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Multilevel quantum Otto heat engines with identical particles

Article

Abstract

A quantum Otto heat engine is studied with multilevel identical particles trapped in one-dimensional box potential as working substance. The symmetrical wave function for Bosons and the anti-symmetrical wave function for Fermions are considered. In two-particle case, we focus on the ratios of \(W^i\) (\(i=B,F\)) to \(W_s\), where \(W^\mathrm{B}\) and \(W^\mathrm{F}\) are the work done by two Bosons and Fermions, respectively, and \(W_s\) is the work output of a single particle under the same conditions. Due to the symmetrical of the wave functions, the ratios are not equal to 2. Three different regimes, low-temperature regime, high-temperature regime, and intermediate-temperature regime, are analyzed, and the effects of energy level number and the differences between the two baths are calculated. In the multiparticle case, we calculate the ratios of \(W^i_M/M\) to \(W_s\), where \(W^i_M/M\) can be seen as the average work done by a single particle in multiparticle heat engine. For other working substances whose energy spectrum has the form of \(E_n\sim n^2\), the results are similar. For the case \(E_n\sim n\), two different conclusions are obtained.

Keywords

Identical particles Particle trapped in potential Otto cycle Multilevel system 

Notes

Acknowledgements

We thank Yu-Han Gou for help. This work is supported by NSF of China under Grant Nos. 61475033 and 11605024 and the Foundation of Department of Education of Liaoning Province (L201683664).

References

  1. 1.
    Nielsen, M.A., Chuang, I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2000)MATHGoogle Scholar
  2. 2.
    Sakurai, J.J.: Modern Quantum Mechanics Revised Edition. Addison-Wesley Publishing Company, Boston (1994)Google Scholar
  3. 3.
    Kieu, T.D.: The second law, Maxwell’s demon, and work derivable from quantum heat engines. Phys. Rev. Lett. 93, 140403 (2004)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Kieu, T.D.: Quantum heat engines, the second law and Maxwell’s demon. Eur. Phys. J. D Atom. Mol. Opt. Plasma Phys. 39, 115 (2006)Google Scholar
  5. 5.
    Quan, H.T., Liu, Y.X., Sun, C.P., Nori, F.: Quantum thermodynamic cycles and quantum heat engines. Phys. Rev. E 76, 031105 (2007)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Quan, H.T.: Quantum thermodynamic cycles and quantum heat engines. II. Phys. Rev. E 79, 041129 (2009)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    Wang, J., He, J., He, X.: Performance analysis of a two-state quantum heat engine working with a single-mode radiation field in a cavity. Phys. Rev. E 84, 041127 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    Wang, J., He, J., He, X.: Quantum Otto engine of a two-level atom with single-mode fields. Phys. Rev. E 85, 041148 (2012)ADSCrossRefGoogle Scholar
  9. 9.
    Niu, X.Y., Huang, X.L., Shang, Y.F., Wang, X.Y.: Effects of superpositions of quantum states on quantum isoenergetic cycles: efficiency and maximum power output Int. J. Mod. Phys. B 29, 1550086 (2015)ADSCrossRefMATHGoogle Scholar
  10. 10.
    Huang, X.L., Shang, Y.F., Guo, D.Y., Yu, Q., Sun, Q.: Performance analysis of quantum diesel heat engines with a two-level atom as working substance. Quantum Inf. Process 16, 174 (2017)ADSCrossRefMATHGoogle Scholar
  11. 11.
    Leggio, B., Antezza, M.: Otto engine beyond its standard quantum limit. Phys. Rev. E 93, 022122 (2016)ADSCrossRefGoogle Scholar
  12. 12.
    Muñoz, E., Peña, F.J.: Quantum heat engine in the relativistic limit: the case of a dirac particle. Phys. Rev. E 86, 061108 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    Correa, L.A., Mehboudi, M.: Testing a quantum heat pump with a two-level spin. Entropy 71, 75 (2016)Google Scholar
  14. 14.
    Yuan, Y., Wang, R., He, J.Z., Ma, Y.L., Wang, J.H.: Coefficient of performance under maximum criterion in a two-level atomic system as a refrigerator. Phys. Rev. E 90, 052151 (2014)ADSCrossRefGoogle Scholar
  15. 15.
    Quan, H.T., Zhang, P., Sun, C.P.: Quantum heat engine with multilevel quantum systems. Phys. Rev. E 72, 056110 (2005)ADSCrossRefGoogle Scholar
  16. 16.
    Gaveau, B., Moreau, M., Schulman, L.S.: Constrained maximal power in small engines. Phys. Rev. E 82, 051109 (2010)ADSCrossRefGoogle Scholar
  17. 17.
    Peña, F.J., Ferré, M., Orellana, P.A., Rojas, R.G., Vargas, P.: Optimization of a relativistic quantum mechanical engine. Phys. Rev. E 94, 022109 (2016)ADSCrossRefGoogle Scholar
  18. 18.
    Çakmak, S., Altintas, F., Gençten, A., Müstecaplıoğlu, Ö.E.: Irreversible work and internal friction in a quantum Otto cycle of a single arbitrary spin. Eur. Phys. J. D 71, 75 (2016)CrossRefGoogle Scholar
  19. 19.
    Wang, J.H., Ye, Z.L., Lai, Y.M., Li, W.S., He, J.Z.: Efficiency at maximum power of a quantum heat engine based on two coupled oscillators. Phys. Rev. E 91, 062134 (2015)ADSCrossRefGoogle Scholar
  20. 20.
    Insinga, A., Andresen, B., Salamon, P.: Thermodynamical analysis of a quantum heat engine based on harmonic oscillators. Phys. Rev. E 94, 012119 (2016)ADSCrossRefGoogle Scholar
  21. 21.
    Abah, O., Lutz, E.: Optimal performance of a quantum Otto refrigerator. Europhys. Lett. 113, 60002 (2016)ADSCrossRefGoogle Scholar
  22. 22.
    Gardas, B., Deffner, S., Saxena, A.: Non-hermitian quantum thermodynamics. Sci. Rep. 6, 23408 (2016)ADSCrossRefGoogle Scholar
  23. 23.
    Lin, S., Song, Z.: Non-Hermitian heat engine with all-quantum-adiabatic-process cycle. J. Phys. A 49, 475301 (2016)ADSMathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Zhang, T., Liu, W.T., Chen, P.X., Li, C.Z.: Four-level entangled quantum heat engines. Phys. Rev. A 75, 062102 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    Thomas, G., Johal, R.S.: Coupled quantum Otto cycle. Phys. Rev. E 83, 031135 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    Huang, X.L., Wang, L.C., Yi, X.X.: Quantum Brayton cycle with coupled systems as working substance. Phys. Rev. E 87, 012144 (2013)ADSCrossRefGoogle Scholar
  27. 27.
    Thomas, G., Johal, R.S.: Friction due to inhomogeneous driving of coupled spins in a quantum heat engine. Eur. Phys. J. B 87, 166 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    Altintas, F., Hardal, A.Ü.C., Müstecapliog̃lu, Ö.E.: Quantum correlated heat engine with spin squeezing. Phys. Rev. E 90, 032102 (2014)ADSCrossRefGoogle Scholar
  29. 29.
    Çakmak, S., Altintas, F., Müstecaplıoǧlu, Ö.E.: Lipkin–Meshkov–Glick model in a quantum Otto cycle. Eur. Phys. J. Plus 131, 197 (2016)CrossRefGoogle Scholar
  30. 30.
    Zhao, L.-M., Zhang, G.-F.: Entangled quantum Otto heat engines based on two-spin systems with the Dzyaloshinski–Moriya interaction. Quantum Inf. Process. 16, 216 (2017)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    Huang, X.L., Xu, H., Niu, X.Y., Fu, Y.D.: A special entangled quantum heat engine based on the two-qubit Heisenberg \(XX\) model. Phys. Scr. 88, 065008 (2013)ADSCrossRefGoogle Scholar
  32. 32.
    Altintas, F., Müstecaploğlu, Ö.E.: General formalism of local thermodynamics with an example: quantum Otto engine with a spin\(-1/2\) coupled to an arbitrary spin. Phys. Rev. E 92, 022142 (2015)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    Azimi, M., Chotorlishvili, L., Mishra, S.K., Vekua, T., Hübner, W., Berakdar, J.: Quantum Otto heat engine based on a multiferroic chain working substance. New J. Phys. 16, 063018 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    Huang, X.L., Sun, Qi, Guo, D.Y., Yu, Qian: Quantum Otto heat engine with three-qubit \(XXZ\) model as working substance. Phys. A 491, 604 (2018)MathSciNetCrossRefGoogle Scholar
  35. 35.
    Basu, D., Nandi, J., Jayannavar, A.M., Marathe, R.: Two coupled, driven Ising spin systems working as an engine. Phys. Rev. E 95, 052123 (2017)ADSCrossRefGoogle Scholar
  36. 36.
    Chotorlishvili, L., Azimi, M., Stagraczyński, S., Toklikishvili, Z., Schüler, M., Berakdar, J.: Superadiabatic quantum heat engine with a multiferroic working medium. Phys. Rev. E 94, 032116 (2016)ADSCrossRefGoogle Scholar
  37. 37.
    Ivanchenko, E.A.: Quantum Otto cycle efficiency on coupled qudits. Phys. Rev. E 92, 032124 (2015)ADSCrossRefGoogle Scholar
  38. 38.
    Abah, O., Roßnagel, J., Jacob, G., Deffner, S., Schmidt-Kaler, F., Singer, K., Lutz, E.: Single-ion heat engine at maximum power. Phys. Rev. Lett. 109, 203006 (2012)ADSCrossRefGoogle Scholar
  39. 39.
    Blickle, V., Bechinger, C.: Realization of a micrometre-sized stochastic heat engine. Nat. Phys. 8, 143 (2012)CrossRefGoogle Scholar
  40. 40.
    Fialko, O., Hallwood, D.W.: Isolated quantum heat engine. Phys. Rev. Lett. 108, 085303 (2012)ADSCrossRefGoogle Scholar
  41. 41.
    Zhang, K., Bariani, F., Meystre, P.: Quantum optomechanical heat engine. Phys. Rev. Lett. 112, 150602 (2014)ADSCrossRefGoogle Scholar
  42. 42.
    Ian, H.: Thermodynamic cycle in a cavity optomechanical system. J. Phys. B 47, 135502 (2014)ADSCrossRefGoogle Scholar
  43. 43.
    Zhang, Y.C., Lin, G.X., Chen, J.C.: Three-terminal quantum-dot refrigerators. Phys. Rev. E 91, 052118 (2015)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Roßnagel, J., Dawkins, S.T., Tolazzi, K.N., Abah, O., Lutz, E., Schmidt-Kaler, F., Singer, K.: A single-atom heat engine. Science 352, 325 (2016)ADSMathSciNetCrossRefMATHGoogle Scholar
  45. 45.
    Alickia, R., Gelbwaser-Klimovskyb, D., Jenkins, A.: A thermodynamic cycle for the solar cell. Ann. Phys. 378, 7 (2017)MathSciNetGoogle Scholar
  46. 46.
    Scully, M.O., Zubairy, M.S., Agarwal, G.S., Walther, H.: Extracting work from a single heat bath via vanishing quantum coherence. Science 299, 862 (2003)ADSCrossRefGoogle Scholar
  47. 47.
    Mehta, P., Polkovnikov, A.: Efficiency bounds for nonequilibrium heat engines. Ann. Phys. 332, 110 (2012)ADSMathSciNetCrossRefMATHGoogle Scholar
  48. 48.
    Huang, X.L., Wang, T., Yi, X.X.: Effects of reservoir squeezing on quantum systems and work extraction. Phys. Rev. E 86, 051105 (2012)ADSCrossRefGoogle Scholar
  49. 49.
    Robnagel, J., Abah, O., Schmidt-Kaler, F., Singer, K., Lutz, E.: Nanoscale heat engine beyond the carnot limit. Phys. Rev. Lett. 112, 030602 (2014)ADSCrossRefGoogle Scholar
  50. 50.
    Zhang, X.Y., Huang, X.L., Yi, X.X.: Quantum Otto heat engine with a non-Markovian reservoir. J. Phys. A 47, 455002 (2014)ADSMathSciNetCrossRefMATHGoogle Scholar
  51. 51.
    Long, R., Liu, W.: Performance of quantum Otto refrigerators with squeezing. Phys. Rev. E 91, 062137 (2015)ADSCrossRefGoogle Scholar
  52. 52.
    Manzano, G., Galve, F., Zambrini, R., Parrondo, J.M.R.: Entropy production and thermodynamic power of the squeezed thermal reservoir. Phys. Rev. E 93, 052120 (2016)ADSCrossRefGoogle Scholar
  53. 53.
    Scully, M.O., Chapin, K.R., Dorfman, K.E., Kim, M.B., Svidzinsky, A.: Quantum heat engine power can be increased by noise-induced coherence. Proc. Natl. Acad. Sci. 108, 15097 (2012)ADSCrossRefGoogle Scholar
  54. 54.
    Huang, X.L., Liu, Y., Wang, Z., Niu, X.Y.: Special coupled quantum Otto cycles. Eur. Phys. J. Plus 129, 4 (2014)ADSCrossRefGoogle Scholar
  55. 55.
    Pathria, R.K.: Statistical Mechanics. Elsevier Pte Ltd, Singapore (1997)MATHGoogle Scholar
  56. 56.
    Wang, R., Wang, J., He, J., Ma, Y.: Performance of a multilevel quantum heat engine of an ideal \(N\)-particle Fermi system. Phys. Rev. E 86, 021133 (2012)ADSCrossRefGoogle Scholar
  57. 57.
    Wang, J.H., He, J.Z.: Optimization on a three-level heat engine working with two noninteracting Fermions in a one-dimensional box trap. J. Appl. Phys. 111, 043505 (2011)ADSCrossRefGoogle Scholar
  58. 58.
    Schmidt, H.J., Schnack, J.: Investigations on finite ideal quantum gases. Phys. A 260, 479 (1998)MathSciNetCrossRefGoogle Scholar
  59. 59.
    Schmidt, H.J., Schnack, J.: Thermodynamic Fermion–Boson symmetry in harmonic oscillator potentials. Phys. A 265, 564 (1998)Google Scholar
  60. 60.
    Wang, J.H., He, J.Z.: Phase transitions for an ideal Bose condensate trapped in a quartic potential. Eur. Phys. J. D Mol. Opt. Plasma Phys. 64, 73 (2011)ADSGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2017

Authors and Affiliations

  • X. L. Huang
    • 1
  • D. Y. Guo
    • 1
  • S. L. Wu
    • 2
  • X. X. Yi
    • 3
  1. 1.School of Physics and Electronic TechnologyLiaoning Normal UniversityDalianChina
  2. 2.School of Physics and Materials EngineeringDalian Nationalities UniversityDalianChina
  3. 3.Center for Quantum Sciences and School of PhysicsNortheast Normal UniversityChangchunChina

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