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Physica Scripta

Thermal entangled quantum Otto engine based on the two qubits Heisenberg model with Dzyaloshinskii–Moriya interaction in an external magnetic field

Hao Wang, Guoxing Wu, Daojiong Chen

Published Jun 14, 2012• 16 citations
Publisher

Abstract

Based on the isotropic two spin-1/2 qubits Heisenberg model with Dzyaloshinskii–Moriya interaction in a constant external magnetic field, we have constructed the entangled quantum Otto engine. Expressions for the basic thermodynamic quantities, i.e. the amount of heat exchange, the net work output and the efficiency, are derived. The influence of thermal entanglement on these basic thermodynamic quantities is investigated. Moreover, some intriguing features and their qualitative explanations in zero and finite magnetic field are given. The validity of the second law of thermodynamics is confirmed in the system. The results obtained here have general significance and will be useful in increasing understanding of the performance of an entangled quantum engine.

DOI
10.1088/0031-8949/86/01/015001

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Abstract In the paper Hao Wang et al (2012 Phys. Scr. 86 015001) have studied the entangled quantum Otto engine and have derived some thermodynamics quantities like the amount of heat energy exchange, the net work output and the efficiency. Our investigations reveal that although the numeric results (figures) are correct, but the analytic formulas for heat, work, and efficiency are not correct.

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Based on the isotropic two spin-1/2 qubits Heisenberg model with Dzyaloshinskii–Moriya interaction in a constant external magnetic field, we have constructed the entangled quantum Otto engine. Expressions for the basic thermodynamic quantities, i.e. the amount of heat exchange, the net work output and the efficiency, are derived. The influence of thermal entanglement on these basic thermodynamic quantities is investigated. Moreover, some intriguing features and their qualitative explanations in zero and finite magnetic field are given. The validity of the second law of thermodynamics is confirmed in the system. The results obtained here have general significance and will be useful in increasing understanding of the performance of an entangled quantum engine.
Based on an isotropic two spin-1/2 qubits Heisenberg model with the Dzyaloshinskii—Moriya interaction in an external magnetic field, we have constructed an entangled quantum refrigerator. Expressions for the basic thermodynamic quantities, i.e., the heat exchanged, the net work input, and the coefficient of performance, are derived. Some intriguing features and their qualitative explanations in zero and non zero magnetic fields are given. The influence of the thermal entanglement on the refrigerator is investigated. The results obtained here have general significance and will be helpful to understand the performance of an entangled quantum refrigerator.
Recently, the influences of the Dzyaloshinski-Moriya (DM) interaction on the performances of the basic thermo-dynamical quantities have attracted a lot of attention. A large number of investigations on the quantum coupling systems with DM interaction have been carried out. However, the specific effects of spin-orbit coupling with the performance on the quantum heat engine have not been taken into account in previous studies. DM interaction is a special kind spin-orbit coupling. To enrich the research of the quantum heat engines, the investigation about the effect of DM interaction on its thermodynamic characteristics should be included. In this study, we construct two entangled quantum engines based on spin-1/2 systems with different DM interactions, with the spin exchange constant and magnetic field fixed. The quantum Otto engine and the quantum Stirling engine are discussed in this article. By numerical calculation, we obtain the expressions for several thermodynamic quantities and plot the isoline maps of the variation of the basic thermodynamic quantities such as heat transfer, work with D1 and D2 and their efficiency in the two engines. The results indicate that the DM interaction plays an important role in the thermodynamic quantities for the quantum Otto engine and the quantum Stirling engine. In addition, the positive work condition is discussed with different DM interactions, with the spin exchange constant and magnetic field. Furthermore fixed, it is found that the efficiency of quantum Otto engine cycle is smaller than the Carnot efficiency while the quantum Stirling cycle can exceed the Carnot efficiency by using the regenerator. Finally, the second law of thermodynamics is shown to be valid in the two entangled quantum systems.
Based on a two-qubit one-dimensional isotropic spin-1∕21∕21∕2 Heisenberg spin chain in a constant external magnetic field, we construct a four-level entangled quantum heat engine (QHE) and investigate the influence of entanglement between two qubits on basic thermodynamic quantities, i.e., the heat transferred and the work done in a cycle, and the efficiency of the QHE. The validity of the second law of thermodynamics is confirmed in the entangled system. We also find several interesting features of the variation of the efficiency with the entanglement of two different thermal equilibrium states in a work cycle in zero and finite magnetic field. An abrupt transition of efficiency is found in zero field.
Based on a two-qubit isotropic Heisenberg XY model under a constant external magnetic field,we construct a four-level entangled quantum heat engine(QHE).The expressions for 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 variations 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.
This paper establishes an entangled otto quantum heat engine(EQHE) working with the two-qubit anisotropic Heisenberg XXZ model.Based on the first law of quantum thermodynamics,we derive the expressions for the net work and the efficiency of EQHE.By numerical calculation we plot three dimensional graphics between the efficiency and the concurrence.It is found that the efficiency of the EQHE is smaller than the Carnot efficiency and the validity of the second law of thermodynamics is confirmed;The region of non-zero efficiency is mainly distributed in C1C2 and the value of efficiency and region of non-zero efficiency increase with the increase of the ratio of the temperature γ.The efficiency of the EQHE is discussed in two special cases Δ=0 and Δ=1.