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

  • H. S. YamadaEmail author
  • K. S. Ikeda
Regular Article

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.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    I. Prigogine, From Being to Becoming: Time and Complexity in the Physical Sciences (W.H. Freeman, San Francisco, 1981)Google Scholar
  2. 2.
    P. Gaspard, Chaos, Scattering and Statistical Mechanics (Cambridge University Press, 1998)Google Scholar
  3. 3.
    K. Ikeda, Ann. Phys. 227, 1 (1993)ADSCrossRefGoogle Scholar
  4. 4.
    H. Yamada, K.S. Ikeda, Phys. Rev. E 65, 046211-1 (2002)ADSCrossRefGoogle Scholar
  5. 5.
    See, for example, L.M. Lifshits, S.A. Gredeskul, L.A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988)Google Scholar
  6. 6.
    E. Abrahams, 50 Years of Anderson Localization (World Scientific Singapore, 2010)Google Scholar
  7. 7.
    H. Yamada, K.S. Ikeda, Phys. Rev. E 59, 5214 (1999)ADSCrossRefGoogle Scholar
  8. 8.
    H. Yamada, K.S. Ikeda, Phys. Lett. A 328, 170 (2004)ADSzbMATHCrossRefGoogle Scholar
  9. 9.
    H.S. Yamada, K.S. Ikeda, Phys. Rev. E 82, R060102 (2010)ADSCrossRefGoogle Scholar
  10. 10.
    H.S. Yamada, K.S. Ikeda, Eur. Phys. J. B 85, 41 (2012)ADSCrossRefGoogle Scholar
  11. 11.
    B.V. Chirikov, F.M. Izrailev, D.L. Shepelyansky, Sov. Sci. Rev. C 2, 209 (1981)MathSciNetzbMATHGoogle Scholar
  12. 12.
    B.V. Chirikov, F.M. Izrailev, D.L. Shepelyansky, Physica D 33, 77 (1988)MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. 13.
    G. Casati, B.V. Chirikov, I. Guarneri, D.L. Shepelyansky, Phys. Rev. Lett. 56, 2437 (1986)ADSCrossRefGoogle Scholar
  14. 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 − 153Google Scholar
  15. 15.
    V.V. Sokolov, O.V. Zhirov, G. Benenti, G. Casati, Phys. Rev. E 78, 046212 (2008)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    G. Benenti, G. Casati, Phys. Rev. E 79, R025201 (2009)ADSCrossRefGoogle Scholar
  17. 17.
    H.S. Yamada, K.S. Ikeda, Bussei Kenkyu 97, 560 (2011)Google Scholar
  18. 18.
    F. Mintert, A.R.R. Carvalho, M. Kus, A. Buchleitner, Phys. Rep. 415, 207 (2005)MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    F. Haug, M. Bienert, W.P. Schleich, T.H. Seligman, M.G. Raizen, Phys. Rev. A 71, 043803 (2005)ADSCrossRefGoogle Scholar
  20. 20.
    T. Gorin, T. Prosen, T.H. Seligman, M. Znidaric, Phys. Rep. 435, 33 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    Ph. Jacquod, C. Petitjean, Adv. Phys. 58, 67 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    H. Haken, G. Strobl, Z. Phys. 262, 135 (1973)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    P.G. Harper, Proc. Phys. Soc. Lond. A 68, 874 (1955)ADSzbMATHCrossRefGoogle Scholar
  24. 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 − 372Google Scholar
  25. 25.
    H. Hiramoto, S. Abe, J. Phys. Soc. Jpn 57, 1365-1371 (1988)ADSGoogle Scholar
  26. 26.
    M. Wilkinson, E.J. Austin, Phys. Rev. B 50, 1420 (1994)ADSCrossRefGoogle Scholar
  27. 27.
    T. Geisel, R. Ketzmerick, G. Petschel, Phys. Rev. Lett. 66, 1651 (1991)ADSCrossRefGoogle Scholar
  28. 28.
    A.K. Gupta, A.K. Sen, J. Phys. I France 2, 2039 (1992)CrossRefGoogle Scholar
  29. 29.
    A. Carverhill, Prob. Theory Rel. Fields 74, 529 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  30. 30.
    L. Arnold. Random Dynamical Systems (Springer-Verlag, New York, 1998)Google Scholar
  31. 31.
    H. Yamada, K.S. Ikeda, in preparationGoogle Scholar
  32. 32.
    M. Esposito, P. Gaspard, J. Stat. Phys. 121, 463 (2005)MathSciNetADSzbMATHCrossRefGoogle Scholar
  33. 33.
    G.S. Jeon, B.J. Kim, S.W. Yiy, M.Y. Choi, J. Phys. A 31, 1353 (1998)ADSzbMATHCrossRefGoogle Scholar
  34. 34.
    M.C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1991)Google Scholar
  35. 35.
    A. Shudo, K.S. Ikeda, Physica D 115, 234 (1998)MathSciNetADSzbMATHCrossRefGoogle Scholar
  36. 36.
    M.Ya. Azbel, JETP 19, 634 (1964)Google Scholar
  37. 37.
    S. Ostlund, R. Pandit, Phys Rev. B 29, 1394 (1984)MathSciNetADSCrossRefGoogle Scholar
  38. 38.
    M. Wilkinson, Proc. Roy. Soc. Lond. A 403, 153 (1984)Google Scholar
  39. 39.
    J.B. Sokoloff, Phys. Rep. 126, 189 (1985)ADSCrossRefGoogle Scholar
  40. 40.
    H. Hiramoto, M. Kohmoto, lnt. J. Mod. Phys. B 6 281 (1992)MathSciNetADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Yamada Physics Research LaboratoryNiigataJapan
  2. 2.Department of PhysicsRitsumeikan University Noji-higashi 1-1-1KusatsuJapan

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