Advertisement

Dynamics of observables in a q-deformed harmonic oscillator

  • Aditi Pradeep
  • Sasidharan Anupama
  • Chethil SudheeshEmail author
Regular Article
  • 5 Downloads

Abstract

Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic quantum systems based on expectation values of dynamical variables has not been reported in the literature. In this paper, we extend the study of dynamical behaviour using expectation values of variables to a q-deformed harmonic oscillator. The system is found to be periodic, quasi-periodic or chaotic depending on the values of the deformation parameter q and the deformed coherent amplitude αq, thus enabling us to explicitly classify the chaotic nature of the system on the basis of these parameters. The chaotic properties of the system are clearly illustrated through recurrence plots, power spectra, first-return-time distributions and Lyapunov exponents of the time series obtained for the expectation values of the dynamic variables.

Graphical abstract

Keywords

Quantum Optics 

References

  1. 1.
    R.V. Jensen, Nature 355, 311 (1992)ADSCrossRefGoogle Scholar
  2. 2.
    G. Casati, B.V. Chirikov, F.M. Izraelev, J. Ford, Stochastic Behavior in Classical and Quantum Hamiltonian Systems (Springer, Berlin, 1979)Google Scholar
  3. 3.
    G. Casati, L. Molinari, Prog. Theor. Phys. Suppl. 98, 287 (1989)ADSCrossRefGoogle Scholar
  4. 4.
    E.G. Vergini, J. Phys. A Math. Gen. 33, 4709 (2000)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    M. Wilkinson, J. Phys. A Math. Gen. 21, 1173 (1988)ADSCrossRefGoogle Scholar
  6. 6.
    C. Sudheesh, S. Lakshmibala, V. Balakrishnan, Phys. Lett. A 373, 2814 (2009)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    C. Sudheesh, S. Lakshmibala, V. Balakrishnan, Europhys. Lett. 90, 50001 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    A. Shankar, S. Lakshmibala, V. Balakrishnan, J. Phys. B At. Mol. Opt. 47, 215505 (2014)ADSCrossRefGoogle Scholar
  9. 9.
    Q. Zeng, J. Ge, H. Luo, Y. Luo, Int. J. Theor. Phys. 56, 2738 (2017)CrossRefGoogle Scholar
  10. 10.
    M. Dupuis, F. Girelli, Phys. Rev. D 90, 104037 (2014)ADSCrossRefGoogle Scholar
  11. 11.
    A.M. Gavrilik, I.I. Kachurik, Y.A. Mishchenko, J. Phys. A Math. Theor. 44, 475303 (2011)ADSCrossRefGoogle Scholar
  12. 12.
    A.A. Altintas, F. Ozaydin, C. Yesilyurt, S. Bugu, M. Arik, Quantum Inf. Process. 13, 1035 (2014)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    S. Behnia, M. Yahyavi, R. Habibpourbisafar, Chaos Solitons Fractals 104, 6 (2017)ADSCrossRefGoogle Scholar
  14. 14.
    A. Algin, A.S. Arikan, J. Stat. Mech. 2017, 043105 (2017)CrossRefGoogle Scholar
  15. 15.
    Q.J. Zeng, Z. Cheng, J.H. Yuan, Eur. Phys. J. B 81, 275 (2011)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    A. Guha, P.K. Das, Physica A 495, 18 (2018)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    A.A.A. Marinho, F.A. Brito, C. Chesman, J. Phys. 568, 012009 (2014)Google Scholar
  18. 18.
    A.A. Marinho, F.A. Brito, C. Chesman, Physica A 411, 74 (2014)ADSMathSciNetCrossRefGoogle Scholar
  19. 19.
    J. Batouli, M. El Baz, A. Maaouni, Phys. Lett. A 379, 1619 (2015)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    S. Dey, A. Fring, L. Gouba, P.G. Castro, Phys. Rev. D 87, 084033 (2013)ADSCrossRefGoogle Scholar
  21. 21.
    S. Sivakumar, J. Opt. B: Quantum Semiclassical Opt. 2, R61 (2000)ADSCrossRefGoogle Scholar
  22. 22.
    J. Récamier, M. Gorayeb, W.L. Mochán, J.L. Paz, Int. J. Theor. Phys. 47, 673 (2008)CrossRefGoogle Scholar
  23. 23.
    M.P. Jayakrishnan, S. Dey, M. Faizal, C. Sudheesh, Ann. Phys. 385, 584 (2017)ADSCrossRefGoogle Scholar
  24. 24.
    V.V. Eremin, A.A. Meldianov, Theor. Math. Phys. 147, 709 (2006)CrossRefGoogle Scholar
  25. 25.
    C. Sudheesh, S. Lakshmibala, V. Balakrishnan, Phys. Lett. A 329, 14 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    R.S. Dumont, P. Brumer, J. Chem. Phys. 88, 1481 (1988)ADSCrossRefGoogle Scholar
  28. 28.
    G. Baxter, Bull. Am. Math. Soc. 66, 472 (1960)CrossRefGoogle Scholar
  29. 29.
    M.T. Rosenstein, J.J. Collins, C.J. De Luca, Physica D 65, 117 (1993)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    A. Wolf, J.B. Swift, H.L. Swinney, J.A. Vastano, Physica D 16, 285 (1985)ADSMathSciNetCrossRefGoogle Scholar
  31. 31.
    V. Buzek, J. Mod. Opt. 38, 801 (1991)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2020

Authors and Affiliations

  • Aditi Pradeep
    • 1
  • Sasidharan Anupama
    • 2
  • Chethil Sudheesh
    • 2
    Email author
  1. 1.Department of PhysicsNational Institute of Technology CalicutKozhikodeIndia
  2. 2.Department of PhysicsIndian Institute of Space Science and TechnologyThiruvananthapuramIndia

Personalised recommendations