Advertisement

The Bradbury Butterfly Effect in Long Josephson Junctions

  • K. N. Yugay
  • E. A. Yashkevich
Article

Abstract

In a well-known science fiction novel by Ray Bradbury, a butterfly in the pre-historic past is accidentally crushed by time travelers and this seemingly insignificant event radically changes history. We will call this the “Bradbury Butterfly” Effect (BBE). We know that such an effect occurs in Long Josephson Junctions as described by a time-dependent nonlinear sine-Gordon equation. This equation states that any alteration within the initial perturbation fundamentally changes the asymptotic state of the system. The actual manifestation of this effect is proven by a numerical simulation of the time-dependent sine-Gordon equation.

Keywords

long Josephson junction sine-Gordon equation Lyapunov exponent dynamical chaos 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    N. Grønbech-Jensen, S. A. Hattel, and M. R. Samuelsen, Phys. Rev. B 45, 12457 (1992).CrossRefGoogle Scholar
  2. 2.
    A. Shnirman, E. Ben-Jacob, and B. Malomed, Phys. Rev. B 56, 14677 (1997).CrossRefGoogle Scholar
  3. 3.
    G. Carapella, Phys. Rev. B 59, 1407 (1999).CrossRefGoogle Scholar
  4. 4.
    M. V. Fistul, E. Goldobin, and A. V. Ustinov, Phys. Rev. B 64, 092501 (2001).CrossRefGoogle Scholar
  5. 5.
    C. Bruder, L. I. Glazman, A. I. Larkin, J. E. Mooij, and A. van Oudenaarden, Phys. Rev. B 59, 1383 (1999).CrossRefGoogle Scholar
  6. 6.
    W. J. Yeh, O. G. Symko, and D. J. Zheng, Phys. Rev. B 42, 4080 (1990).CrossRefGoogle Scholar
  7. 7.
    A. Davidson and P. Santhanam, Phys. Rev. B 46, 3368 (1992).CrossRefGoogle Scholar
  8. 8.
    A. Kenfack and T. C. Kofané, Phys. Rev. B 52, 10359 (1995).CrossRefGoogle Scholar
  9. 9.
    G. Carapella, N. Martucciello, and G. Costabile, Phys. Rev. B 66, 134531 (2002).CrossRefGoogle Scholar
  10. 10.
    A. K. Setty and G. F. Giuliani, Phys. Rev. B 61, 12285 (2000).Google Scholar
  11. 11.
    E. Goldobin, D. Koelle, and R. Kleiner, Phys. Rev. B 66, 100508R (2002).CrossRefGoogle Scholar
  12. 12.
    E. Goldobin, D. Koelle, and R. Kleiner, Phys. Rev. B 67, 224515 (2003).CrossRefGoogle Scholar
  13. 13.
    E. Goldobin, A. Sterck, T. Gaber, D. Koelle, and R. Kleiner, Phys. Rev. Lett. 92, 057005 (2004).CrossRefGoogle Scholar
  14. 14.
    A. Zenchuk and E. Goldobin, Phys. Rev. B 69, 024515 (2004).CrossRefGoogle Scholar
  15. 15.
    A. Buzdin and A. E. Koshelev, Phys. Rev. B 67, 220504R (2003).CrossRefGoogle Scholar
  16. 16.
    N. Lazarides, Phys. Rev. B 69, 212501 (2004).CrossRefGoogle Scholar
  17. 17.
    M. V. Fistul, A. Wallraff, Y. Koval, A. Lukashenko, B. A. Malomed, and A. V. Ustinov, Phys. Rev. Lett. 91, 257004 (2003).CrossRefGoogle Scholar
  18. 18.
    B. A. Malomed and A. V. Ustinov, Phys. Rev. B 69, 064502 (2004).CrossRefGoogle Scholar
  19. 19.
    L. L. Sohn, M. S. Rzchowski, J. U. Free, and M. Tinkham, Phys. Rev. B 47, 967 (1993).CrossRefGoogle Scholar
  20. 20.
    L. L. Sohn, M. T. Tuominen, M. S. Rzchowski, J. U. Free, and M. Tinkham, Phys. Rev. B 47, 975 (1993).CrossRefGoogle Scholar
  21. 21.
    E. Trias, T. P. Orlando, and H. S. J. van der Zant, Phys. Rev. B 54, 6368 (1996).CrossRefGoogle Scholar
  22. 22.
    F. M. Araujo-Moreira, P. Barbara, A. B. Cawthome, and C. J. Lobb, Phys. Rev. Lett. 78, 4625 (1997).CrossRefGoogle Scholar
  23. 23.
    F. V. Kusmartsev, D. M. Faruque, and D. J. Khomskii, Phys. Lett. A 249, 541 (1998).CrossRefGoogle Scholar
  24. 24.
    K. N. Yugay, N. V. Blinov, and I. V. Shirokov, Phys. Rev. B 49, 12036 (1994).CrossRefGoogle Scholar
  25. 25.
    K. N. Yugay, N. V. Blinov, and I. V. Shirokov, Phys. Rev. B 51, 12737 (1995).CrossRefGoogle Scholar
  26. 26.
    K. N. Yugay, N. V. Blinov, and I. V. Shirokov, Fiz. Niz. Temp. 25, 712 (1999) (Low Temp. Phys. 25, 530 (1999)).Google Scholar
  27. 27.
    K. N. Yugay, N. V. Blinov, and I. V. Shirokov, Fiz. Niz. Temp. 26, 1067 (2000) (Low Temp. Phys. 26, 1067 (2000)).Google Scholar
  28. 28.
    E. A. Yashkevich and K. N. Yugay, Vestnik Omsk Univ. 2, 22 (2001).Google Scholar
  29. 29.
    K. N. Yugay, E. A. Yashkevich, J. U. Kim, and Y. Huh, J. Korean Phys. Soc. 46, 1418 (2005).Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Dostoevsky Omsk State UniversityOmskRussia

Personalised recommendations