|
|
|
Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir |
| Haoguang Liu(刘浩广)1,2, Jizhou He(何济洲)1, and Jianhui Wang(王建辉)1,3,† |
1 Department of Physics, Nanchang University, Nanchang 330031, China;
2 College of Science and Technology, Nanchang Aeronautical University, Nanchang 332020, China;
3 State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai 200433, China |
|
|
|
|
Abstract We investigate the finite-time performance of a quantum endoreversible Carnot engine cycle and its inverse operation — Carnot refrigeration cycle, employing a spin-$1/2$ system as the working substance. The thermal machine is alternatively driven by a hot boson bath of inverse temperature $\beta_{\rm h}$ and a cold boson bath at inverse temperature $\beta_{\rm c}(>\beta_{\rm h})$. While for the engine model the hot bath is constructed to be squeezed, in the refrigeration cycle the cold bath is established to be squeezed, with squeezing parameter $r$. We obtain the analytical expressions for both efficiency and power in heat engines and for coefficient of performance and cooling rate in refrigerators. We find that, in the high-temperature limit, the efficiency at maximum power is bounded by the analytical value $\eta_+=1-\sqrt{\text{sech}(2r)(1-\eta_{\rm C})}$, and the coefficient of performance at the maximum figure of merit is limited by $ \varepsilon_+=\frac{\sqrt{\text{sech}(2r)(1+\varepsilon_{\rm C}})}{\sqrt{\text{sech}(2r)(1+\varepsilon_{\rm C})-\varepsilon_{\rm C}}}-1$, where $\eta_{\rm C}=1-\beta_{\rm h}/\beta_{\rm c}$ and $\varepsilon_{\rm C}=\beta_{\rm h}/(\beta_{\rm c}-\beta_{\rm h})$ are the respective Carnot values of the engines and refrigerators. These analytical results are identical to those obtained from the Carnot engines based on harmonic systems, indicating that the efficiency at maximum power and coefficient at maximum figure of merit are independent of the working substance.
|
Received: 18 July 2022
Revised: 12 October 2022
Accepted manuscript online: 11 November 2022
|
|
PACS:
|
05.70.Ln
|
(Nonequilibrium and irreversible thermodynamics)
|
|
| Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11875034) and the Opening Project of Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology. |
Corresponding Authors:
Jianhui Wang
E-mail: wangjianhui@ncu.edu.cn
|
Cite this article:
Haoguang Liu(刘浩广), Jizhou He(何济洲), and Jianhui Wang(王建辉) Performance optimization on finite-time quantum Carnot engines and refrigerators based on spin-1/2 systems driven by a squeezed reservoir 2023 Chin. Phys. B 32 030503
|
[1] Vinjanampathy S and Anders J 2016 Contemp. Phys. 57 545
[2] Mahler G 2014 Quantum Thermodynamic Processes (Singapore: Jenny Stanford Publishing)
[3] Li W, Fu J, Yang Y Y and He J Z 2019 Acta Phys. Sin. 68 220501 (in Chinese)
[4] Deffner S and Campbell S 2019 J. Phys. A: Math. Gen. 50 453001
[5] Alicki R and Kosloff R 2018 Thermodynamics in the Quantum Regime. Fundamental Theories of Physics Vol. 195 (Cham: Springer)
[6] Scovil H E D and Schulz-DuBois E O 1959 Phys. Rev. Lett. 2 262
[7] Liu F 2014 Phys. Rev. E 90 032121
[8] Wang Z, Wang L Q, Chen J Z, Wang C and Ren J 2022 Frontiers of Physics 17 13201
[9] Entin W O, Jiang J H and Imry Y 2014 Phys. Rev. E 89 012123
[10] Zhang R, Lu C C, Li Q W, Liu W and Bai L 2018 Acta Phys. Sin. 67 040502 (in Chinese)
[11] He X, He J Z and Xiao Y L 2012 Acta Phys. Sin. 61 150302 (in Chinese)
[12] Latune C L, Sinayskiy I and Petruccione F 2019 Sci. Rep. 9 3191
[13] Scully M O, Zubairy M S, Agarwal G S and Walther H 2003 Science 299 862
[14] Türkpençe D and Müstecapliõglu O E 2016 Phys. Rev. E 93 012145
[15] Latune C L, Sinayskiy I and Petruccione F 2019 Phys. Rev. A 99 052105
[16] Bera M N, Riera A, Lewenstein M and Winter A 2017 Nat. Commun. 8 2180
[17] Perarnau-Llobet M, Hovhannisyan K V, Huber M, Skrzypczyk P, Brunner N and Acín A 2015 Phys. Rev. X 5 041011
[18] Altintas F, Hardal A U C and Müstecapliõglu O E 2014 Phys. Rev. E 90 032102
[19] Fei Z Y, Quan H T and Liu F 2018 Phys. Rev. E 98 012132
[20] Wang C, Zhang Y Y and Chen Q H 2012 Phys. Rev. E 85 052112
[21] He J, Chen J and Hua B 2002 Phys. Rev. E 65 036145
[22] De Cisneros B J, Arias-Hernández L A and Hernández A C 2006 Phys. Rev. E 73 057103
[23] de Tomás C, Roco J M M, Hernández A C, Wang Y and Tu Z C 2013 Phys. Rev. E 87 012105
[24] Allahverdyan A E, Hovhannisyan K and Mahler G 2010 Phys. Rev. E 81 051129
[25] Velasco S, Roco J M M, Medina A and Hernández A C 1997 Phys. Rev. Lett. 78 3241
[26] Yan Z and Chen J 1990 J. Phys. D: Appl. Phys. 23 136
[27] Tomás C de, Hernández A C and Roco J M M 2012 Phys. Rev. E 85 010104
[28] Wang Y, Li M, Tu Z C, Hernández A C and Roco J M M 2012 Phys. Rev. E 86 011127
[29] Izumida Y, Okuda K, Hernández A C and Roco J M M 2013 Europhys. Lett. 101 10005
[30] Curzon F and Ahlborn B 1975 Am. J. Phys. 43 22
[31] Wang J, He J and Ma Y 2019 Phys. Rev. E 100 052126
[32] Salamon P, Nitzan A, Andresen B and Berry R S 1980 Phys. Rev. A 21 2115
[33] Chen L and Yan Z 1989 J. Chem. Phys. 90 3740
[34] Chen J 1994 J. Phys. D: Appl. Phys. 27 1144
[35] Quan H T, Liu Y X, Sun C P and Franco Nori 2007 Phys. Rev. E 76 031105
[36] Quan H T 2009 Phys. Rev. E 79 041129
[37] Yang Y Y, Xu S and He J Z 2020 Chin. Phys. Lett. 37 120502
[38] Lin Z B, Li W, Fu J, Yang Y Y and He J Z 2019 Chin. Phys. Lett. 36 060501
[39] Zhang Y C and He J Z 2013 Chin. Phys. Lett. 30 010501
[40] Zhang Y P, He J Z and Xiao Y L 2011 Chin. Phys. Lett. 28 100506
[41] Roßnagel J, Abah O, Schmidt-Kaler F, Singer K and Lutz E 2014 Phys. Rev. Lett. 112 030602
[42] Huang X L, Wang T and Yi X X 2012 Phys. Rev. E 86 051105
[43] Kosloff R and Rezek Y 2017 Entropy 19 136
[44] Agarwalla B K, Jiang J H and Segal D Phys. Rev. B 96 104304
[45] Manzano G, Galve F, Zambrini R and Parrondo J M R 2016 Phys. Rev. E 93 052120
[46] Xiao B and Li R 2018 Phys. Lett. A 382 3051
[47] Zhao L M and Zhang G F 2017 Acta Phys. Sin. 66 240502 (in Chinese)
[48] Long R and Liu W 2015 Phys. Rev. E 91 062137
[49] Klaers J, Faelt S, Imamoglu A and Togan E 2017 Phys. Rev. X 7 031044
[50] Correa L A, Palao J P, Alonso D and Adesso G 2014 Sci. Rep. 4 3949
[51] de Assis R J, Sales J, Mendes U C and de Almeida N G 2021 J. Phys. B: At. Mol. Opt. Phys. 54 095501
[52] Wang C and Xu D Z 2020 Chin. Phys. B 29 80504
[53] Allahverdyan A E, Hovhannisyan K V, Melkikh A V and Gevorkian S G 2013 Phys. Rev. Lett. 111 050601
[54] Izumida Y and Okuda K 2008 Europhys. Lett. 83 60003
[55] Esposito M, Kawai R, Lindenberg K and Van den Broeck C 2010 Phys. Rev. E 81 041106
[56] Esposito M, Kawai R, Lindenberg K and Vanden Broeck C 2010 Phys. Rev. Lett. 105 150603
[57] Guo J, Wang J, Wang Y and Chen J 2013 J. Appl. Phys. 113 143510
[58] Wang Y and Tu Z C 2012 Europhys. Lett. 98 40001
[59] Wang J, He J and Wu Z 2012 Phys. Rev. E 85 031145
[60] Wang J and He J 2012 Phys. Rev. E 86 051112
[61] Wang Y and Tu Z C 2013 Commun. Theor. Phys. 59 175
[62] Liu Y F, Lu J C, Wang R Q, Wang C and Jiang J H 2020 Chin. Phys. B 29 40504
[63] Geva E and Kosloff R 1992 J. Chem. Phys. 96 3054
[64] Cohen-Tannoudji C, Diu B and Laloe F 1977 Quantum mechanics (New York: Wiley)
[65] Marian P and Marian T A 1993 Phys. Rev. A 47 4474
[66] Rezek Y and Kosloff R 2006 New J. Phys. 8 83
[67] Wang J, Wu Z Q and He J Z 2012 Phys. Rev. E 85 041148
[68] Alicki R and Leudi K 1987 Quantum Dynamical Semigroups and Applications (Springer-Verlag, Berlin)
[69] Alicki R 1979 J. Phys. A: Math. Gen. 12 L103
[70] Geva E and Kosloff R 1992 J. Chem. Phys. 97 4398
[71] Geva E and Kosloff R 1994 Phys. Rev. E 49 3903 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
