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A heat engine model of a sing particle confined in a one-dimensional harmonic trap is established. The model, as a quantum-mechanical analog of the Carnot engine, does work to outside when both the width of the potential and the quantum state change very slowly. On the assumption that the width of the potential moves at a very slow speed and the heat leakage is included, we derive the general expressions for several performance parameters, such as work, power output, efficiency, etc. We find the optimally operating regions and the optimal values of performance parameters of the heat engine cycle.
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Keywords:
- quantum heat engine /
- one-dimensional harmonic trap /
- maximum power output /
- performance parameters
[1] Scovil H E D, Schulz-Dubois E O 1959 Phys. Rev. Lett. 2 262
[2] Scully M O 2001 Phys. Rev. Lett. 87 220601
[3] Scully M O 2002 Phys. Rev. Lett. 88 050602
[4] Bender C M, Brody D C, Meister B K 2000 J. Phys. A 33 4427
[5] Quan H T 2009 Phys. Rev. E 79 041129
[6] Scully M O, Zubairy M S, Agarwal G S, Walther H 2003 Science 299 862
[7] He J Z, Chen J C, Hua B 2002 Phys. Rev. E 65 036145
[8] Wu F, Chen L G, Sun F R, Wu C, Li Q 2006 Phys. Rev. E 73 016103
[9] Feldmann T, Kosloff R 2000 Phys. Rev. E 61 4774
[10] Wu F, Chen L G, Wu S, Sun F R, Wu C 2006 J. Chem. Phys. 124 214702
[11] Wang J H, He J Z, Mao Z Y 2007 Sci. China G 50 163
[12] Quan H T, Liu Y X, Sun C P, Nori F 2007 Phys. Rev. E 76 031105
[13] Quan H T, Zhang P, Sun C P 2006 Phys. Rev. E 73 036122
[14] Abe S 2011 Phys. Rev. E 83 04111
[15] Henrich M J, Mahler G, Michel M 2007 Phys. Rev. E 75 051118
[16] He J Z, Wang J H, Deng X F 2010 Int. J. Mod. Phys. B 24 4595
[17] Wu F, Chen L G, Sun F R, Wu C, Guo F Z 2006 J. Appl. Phys. 99 054904
[18] Wang X M, He J Z, He X, Xiao Y L 2010 Acta Phys. Sin. 59 4460 (in Chinese) [王秀梅, 何济洲, 何弦, 肖宇玲 2010 物理学报 59 4460]
[19] He J Z, He B X 2010 Acta Phys. Sin. 59 2345 (in Chinese) [何济洲, 贺兵香 2010 物理学报 59 2345]
[20] He J Z, He B X 2010 Acta Phys. Sin. 59 101 (in Chinese) [何济洲, 贺兵香 2010 物理学报 59 101]
[21] Wang X M, He J Z,Wang J H 2008 Acta Electron. Sin. 36 2178 (in Chinese) [王小敏, 何济洲, 王建辉 2008 电子学报 36 2178]
[22] Liu X W, Chen L G, Wu F, Sun F R 2010 Phys. Scr. 81 025003
[23] Liu X W, Chen L G, Wu F, Sun F R 2009 Sci. China G 52 1976
[24] Lin B H, Chen J C 2005 J. Phys. A 38 69
[25] Zeng J Y 2001 Quantum Mechanics (Vol. 2) (4th ed) (Beijing: Science Press) pp203---205 (in Chinese) [曾谨言 2001 量子力学(卷二) (第四版) (北京: 科学出版社) 第203---205页]
[26] Xiong H W, Liu S J, Huang G X, Xu Z X 2002 Phys. Rev. A 65 033609
[27] Wang J H, He J Z, He X 2011 Phys. Rev. E 84 041127
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[1] Scovil H E D, Schulz-Dubois E O 1959 Phys. Rev. Lett. 2 262
[2] Scully M O 2001 Phys. Rev. Lett. 87 220601
[3] Scully M O 2002 Phys. Rev. Lett. 88 050602
[4] Bender C M, Brody D C, Meister B K 2000 J. Phys. A 33 4427
[5] Quan H T 2009 Phys. Rev. E 79 041129
[6] Scully M O, Zubairy M S, Agarwal G S, Walther H 2003 Science 299 862
[7] He J Z, Chen J C, Hua B 2002 Phys. Rev. E 65 036145
[8] Wu F, Chen L G, Sun F R, Wu C, Li Q 2006 Phys. Rev. E 73 016103
[9] Feldmann T, Kosloff R 2000 Phys. Rev. E 61 4774
[10] Wu F, Chen L G, Wu S, Sun F R, Wu C 2006 J. Chem. Phys. 124 214702
[11] Wang J H, He J Z, Mao Z Y 2007 Sci. China G 50 163
[12] Quan H T, Liu Y X, Sun C P, Nori F 2007 Phys. Rev. E 76 031105
[13] Quan H T, Zhang P, Sun C P 2006 Phys. Rev. E 73 036122
[14] Abe S 2011 Phys. Rev. E 83 04111
[15] Henrich M J, Mahler G, Michel M 2007 Phys. Rev. E 75 051118
[16] He J Z, Wang J H, Deng X F 2010 Int. J. Mod. Phys. B 24 4595
[17] Wu F, Chen L G, Sun F R, Wu C, Guo F Z 2006 J. Appl. Phys. 99 054904
[18] Wang X M, He J Z, He X, Xiao Y L 2010 Acta Phys. Sin. 59 4460 (in Chinese) [王秀梅, 何济洲, 何弦, 肖宇玲 2010 物理学报 59 4460]
[19] He J Z, He B X 2010 Acta Phys. Sin. 59 2345 (in Chinese) [何济洲, 贺兵香 2010 物理学报 59 2345]
[20] He J Z, He B X 2010 Acta Phys. Sin. 59 101 (in Chinese) [何济洲, 贺兵香 2010 物理学报 59 101]
[21] Wang X M, He J Z,Wang J H 2008 Acta Electron. Sin. 36 2178 (in Chinese) [王小敏, 何济洲, 王建辉 2008 电子学报 36 2178]
[22] Liu X W, Chen L G, Wu F, Sun F R 2010 Phys. Scr. 81 025003
[23] Liu X W, Chen L G, Wu F, Sun F R 2009 Sci. China G 52 1976
[24] Lin B H, Chen J C 2005 J. Phys. A 38 69
[25] Zeng J Y 2001 Quantum Mechanics (Vol. 2) (4th ed) (Beijing: Science Press) pp203---205 (in Chinese) [曾谨言 2001 量子力学(卷二) (第四版) (北京: 科学出版社) 第203---205页]
[26] Xiong H W, Liu S J, Huang G X, Xu Z X 2002 Phys. Rev. A 65 033609
[27] Wang J H, He J Z, He X 2011 Phys. Rev. E 84 041127
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