Skip to main content
SpringerLink
Log in

Time-reversal characteristics of quantum normal diffusion: time-continuous models

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

In quantum map systems exhibiting normal diffusion, time-reversal characteristics converge to a universal scaling behavior which implies a prototype of irreversible quantum process [H.S. Yamada, K.S. Ikeda, Eur. Phys. J. B 85, 41 (2012)]. In the present paper, we extend the investigation of time-reversal characteristic to time-continuous quantum systems which show normal diffusion. Typical four representative models are examined, which is either deterministic or stochastic, and either has or not has the classical counterpart. Extensive numerical examinations demonstrate that three of the four models have the time-reversal characteristics obeying the same universal limit as the quantum map systems. The only nontrivial counterexample is the critical Harper model, whose time-reversal characteristics significantly deviates from the universal curve. In the critical Harper model modulated by a weak noise that does not change the original diffusion constant, time-reversal characteristic recovers the universal behavior.

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. I. Prigogine, From Being to Becoming: Time and Complexity in the Physical Sciences (W.H. Freeman, San Francisco, 1981)

  2. P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, 1998)

  3. K. Ikeda, Ann. Phys. 227, 1 (1993)

    Article  ADS  Google Scholar 

  4. H. Yamada, K.S. Ikeda, Phys. Rev. E 65, 046211-1 (2002)

    Article  ADS  Google Scholar 

  5. See, for example, L.M. Lifshits, S.A. Gredeskul, L.A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988)

  6. E. Abrahams, 50 Years of Anderson Localization (World Scientific Singapore, 2010)

  7. H. Yamada, K.S. Ikeda, Phys. Rev. E 59, 5214 (1999)

    Article  ADS  Google Scholar 

  8. H. Yamada, K.S. Ikeda, Phys. Lett. A 328, 170 (2004)

    Article  ADS  MATH  Google Scholar 

  9. H.S. Yamada, K.S. Ikeda, Phys. Rev. E 82, R060102 (2010)

    Article  ADS  Google Scholar 

  10. H.S. Yamada, K.S. Ikeda, Eur. Phys. J. B 85, 41 (2012)

    Article  ADS  Google Scholar 

  11. B.V. Chirikov, F.M. Izrailev, D.L. Shepelyansky, Sov. Sci. Rev. C 2, 209 (1981)

    MathSciNet  MATH  Google Scholar 

  12. B.V. Chirikov, F.M. Izrailev, D.L. Shepelyansky, Physica D 33, 77 (1988)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. G. Casati, B.V. Chirikov, I. Guarneri, D.L. Shepelyansky, Phys. Rev. Lett. 56, 2437 (1986)

    Article  ADS  Google Scholar 

  14. K. Ikeda, Time irreversibility of classically chaotic quantum dynamics, in Quantum Chaos: Between Order and Disorder, edited by G. Casati, B.V. Chirikov (Cambridge Univ. Press, 1996), pp. 145 − 153

  15. V.V. Sokolov, O.V. Zhirov, G. Benenti, G. Casati, Phys. Rev. E 78, 046212 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  16. G. Benenti, G. Casati, Phys. Rev. E 79, R025201 (2009)

    Article  ADS  Google Scholar 

  17. H.S. Yamada, K.S. Ikeda, Bussei Kenkyu 97, 560 (2011)

    Google Scholar 

  18. F. Mintert, A.R.R. Carvalho, M. Kus, A. Buchleitner, Phys. Rep. 415, 207 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  19. F. Haug, M. Bienert, W.P. Schleich, T.H. Seligman, M.G. Raizen, Phys. Rev. A 71, 043803 (2005)

    Article  ADS  Google Scholar 

  20. T. Gorin, T. Prosen, T.H. Seligman, M. Znidaric, Phys. Rep. 435, 33 (2006)

    Article  ADS  Google Scholar 

  21. Ph. Jacquod, C. Petitjean, Adv. Phys. 58, 67 (2009)

    Article  ADS  Google Scholar 

  22. H. Haken, G. Strobl, Z. Phys. 262, 135 (1973)

    Article  MathSciNet  ADS  Google Scholar 

  23. P.G. Harper, Proc. Phys. Soc. Lond. A 68, 874 (1955)

    Article  ADS  MATH  Google Scholar 

  24. Y. Last, Almost everything about the almost Mathieu operator I, in XIth International Congress of Mathematical Physics, edited by D. Iagolnitzer (International Press Inc., 1995), pp. 366 − 372

  25. H. Hiramoto, S. Abe, J. Phys. Soc. Jpn 57, 1365-1371 (1988)

    ADS  Google Scholar 

  26. M. Wilkinson, E.J. Austin, Phys. Rev. B 50, 1420 (1994)

    Article  ADS  Google Scholar 

  27. T. Geisel, R. Ketzmerick, G. Petschel, Phys. Rev. Lett. 66, 1651 (1991)

    Article  ADS  Google Scholar 

  28. A.K. Gupta, A.K. Sen, J. Phys. I France 2, 2039 (1992)

    Article  Google Scholar 

  29. A. Carverhill, Prob. Theory Rel. Fields 74, 529 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  30. L. Arnold. Random Dynamical Systems (Springer-Verlag, New York, 1998)

  31. H. Yamada, K.S. Ikeda, in preparation

  32. M. Esposito, P. Gaspard, J. Stat. Phys. 121, 463 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. G.S. Jeon, B.J. Kim, S.W. Yiy, M.Y. Choi, J. Phys. A 31, 1353 (1998)

    Article  ADS  MATH  Google Scholar 

  34. M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1991)

  35. A. Shudo, K.S. Ikeda, Physica D 115, 234 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. M.Ya. Azbel, JETP 19, 634 (1964)

    Google Scholar 

  37. S. Ostlund, R. Pandit, Phys Rev. B 29, 1394 (1984)

    Article  MathSciNet  ADS  Google Scholar 

  38. M. Wilkinson, Proc. Roy. Soc. Lond. A 403, 153 (1984)

    Google Scholar 

  39. J.B. Sokoloff, Phys. Rep. 126, 189 (1985)

    Article  ADS  Google Scholar 

  40. H. Hiramoto, M. Kohmoto, lnt. J. Mod. Phys. B 6 281 (1992)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yamada Physics Research Laboratory, Aoyama 5-7-14-205, 950-2002, Niigata, Japan

    H. S. Yamada

  2. Department of Physics, Ritsumeikan University Noji-higashi 1-1-1, 525, Kusatsu, Japan

    K. S. Ikeda

Authors
  1. H. S. Yamada
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. S. Ikeda
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to H. S. Yamada.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yamada, H.S., Ikeda, K.S. Time-reversal characteristics of quantum normal diffusion: time-continuous models. Eur. Phys. J. B 85, 195 (2012). https://doi.org/10.1140/epjb/e2012-30112-5

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2012-30112-5

Keywords

Search

Navigation