带有Dzyaloshinski-Mariya相互作用的两比特纠缠量子Otto热机和量子Stirling热机

赵丽梅; 张国锋

doi:10.7498/aps.66.240502

摘要

研究了以带有Dzyaloshinski-Mariya（DM）相互作用的两比特自旋体系为工质的量子纠缠Otto热机和量子Stirling热机.两种不同热机在各自的循环过程中，通过保持其他参量不变，只有DM相互作用发生改变，从而分析热机循环中DM相互作用与热传递、做功以及效率等热力学量之间的关系.研究结果表明：DM相互作用对两种热机的基本量子热力学量都具有重要的影响，但量子Stirling热机由于回热器的使用，其循环效率会大于量子Otto纠缠热机的效率，甚至会超过Carnot效率；得到了量子Otto纠缠热机和量子Stirling热机做正功的条件.因此，在这两个纠缠体系中，热力学第二定律都依然成立.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
北京航空航天大学物理科学与核能工程学院, 北京 100191

通信作者: 张国锋, gf1978zhang@buaa.edu.cn

基金项目: 国家自然科学基金（批准号：11574022）资助的课题.

Authors and contacts

1.
School of Physics and Nuclear Energy Engineering, Beihang University, Beijing 100191, China

Corresponding author: Zhang Guo-Feng, gf1978zhang@buaa.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11574022).

参考文献

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[17]	Huang X L, Wang T, Yi X X 2012 Phys. Rev. E 86 051105
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[19]	Wu F, Chen L, Sun F, Wu C, Li Q 2006 Phys. Rev. E 73 016103
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[25]	Hubner W, Lefkidis G, Dong C D, Chaudhuri D 2014 Phys. Rev. B 90 024401
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[29]	Woo C H, Wen H, Semenov A A, Dudarev S L, Ma P W 2015 Phys. Rev. B 91 104306
[30]	Roßnagel J, Abah O, Schmidt-Kaler F, Singer K, Lutz E 2014 Phys. Rev. Lett. 112 030602
[31]	Zhang X Y, Huang X L, Yi X X 2014 J. Phys. A: Math. Theor. 47 455002.
[32]	Wang R, Wang J, He J, Ma Y 2013 Phys. Rev. E 87 042119
[33]	Uzdin R, Kosloff R 2014 Europhys. Lett. 108 40001
[34]	Altintas F, Hardal A U C, Mustecaplioglu O E 2015 Phys. Rev. A 91 023816
[35]	Quan H T, Zhang P, Sun C P 2006 Phys. Rev. E 73 036122
[36]	Dzyaloshinskii I 1958 J. Phys. Chem. Sol. 4 241
[37]	Moriya T 1960 Phys. Rev. Lett. 4 228
[38]	Sun Q F, Xie X C, Wang J 2007 Phys. Rev. Lett. 98 196801
[39]	Zhang G F 2008 Eur. Phys. J. D 49 123
[40]	Li D C, Wang X P, Cao Z L 2008 J. Phys. Condens. Matter 20 325229
[41]	Zhong X M, Nguyen B A, Yun J X 2016 Phys. Rev. E 94 042135
[42]	RoSSnagel J, Dawkins S T, Tolazzi K N 2016 Science 352 325
[43]	Niu X Y, Huang X L, Shang Y F, Wang X Y 2015 Int. J. Mod. Phys. B 29 1550086
[44]	Huang X L, Niu X Y, Xiu X M, Yi X X 2014 Eur. Phys. J. D 68 32

施引文献

[1]	Scovil H E D, Schulz-Dubois E O 1959 Phys. Rev. Lett. 2 262
[2]	Geusic J E, Schulz-Dubois E O, Scovil H E D 1967 Phys. Rev. 156 343
[3]	Kieu T D 2004 Phys. Rev. Lett. 93 140403
[4]	Kieu T D 2006 Eur. Phys. J. D 39 115
[5]	Altintas F, Hardal A U C, Mustecaplioglu O E 2015 Phys. Rev. A 91 023816
[6]	Wang X G 2001 Phys. Rev. A 64 012313
[7]	Thomas G, Johal R S 2011 Phys. Rev. E 83 031135
[8]	Huang X L, Wang L C, Yi X X 2013 Phys. Rev. E 87 012144
[9]	Zhou Y, Zhang G F, Li S S 2009 Europhys. Lett. 86 50004
[10]	Zhang G F 2007 Phys. Rev. A 75 034304
[11]	Feldmann T, Kosloff R 2004 Phys. Rev. E 70 046110
[12]	Feldmann T, Kosloff R 2003 Phys. Rev. E 68 016101
[13]	Kosloff R, Feldmann T 2002 Phys. Rev. E 65 055102
[14]	Henrich M J, Mahler G, Michel M 2007 Phys. Rev. E 75 051118
[15]	Zhang T, Liu W T, Chen P X, Li Z 2007 Phys. Rev. A 75 062102
[16]	Thomas G, Johal R S 2014 Eur. Phys. J. B 87 166
[17]	Huang X L, Wang T, Yi X X 2012 Phys. Rev. E 86 051105
[18]	Huang X L, Liu Y, Wang Z, Niu X Y 2014 Eur. Phys. J. Plus 129 4
[19]	Wu F, Chen L, Sun F, Wu C, Li Q 2006 Phys. Rev. E 73 016103
[20]	Ivanchenko E A 2015 Phys. Rev. E 92 032124
[21]	Altintas F, MstecaplioǧluÖ E 2015 Phys. Rev. E 92 022142
[22]	He X, He J, Zheng J 2012 Physica A 391 6594
[23]	Cakmak S, Altintas F, MstecaplioǧluÖ E 2016 Eur. Phys. J. Plus 131 197
[24]	Wang H, Liu S, He J 2009 Phys. Rev. E 79 041113
[25]	Hubner W, Lefkidis G, Dong C D, Chaudhuri D 2014 Phys. Rev. B 90 024401
[26]	Azimi M, Chotorlishvili L, Mishra S K, Vekua T, Hubner W, Berakdar J 2014 New J. Phys. 16 063018
[27]	Albayrak E 2013 Int. J. Quantum. Inform. 11 1350021
[28]	Dillenschneider R, Lutz E 2009 Europhys. Lett. 88 50003
[29]	Woo C H, Wen H, Semenov A A, Dudarev S L, Ma P W 2015 Phys. Rev. B 91 104306
[30]	Roßnagel J, Abah O, Schmidt-Kaler F, Singer K, Lutz E 2014 Phys. Rev. Lett. 112 030602
[31]	Zhang X Y, Huang X L, Yi X X 2014 J. Phys. A: Math. Theor. 47 455002.
[32]	Wang R, Wang J, He J, Ma Y 2013 Phys. Rev. E 87 042119
[33]	Uzdin R, Kosloff R 2014 Europhys. Lett. 108 40001
[34]	Altintas F, Hardal A U C, Mustecaplioglu O E 2015 Phys. Rev. A 91 023816
[35]	Quan H T, Zhang P, Sun C P 2006 Phys. Rev. E 73 036122
[36]	Dzyaloshinskii I 1958 J. Phys. Chem. Sol. 4 241
[37]	Moriya T 1960 Phys. Rev. Lett. 4 228
[38]	Sun Q F, Xie X C, Wang J 2007 Phys. Rev. Lett. 98 196801
[39]	Zhang G F 2008 Eur. Phys. J. D 49 123
[40]	Li D C, Wang X P, Cao Z L 2008 J. Phys. Condens. Matter 20 325229
[41]	Zhong X M, Nguyen B A, Yun J X 2016 Phys. Rev. E 94 042135
[42]	RoSSnagel J, Dawkins S T, Tolazzi K N 2016 Science 352 325
[43]	Niu X Y, Huang X L, Shang Y F, Wang X Y 2015 Int. J. Mod. Phys. B 29 1550086
[44]	Huang X L, Niu X Y, Xiu X M, Yi X X 2014 Eur. Phys. J. D 68 32

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