Time-reversal characteristics of quantum normal diffusion

Regular Article

Abstract

This paper concerns the time-reversal characteristics of intrinsic normal diffusion in quantum systems. Time-reversible properties are quantified by the time-reversal test; the system evolved in the forward direction for a certain period is time-reversed for the same period after applying a small perturbation at the reversal time, and the separation between the time-reversed perturbed and unperturbed states is measured as a function of perturbation strength, which characterizes sensitivity of the time reversed system to the perturbation and is called the time-reversal characteristic. Time-reversal characteristics are investigated for various quantum systems, namely, classically chaotic quantum systems and disordered systems including various stochastic diffusion system. When the system is normally diffusive, there exists a fundamental quantum unit of perturbation, and all the models exhibit a universal scaling behavior in the time-reversal dynamics as well as in the time-reversal characteristics, which leads us to a basic understanding of the nature of quantum irreversibility.

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.
    K. Ikeda, Ann. Phys. 227, 1 (1993)ADSCrossRefGoogle Scholar
  3. 3.
    H. Yamada, K.S. Ikeda, Phys. Rev. E 65, 046211-1 (2002) ADSCrossRefGoogle Scholar
  4. 4.
    H. Yamada, K.S. Ikeda, Phys. Rev. E 59, 5214 (1999) ADSCrossRefGoogle Scholar
  5. 5.
    A.O. Caldeira, A.J. Leggett, Physica A 121, 587 (1983) MathSciNetADSMATHCrossRefGoogle Scholar
  6. 6.
    A.O. Caldeira, A.J. Leggett, Phys. Rev. A 31, 1059 (1985) ADSCrossRefGoogle Scholar
  7. 7.
    T. Dittrich, R. Graham, Ann. Phys. 200, 363 (1990) MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    S. Adachi, M. Toda, K. Ikeda, Phys. Rev. Lett. 61, 655 (1988)ADSCrossRefGoogle Scholar
  9. 9.
    S. Adachi, M. Toda, K. Ikeda, Phys. Rev. Lett. 61, 659 (1988)ADSCrossRefGoogle Scholar
  10. 10.
    D.H. Dunlap, K. Kundu, P. Phillips, Phys. Rev. B 40, 10999 (1989) ADSCrossRefGoogle Scholar
  11. 11.
    D.H. Dunlap, H.L. Wu, T. Phillips, Phys. Rev. Lett. 65, 88 (1990)ADSCrossRefGoogle Scholar
  12. 12.
    X.Q. Huang, R.W. Peng, F. Qiu, S.S. Jiang, A. Hu, Eur. Phys. J. B 23, 275 (2001)ADSCrossRefGoogle Scholar
  13. 13.
    T. Kawarabayashi, T. Ohtsuki, Phys. Rev. B 53, 6975 (1996) ADSCrossRefGoogle Scholar
  14. 14.
    F.M. Izrailev, T. Kottos, A. Politi, G.P. Tsironis, Phys. Rev. E 55, 4951 (1997) ADSCrossRefGoogle Scholar
  15. 15.
    A. Politi, S. Ruffo, L. Tessieri, Eur. Phys. J. B 14, 673 (2000)ADSCrossRefGoogle Scholar
  16. 16.
    H.S. Yamada, K.S. Ikeda, Phys. Rev. E 82, R060102 (2010) ADSCrossRefGoogle Scholar
  17. 17.
    H. Haken, G. Strobl, Z. Phys. 262, 135 (1973) MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    V. Capek, Z. Phys. B 60, 101 (1985)ADSCrossRefGoogle Scholar
  19. 19.
    A. Peres, Phys. Rev. A 30, 1610 (1984) MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    R.A. Jalabert, H.M. Pastawski, Phys. Rev. Lett. 86, 2490 (2001) ADSCrossRefGoogle Scholar
  21. 21.
    Ph. Jacquod, P.G. Silvestrov, C.W.J. Beenakker, Phys. Rev. E 64, 055203 (2001) ADSCrossRefGoogle Scholar
  22. 22.
    T. Prosen, Phys. Rev. E 65, 036208 (2002) MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    G. Benenti, G. Casati, Phys. Rev. E 65, 066205 (2002) MathSciNetADSCrossRefGoogle Scholar
  24. 24.
    J. Vanicek, E.J. Heller, Phys. Rev. E 68, 056208 (2003) ADSCrossRefGoogle Scholar
  25. 25.
    M. Hiller, T. Kottos, D. Cohen, T. Geisel, Phys. Rev. Lett. 92, 010402 (2004) ADSCrossRefGoogle Scholar
  26. 26.
    F. Mintert, A.R.R. Carvalho, M. Kus, A. Buchleitner, Phys. Rep. 415, 207 (2005) MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    F. Haug, M. Bienert, W.P. Schleich, T.H. Seligman, M.G. Raizen, Phys. Rev. A 71, 043803 (2005) ADSCrossRefGoogle Scholar
  28. 28.
    T. Gorin, T. Prosen, T.H. Seligman, M. Znidaric, Phys. Rep. 435, 33 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    Ph. Jacquod, C. Petitjean, Adv. Phys. 58, 67 (2009)ADSCrossRefGoogle Scholar
  30. 30.
    K. Ikeda, Time irreversibility of classically chaotic quantum dynamics, edited by G. Casati, B.V. Chirikov (Cambridge Univ. Press, 1996), pp. 145 − 153Google Scholar
  31. 31.
    B.V. Chirikov, F.M. Izrailev, D.L. Shepelyansky, Sov. Sci. Rev. C 2, 209 (1981)MathSciNetMATHGoogle Scholar
  32. 32.
    B.V. Chirikov, F.M. Izrailev, D.L. Shepelyansky, Physica D 33, 77 (1988)MathSciNetADSMATHCrossRefGoogle Scholar
  33. 33.
    G. Casati, B.V. Chirikov, I. Guarneri, D.L. Shepelyansky, Phys. Rev. Lett. 56, 2437 (1986) ADSCrossRefGoogle Scholar
  34. 34.
    K. Shiokawa, B.L. Hu, Phys. Rev. E 52, 2497 (1995) MathSciNetADSCrossRefGoogle Scholar
  35. 35.
    V.V. Sokolov, O.V. Zhirov, G. Benenti, G. Casati, Phys. Rev. E 78, 046212 (2008) MathSciNetADSCrossRefGoogle Scholar
  36. 36.
    G. Benenti, G. Casati, Phys. Rev. E 79, R025201 (2009) ADSCrossRefGoogle Scholar
  37. 37.
    H.S. Yamada, K.S. Ikeda, Bussei Kenkyu 97, 560 (2011)Google Scholar
  38. 38.
    H. Yamada, K.S. Ikeda, Phys. Lett. A 328, 170 (2004) ADSMATHCrossRefGoogle Scholar
  39. 39.
    L. Arnold, Random Dynamical Systems (Springer-Verlag, New York, 1998)Google Scholar
  40. 40.
    J. Von Neumann, Mathematical Foundations of Quantum Mechanics (Princeton Landmarks in Mathematics and Physics, Princeton Univ Pr, 1996)Google Scholar
  41. 41.
    N.J. Cerfa, C. Adamib, Physica D 120, 62 (1998)MathSciNetADSCrossRefGoogle Scholar
  42. 42.
    A.M. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000) Google Scholar
  43. 43.
    E. Abrahams, 50 Years of Anderson Localization (World Scientific Pub Co Inc., 2010)Google Scholar
  44. 44.
    A.A. Chernikov, R.Z. Sagdeev, G.M. Zaslavsky, Physica D 33, 65 (1988)MathSciNetADSMATHCrossRefGoogle 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 UniversityKusatsuJapan

Personalised recommendations