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Thermal properties of relativistic Dunkl oscillators

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Abstract

For a better understanding of the physical systems, even at the quantum level, the thermal quantities can be investigated. Recently, we realized that the parity of the system can also be examined simultaneously, by substituting the Dunkl operator to the ordinary differential operator in quantum mechanics. In this manuscript, we consider two relativistic Dunkl oscillators and investigate their thermal quantities with well-known statistical methods. Besides, we establish a relationship between the Dunkl–Dirac oscillator and the Dunkl–Anti–Jayne–Cummings model by defining the Dunk creation and annihilation operators. Therefore, we conclude that our model can be regarded as an appropriate scenario for the theory of an open quantum system coupled to a thermal bath.

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The authors declare that the data supporting the findings of this study are available within the article.

References

  1. E.P. Wigner, Phys. Rev. 77, 711 (1950)

    Article  ADS  MathSciNet  Google Scholar 

  2. L.M. Yang, Phys. Rev. D 84, 788 (1951)

    Article  ADS  Google Scholar 

  3. W.S. Chung, H. Hassanabadi, Eur. Phys. J. Plus 136, 239 (2021)

    Article  Google Scholar 

  4. C.F. Dunkl, Trans. Am. Math. Soc. 311, 167 (1989)

    Article  Google Scholar 

  5. R.D. Mota, D. Ojeda-Guillén, M. Salazar-Ramírez, V.D. Granados, Mod. Phys. Lett. A 36, 2150171 (2021)

    Article  ADS  Google Scholar 

  6. G.J. Heckman, Prog. Math. 101, 181 (1991)

    Article  Google Scholar 

  7. C.F. Dunkl, Y. Xu, Orthogonal Polynomials of Several Variables, Encyclopedia of Mathematics and Its Applications, vol. 81 (Cambridge University Press, Cambridgre, 2001)

    Book  Google Scholar 

  8. H. de Bie, B. Orsted, P. Somberg, and V. Souc̆ek, Trans. Am. Math. Soc. 364, 3875 (2012)

  9. S. Kakei, J. Phys. A 29, L619 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  10. L. Lapointe, L. Vinet, Commun. Math. Phys. 178, 425 (1996)

    Article  ADS  Google Scholar 

  11. V.X. Genest, M.E.H. Ismail, L. Vinet, A. Zhedanov, J. Phys. A: Math. Theor. 46, 145201 (2013)

    Article  ADS  Google Scholar 

  12. V.X. Genest, L. Vinet, A. Zhedanov, J. Phys. A: Math. Theor. 46, 325201 (2013)

    Article  Google Scholar 

  13. V.X. Genest, L. Vinet, A. Zhedanov, J. Phys: Conf. Ser. 512, 012010 (2014)

    Google Scholar 

  14. V.X. Genest, A. Lapointe, L. Vinet, Phys. Lett. A 379, 923 (2015)

    Article  MathSciNet  Google Scholar 

  15. S. Sargolzaeipor, H. Hassanabadi, W.S. Chung, Mod. Phys. Lett. A 33, 1850146 (2018)

    Article  ADS  Google Scholar 

  16. S. Ghazouani, I. Sboui, M.A. Amdouni, M.B. Rhouma, J. Phys. A: Math. Theor. 52, 225202 (2019)

    Article  ADS  Google Scholar 

  17. R.D. Mota, D. Ojeda-Guillén, M. Salazar-Ramírez, V.D. Granados, Ann. Phys. 411, 167964 (2019)

    Article  Google Scholar 

  18. W.S. Chung, H. Hassanabadi, Mod. Phys. Lett. A 34, 1950190 (2019)

    Article  ADS  Google Scholar 

  19. W.S. Chung, H. Hassanabadi, Rev. Mex. Fis. 66, 308 (2020)

    Article  Google Scholar 

  20. Y. Kim, W.S. Chung, H. Hassanabadi, Rev. Mex. Fis. 66, 411 (2020)

    Article  Google Scholar 

  21. H. Hassanabadi, M. de Montigny, W.S. Chung, P. Sedaghatnia, Phys. A 580, 126154 (2021)

    Article  Google Scholar 

  22. S.-H. Dong, W.-H. Huang, W.S. Chung, H. Hassanabadi, EPL 135, 30006 (2021)

    Article  ADS  Google Scholar 

  23. R.D. Mota, D. Ojeda-Guillén, M. Salazar-Ramírez, V.D. Granados, Mod. Phys. Lett. A 36, 2150171 (2021)

    Article  ADS  Google Scholar 

  24. R.D. Mota, D. Ojeda-Guillén, M. Salazar-Ramírez, V.D. Granados, Mod. Phys. Lett. A 36(10), 2150066 (2021)

    Article  ADS  Google Scholar 

  25. A. Merad, M. Merad, Few-Body Syst. 62, 98 (2021)

    Article  ADS  Google Scholar 

  26. B. Hamil, B. C. Lütfüoğlu. arXiv:2112.09948 [quant-ph]

  27. M. Mohadesi, B. Mirza, Commun. Theor. Phys. 42, 664 (2004)

    Article  ADS  Google Scholar 

  28. M.H. Pacheco, R.R. Landim, C.A.S. Almeida, Phys. Lett. A 311, 93 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  29. M.H. Pacheco, R.V. Maluf, C.A.S. Almeida, R.R. Landim, EPL 108, 10005 (2014)

    Article  ADS  Google Scholar 

  30. N. Korichi, A. Boumali, H. Hassanabadi, Phys. A 587, 126508 (2022)

    Article  Google Scholar 

  31. A. Boumali, EJTP 12, 1 (2015)

    Google Scholar 

  32. A. Arda, C. Tezcan, R. Sever, Few-Body Syst. 57, 93 (2016)

    Article  ADS  Google Scholar 

  33. S. Hassanabadi, M. Ghominejad, Adv. High Energy Phys. 2014, 185169 (2014)

    Google Scholar 

  34. S.H. Dong, M. Lozada-Cassou, J. Yu, F. Gimenez-Angeles, A.L. Rivera, Int. J. Quantum Chem. 107, 366 (2007)

    Article  ADS  Google Scholar 

  35. M. Heddar, M. Falek, M. Moumni, B.C. Lütfüoğlu, Mod. Phys. Lett. A 36(40), 2150280 (2021)

    Article  ADS  Google Scholar 

  36. I.S. Gradshteyn, I.M. Ryzhik, Table of Integrals, Series and Products (Academic Press, New York, 1979)

    MATH  Google Scholar 

  37. S. Bruce, P. Minning, Nuovo Cimento 106, 711 (1993)

    Article  ADS  Google Scholar 

  38. M. Moshinsky, A. Szczepaniak, J. Phys. A: Math. Gen. 22, L817 (1989)

    Article  ADS  Google Scholar 

  39. M.H. Pacheco, R.R. Landim, C.A.S. Almeida, Phys. Lett. A 311, 93 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  40. A. Boumali, H. Hassanabadi, Eur. Phys. J. Plus 128, 124 (2013)

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referees for their precious critics and comments. One of the authors of this manuscript, BCL, is supported by the Internal Project, [2022/2218], of Excellent Research of the Faculty of Science of Hradec Králové University.

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Authors and Affiliations

  1. Département de TC de SNV, Université Hassiba Benbouali, Chlef, Algeria

    B. Hamil

  2. Department of Physics, University of Hradec Králové, Rokitanského 62, 500 03, Hradec Králové, Czechia

    B. C. Lütfüoğlu

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  1. B. Hamil
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  2. B. C. Lütfüoğlu
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Correspondence to B. C. Lütfüoğlu.

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Hamil, B., Lütfüoğlu, B.C. Thermal properties of relativistic Dunkl oscillators. Eur. Phys. J. Plus 137, 812 (2022). https://doi.org/10.1140/epjp/s13360-022-03055-1

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