Multilevel quantum Otto heat engines with identical particles



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.


Identical particles Particle trapped in potential Otto cycle Multilevel system 



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).


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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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