Skip to main content
SpringerLink
Log in

Time Dependence of Joint Entropy of Oscillating Quantum Systems

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The time dependent entropy (or Leipnik’s entropy) of harmonic and damped harmonic oscillator systems is studied by using time dependent wave function obtained by the Feynman path integral method. The Leipnik entropy and its envelope change as a function of time, angular frequency and damping factor. Our results for simple harmonic oscillator are in agreement with the literature. However, the joint entropy of damped harmonic oscillator shows remarkable discontinuity with time for certain values of damping factor. The envelope of the joint entropy curve increases with time monotonically. These results show the general properties of the envelope of the joint entropy curve for quantum systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aydiner, E., Orta, C., Sever, R.: arXiv:quant-ph/0602203

  2. Zurek, W.H.: Phys. Today 44(10), 36 (1991)

    Article  Google Scholar 

  3. Omnes, R.: Rev. Mod. Phys. 64, 339 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  4. Anastopoulos, C.: Ann. Phys. 303, 275 (2003)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  5. Halliwell, J.J.: Phys. Rev. D 48, 2739 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  6. Anderson, A., Halliwell, J.J.: Phys. Rev. D 48, 2753 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  7. Anastopoulos, C., Halliwell, J.J.: Phys. Rev. D 51, 6870 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  8. Anastopoulos, C.: Phys. Rev. D 59, 045001 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  9. Leipnik, R.: Inf. Control. 2, 64 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  10. Dodonov, V.V.: J. Opt. B: Quantum Semiclass. Opt. 4, S98 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  11. Trigger, S.A.: Bull. Lebedev Phys. Inst. 9, 44 (2004)

    ADS  Google Scholar 

  12. Dunkel, J., Trigger, S.A.: Phys. Rev. A 71, 052102 (2005)

    Article  ADS  Google Scholar 

  13. Garbaczewski, P.: Phys. Rev. A 72, 056101 (2005)

    Article  ADS  Google Scholar 

  14. Cerf, N.J., Adami, C.: Phys. Rev. Lett. 79, 5194–5197 (1997)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. Wigner, E.: Phys. Rev. 40, 749 (1932)

    Article  MATH  ADS  Google Scholar 

  16. Britten, W.E., Chappell, W.R.: Rev. Mod. Phys. 34, 620 (1962)

    Article  ADS  Google Scholar 

  17. Born, M.: Z. Phys. 40, 167 (1926)

    ADS  Google Scholar 

  18. Feynmann, R.P., Hibbs, A.R.: Quantum Mechanics and Path Integrals. McGraw-Hill, USA (1965)

    Google Scholar 

  19. Khandekar, D.C., Lawande, S.V., Bhagwat, K.V.: Path-Integral Methods and Their Applications. World Scientific, Singapore (1993)

    MATH  Google Scholar 

  20. Kleinert, H.: Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets, 3rd edn. World Scientific, Singapore (2004)

    MATH  Google Scholar 

  21. Um, C.I., Yeon, K.H., George, T.F.: Phys. Rep. 362, 63–192 (2002)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. Yeon, K.H., Um, C.I.: Phys. Rev. A 36, 11 (1987)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics Education, Hacettepe University, 06800, Ankara, Turkey

    Özgür Özcan

  2. Department of Physics, Hacettepe University, 06800, Ankara, Turkey

    Ethem Aktürk

  3. Department of Physics, Middle East Technical University, 06531, Ankara, Turkey

    Ramazan Sever

Authors
  1. Özgür Özcan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ethem Aktürk
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ramazan Sever
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ethem Aktürk.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Özcan, Ö., Aktürk, E. & Sever, R. Time Dependence of Joint Entropy of Oscillating Quantum Systems. Int J Theor Phys 47, 3207–3218 (2008). https://doi.org/10.1007/s10773-008-9756-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-008-9756-4

Keywords

Search

Navigation