, differently from quasi-static transformations, the state of the system is not able to continuously relax to the equilibrium ensemble. Our approach allows to formally evaluate perturbations up to arbitrary order to the work and heat exchange associated to an arbitrary process. Within first order in the perturbation expansion, we identify a general formula for the efficiency at maximum power of a finite-time Carnot engine. We also clarify under which assumptions and in which limit one can recover previous phenomenological results as, for example, the Curzon-Ahlborn efficiency.A central result in the study of open quantum systems [1, 2] is the Markovian Master Equation (MME) approach which, under realistic assumptions, describes the temporal evolution of a system of interest A induced by a weak coupling with a large external environment E. This consists in a first order linear differential equatioṅ ρ(t) = L[ρ(t)] where ρ(t) is the density matrix of A and where the generator of the dynamics is provided by a quantum Liouvillian superoperator L that can be casted in the so called Gorini-Kossakowski-Sudarshan-Lindblad form [3][4][5]. For autonomous systems the latter does not exhibit an explicit time dependence and the dynamics of A exponentially relaxes to a (typically unique) equilibrium steady state ρ 0 identified by the null eigenvector equation L[ρ 0 ] = 0. MMEs can also be employed to describe the temporal evolution of A when it is tampered by the presence of slow varying, external driving forces. Indeed, as long as these operate on a time scale which is much larger than the characteristic bath correlations times and the inverse frequencies of the system of interest, the effective coupling between A and E adapts instantaneously to the driving control, resulting on a MME governed by a time-dependent Liouvillian generator, i.e.An explicit integration of this equation is in general difficult to obtain. Yet, if the control forces are so slow that their associated time scale is also larger with respect to the relaxation time of the system induced by the interaction with E, one expects ρ(t) to approximately follow the instantaneous equilibrium state ρ 0 (t) that nullifies L t . Our aim is to estimate quantitative deviations from this ultra-slow driving regime. For this purpose we develop a perturbation theory valid in the limit of slowly varying Liouvillians L t and derive a formal solution of Eq. (1) which allows one to evaluate non-equilibrium corrections up to arbitrary order. The main motivation of our analysis is to model thermodynamic processes and cycles beyond the usual reversible limit which is strictly valid only for infinitely long quasi-static transformations. Finite-time thermodynamics [7,8]...

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“…(23) MME obtained from standard microscopic models. Substituting (23) in (22), we get our final result (see Fig. 1 for a plot):…”

Section: ρ(T) = L T [ρ(T)]mentioning

confidence: 99%

Section: ρ(T) = L T [ρ(T)]mentioning

confidence: 99%

Slow Dynamics and Thermodynamics of Open Quantum Systems

2017

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“…Quantum analogues of Carnot cycles, Otto cycles and other brownian machines have been analysed [14,15]. Further, both infinite [2][3][4] and finite-time [16][17][18][19][20][21][22] thermodynamic cycles have attracted attention.…”

Section: Introductionmentioning

confidence: 99%

Coupled quantum Otto cycle

2011

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We study the 1-d isotropic Heisenberg model of two spin-1/2 systems as a quantum heat engine. The engine undergoes a four-step Otto cycle where the two adiabatic branches involve changing the external magnetic field at a fixed value of the coupling constant. We find conditions for the engine efficiency to be higher than the uncoupled model; in particular, we find an upper bound which is tighter than the Carnot bound. A new domain of parameter values is pointed out which was not feasible in the interaction-free model. Locally, each spin seems to effect the flow of heat in a direction opposite to the global temperature gradient. This seeming contradiction to the second law can be resolved in terms of local effective temperature of the spins.

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“…The current activity in quantum thermodynamics includes quantum heat engines or refrigerators , work-extraction process from quantum systems [25][26][27], conditions of positive work [28], and so on. Quantum heat engines produce work using quantum system as the working substance, such as spin system [2,[9][10][11][12][13][14][15][16][17], harmonic oscillator system [3][4][5][6][7][8], twolevel or multilevel system [18,20,22], cavity quantum electrodynamics system [19,21], coupled two-level system [23], et al Because of the quantum features of the working substance, many unusual and exotic properties have found. For example, QHE can produce a finite power at efficiency close to the Carnot bound [25] and also surpass the Carnot efficiency bound in some condition [21].…”

Section: Introductionmentioning

confidence: 99%

Thermal Entangled Quantum Heat Engine Working with a Three-Qubit Heisenberg XX Model

Zheng

2012

Int J Theor Phys

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Based on a three-qubit isotropic Heisenberg XX model with a constant external magnetic field, we construct an entangled quantum heat engine (QHE). The expressions for several thermodynamic quantities such as the heat transferred, the work and the efficiency are derived. Moreover, the influence of the entanglement on the thermodynamic quantities is investigated analytically and numerically. Several interesting features of the variation of the heat transferred, the work and the efficiency with the concurrences of the thermal entanglement of two different thermal equilibrium states in zero and nonzero magnetic fields are obtained. At last, we discussed the maximum efficiency of the QHE.

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Performance of an irreversible quantum Carnot engine with spin 1∕2

Cited by 60 publications

References 45 publications

Slow Dynamics and Thermodynamics of Open Quantum Systems

Slow Dynamics and Thermodynamics of Open Quantum Systems

Coupled quantum Otto cycle

Thermal Entangled Quantum Heat Engine Working with a Three-Qubit Heisenberg XX Model

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