Skip to main content
SpringerLink
Log in

Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction

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

Abstract

The role of thermal and non-Gaussian noise on the dynamics of driven short overdamped Josephson junctions is studied. The mean escape time of the junction is investigated considering Gaussian, Cauchy-Lorentz and Lévy-Smirnov probability distributions of the noise signals. In these conditions we find resonant activation and the first evidence of noise enhanced stability in a metastable system in the presence of Lévy noise. For Cauchy-Lorentz noise source, trapping phenomena and power law dependence on the noise intensity are observed.

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. B. Lindner, M. Kostur, L. Schimansky-Geier, Fluc. Noise Lett. 1, R25 (2001)

    Article  Google Scholar 

  2. P. Reimann, C. Van den Broeck, H. Linke, P. Hänggi, J.M. Rubi, A. Pérez-Madrid, Phys. Rev. Lett. 87, 010602 (2001)

    Article  ADS  Google Scholar 

  3. P. Reimann, C. Van den Broeck, H. Linke, P. Hänggi, J.M. Rubi, A. Pérez-Madrid, Phys. Rev. E 65, 031104 (2002)

    Article  ADS  Google Scholar 

  4. A.A. Dubkov, B. Spagnolo, Phys. Rev. E 72, 041104 (2005)

    Article  ADS  Google Scholar 

  5. G. Wendin, V.S. Shumeiko, Low Temp. Phys. 33, 724 (2007)

    Article  ADS  Google Scholar 

  6. J.H. Kim, R.P. Dhungana, K.S. Park, Phys. Rev. B 73, 214506 (2006)

    Article  ADS  Google Scholar 

  7. A.B. Zorin, E.M. Tolkacheva, M.I. Khabipov, F.-I. Buchholz, J. Niemeyer, Phys. Rev. B 74, 014508 (2006)

    Article  ADS  Google Scholar 

  8. A.J. Berkley, H. Xu, M.A. Gubrud, R.C. Ramos, J.R. Anderson, C.J. Lobb, F.C. Wellstood, Phys. Rev. B 68, 060502 (2003)

    Article  ADS  Google Scholar 

  9. C.H. Wu, Y.T. Chou, W.C. Kuo, J.H. Chen, L.M. Wang, J.C. Chen, K.L. Chen, U.C. Sou, H.C. Yang, J.T. Jeng, Nanotechnology 19, 315304 (2008)

    Article  ADS  Google Scholar 

  10. Y. Nakamura, Yu. A. Pashkin, J.S. Tsai, Nature 398, 786 (1999)

    Article  ADS  Google Scholar 

  11. J.R. Friedman, V. Patel, W. Chen, S.K. Tolpygo, J.E. Lukens, Nature 406, 43 (2000)

    Article  ADS  Google Scholar 

  12. J.M. Martinis, S. Nam, J. Aumentado, C. Urbina, Phys. Rev. Lett. 89, 117901 (2002)

    Article  ADS  Google Scholar 

  13. L. Hao, J.C. Macfarlane, Physica C: Superconductivity 292, 315 (1997)

    Article  ADS  Google Scholar 

  14. H. Xu, A.J. Berkley, R.C. Ramos, M.A. Gubrud, P.R. Johnson, F.W. Strauch, A.J. Dragt, J.R. Anderson, C.J. Lobb, F.C. Wellstood, Phys. Rev. B 71, 064512 (2005)

    Article  ADS  Google Scholar 

  15. C.M. Falco, W.H. Parker, S.E. Trullinger, P.K. Hansma, Phys. Rev. B 10, 1865 (1974)

    Article  ADS  Google Scholar 

  16. J.T. Peltonen, A.V. Timofeev, M. Meschke, J.P. Pekola, J. Low Temp. Phys. 146, 135 (2006)

    Article  ADS  Google Scholar 

  17. A. Marx, U. Fath, W. Ludwig, R. Gross, T. Amrein, Phys. Rev. B 51, 6735 (1995)

    Article  ADS  Google Scholar 

  18. A. Marx, U. Fath, L. Alff, R. Gross, Appl. Phys. Lett. 67, 1929 (1995)

    Article  ADS  Google Scholar 

  19. V. Lacquaniti, C. Cagliero, S. Maggi, R. Steni, Appl. Phys. Lett. 86, 042501 (2005)

    Article  ADS  Google Scholar 

  20. V. Lacquaniti, D. Andreone, S. Maggi, R. Rocci, A. Sosso, R. Steni, Physica C 435, 99 (2006)

    Article  ADS  Google Scholar 

  21. V. Lacquaniti, D. Andreone, N. De Leo, M. Fretto, S. Maggi, A. Sosso, M. Belogolovskii, IEEE Trans. Appl. Supercond. 17, 609 (2007)

    Article  ADS  Google Scholar 

  22. V. Lacquaniti, N. De Leo, M. Fretto, S. Maggi, A. Sosso, Appl. Phys. Lett. 91, 252505 (2007)

    Article  ADS  Google Scholar 

  23. V. Lacquaniti, D. Andreone, C. Cassiago, N. De Leo, M. Fretto, S. Maggi, A. Sosso, M. Belogolovskii, J. Phys. Conf. Ser. 97, 012174 (2008)

    Article  Google Scholar 

  24. P. Febvre, D. Bouis, N. De Leo, M. Fretto, A. Sosso, V. Lacquaniti, J. Appl. Phys. 107, 103927 (2010)

    Article  ADS  Google Scholar 

  25. A.V. Rylyakov, K.K. Likharev, IEEE Trans. Appl. Supercond. 9, 3539 (1999)

    Article  Google Scholar 

  26. K.K. Likharev, V.K. Semenov, IEEE Trans. Appl. Supercond. 1, 3 (1991)

    Article  ADS  Google Scholar 

  27. T. Filippov, M. Znosko, Supercond. Sci. Tecnol. 12, 776 (1999)

    Article  ADS  Google Scholar 

  28. V.M. Buchstaber, O.V. Karpov, S.I. Tertychnyi, J. Exp. Theor. Phys. 97, 624 (2003)

    Article  ADS  Google Scholar 

  29. K. Fujiwara et al., IEEE Trans. Appl. Supercond. 15, 427 (2005)

    Article  Google Scholar 

  30. H. Terai, Z. Wang, Y. Hishimoto, S. Yorozu, A. Fujimaki, N. Yoshikawa, Appl. Phys. Lett. 84, 2133 (2004)

    Article  ADS  Google Scholar 

  31. A.V. Gordeeva, A.L. Pankratov, J. Appl. Phys. 103, 103913 (2008)

    Article  ADS  Google Scholar 

  32. A.L. Pankratov, B. Spagnolo, Phys. Rev. Lett. 93, 177001 (2004)

    Article  ADS  Google Scholar 

  33. A.V. Gordeeva, A.L. Pankratov, B. Spagnolo, Int. J. Bifurc. Chaos 18, 2825 (2008)

    Article  Google Scholar 

  34. J.C. Fenton, P.A. Warburton, J. Phys. Conf. Ser. 150, 052052 (2009)

    Article  ADS  Google Scholar 

  35. J.C. Fenton, P.A. Warburton, Phys. Rev. B 78, 054526 (2008)

    Article  ADS  Google Scholar 

  36. Y. Yu, S. Han, Phys. Rev. Lett. 91, 127003 (2003)

    Article  ADS  Google Scholar 

  37. G. Sun, N. Dong, G. Mao, J. Chen, W. Xu, Z. Ji, L. Kang, P. Wu, Y. Yu, D. Xing, Phys. Rev. E 75, 021107 (2007)

    Article  ADS  Google Scholar 

  38. C. Pan, X. Tan, Y. Yu, G. Sun, L. Kang, W. Xu, J. Chen, P. Wu, Phys. Rev. E 79, R030104 (2009)

    Article  ADS  Google Scholar 

  39. M.R. Souryal, E.G. Larsson, B. Peric, B.R. Vojcic, IEEE Trans. Sign. Proc. 56, 266 (2008)

    Article  MathSciNet  ADS  Google Scholar 

  40. B. Dybiec, E. Gudowska-Nowak, Phys. Rev. E 69, 016105 (2004)

    Article  ADS  Google Scholar 

  41. E.W. Montroll, M.F. Shlesinger, in Nonequilibrium Phenomena II: From Stochastics to Hydrodynamics, edited by J.L. Lebowitz, E.W. Montroll (North-Holland, Amsterdam, 1984)

  42. M.F. Shlesinger, G.M. Zaslavsky, U. Frisch, Levy Flights and Related Topics in Physics (Springer-Verlag, Berlin, 1995)

  43. J.T. Peltonen, A.V. Timofeev, M. Meschke, T.T. Heikkilä, J.P. Pekola, Physica E 40, 111 (2007)

    Article  ADS  Google Scholar 

  44. B. Huard, H. Pothier, N.O. Birge, D. Esteve, X. Waintal, J. Ankerhold, Ann. Phys. 16, 736 (2007)

    Article  Google Scholar 

  45. A.V. Chechkin, V. Yu. Gonchar, J. Klafter, R. Metzler, Adv. Chem. Phys. 133, 439 (2006)

    Google Scholar 

  46. R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  47. V.V. Uchaikin, Physics-Uspekhi 46, 821 (2003)

    Article  ADS  Google Scholar 

  48. A.A. Dubkov, A. La Cognata, B. Spagnolo, J. Stat. Mech.: Theory Exp. P01002 (2009)

  49. A.A. Dubkov, B. Spagnolo, V.V. Uchaikin, Int. J. Bifurc. Chaos 18, 2649 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  50. D. del-Castillo-Negrete, V.Yu. Gonchar, A.V. Chechkin, Physica A 387, 6693 (2008)

    Article  ADS  Google Scholar 

  51. B. Dybiec, E. Gudowska-Nowak, I.M. Sokolov, Phys. Rev. E 78, 011117 (2008)

    Article  ADS  Google Scholar 

  52. B.Q. Ai, Y.F. He, J. Stat. Mech.-Theory E. P04010 (2010)

  53. D. Brockmann, T. Geisel, Phys. Rev. Lett. 90, 170601 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  54. A.A. Greenenko, A.V. Chechkin, N.F. Shulga, Phys. Lett. A 324, 82 (2004)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  55. A.I. Shushin, Chem. Phys. 370, 244 (2010)

    Article  ADS  Google Scholar 

  56. A. Weron, Stat. Prob. Lett. 28, 165 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  57. J. Bertoin, Lévy Processes (Cambridge University Press, Cambridge, 1996)

  58. K.I. Sato, Lévy Processes and Infinitely Divisible Distributions (Cambridge University Press, Cambridge, 1999)

  59. B.V. Gnedenko, A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Cambridge, MA, 1954)

  60. B. de Finetti, Rendiconti della R. Accademia Nazionale dei Lincei (Ser. VI) 10, 325 (1929)

    Google Scholar 

  61. B. de Finetti, Theory of Probability (Wiley, New York, 1975), Vols. 1, 2

  62. A. Khintchine, P. Lévy, Comptes Rendus 202, 374 (1936)

    Google Scholar 

  63. A. Ya. Khintchine, Limit Distributions for the Sum of Independent Random Variables (O.N.T.I., Moscow, 1938) [in Russian]

  64. W. Feller, An Introduction to Probability Theory and its Applications (John Wiley & Sons, Inc., New York, 1971), Vol. 2

  65. R.N. Mantegna, H.E. Stanley, An Introduction to Econophysics. Correlations and Complexity in Finance (Cambridge University Press, Cambridge, 2000)

  66. J.P. Nolan, Stable Distributions: Models for Heavy-Tailed Data (Birkhauser-Springer, Berlin, 2002)

  67. H. Bergström, Ark. Mathematicae II 18, 375 (1952)

    Article  Google Scholar 

  68. A. Barone, G. Paternò, Physics and Application of the Josephson Effect (Wiley, New York, 1982)

  69. K.K. Likharev, Rev. Mod. Phys. 51, 101 (1979)

    Article  ADS  Google Scholar 

  70. Y. Yu, S. Han, X. Chu, S. I. Chu, Z. Wang, Science 296, 889 (2002)

    Article  ADS  Google Scholar 

  71. V.I. Mel'nikov, Phys. Rep. 209, 1 (1991)

    Article  ADS  Google Scholar 

  72. G. Samorodnitsky, M.S. Taqqu, Stable non-Gaussian Random Processes (Chapman & Hall, New York, 1994), p. 619

  73. A.V. Chechkin, V.Yu. Gonchar, J. Klafter, R. Metzler, Europhys. Lett. 72, 348 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  74. U. Weiss, Quantum Dissipative Systems (World Scientific, Singapore, 1999)

  75. P. Hänggi, P. Talkner, M. Borkovec, Rev. Mod. Phys. 62, 251 (1990)

    Article  ADS  Google Scholar 

  76. C.R. Doering, J.C. Gadoua, Phys. Rev. Lett. 69, 2318 (1992)

    Article  ADS  Google Scholar 

  77. R.N. Mantegna, B. Spagnolo, Phys. Rev. Lett. 84, 3025 (2000)

    Article  ADS  Google Scholar 

  78. R.N. Mantegna, B. Spagnolo, J. Phys. IV (France) 8, 247 (1998)

    Google Scholar 

  79. P. Pechukas, P. Hänggi, Phys. Rev. Lett. 73, 2772 (1994)

    Article  ADS  Google Scholar 

  80. M. Marchi, F. Marchesoni, L. Gammaitoni, E. Menichella- Saetta, S. Santucci, Phys. Rev. E 54, 3479 (1996)

    Article  ADS  Google Scholar 

  81. J. Iwaniszewski, I.K. Kaufman, P.V.E. McClintock, A.J. McKane, Phys. Rev. E 61, 1170 (2000)

    Article  ADS  Google Scholar 

  82. M. Boguñá, J.M. Porra, J. Masoliver, K. Lindenberg, Phys. Rev. E 57, 3990 (1998)

    Article  ADS  Google Scholar 

  83. B. Dybiec, E. Gudowska-Nowak, Phys. Rev. E 66, 026123 (2002)

    Article  ADS  Google Scholar 

  84. B. Dybiec, E. Gudowska-Nowak, J. Stat. Mech.-Theory E. P05004 (2009)

  85. V.N. Chizhevsky, Phys. Rev. E 80, 061139 (2009)

    Article  ADS  Google Scholar 

  86. R.N. Mantegna, B. Spagnolo, Phys. Rev. Lett. 76, 563 (1996)

    Article  ADS  Google Scholar 

  87. N. Agudov, B. Spagnolo, Phys. Rev. E 64, R035102 (2001)

    Article  ADS  Google Scholar 

  88. A.A. Dubkov, N.V. Agudov, B. Spagnolo, Phys. Rev. E 69, 061103 (2004)

    Article  ADS  Google Scholar 

  89. A. Fiasconaro, B. Spagnolo, S. Boccaletti, Phys. Rev. E. 72, 061110 (2005)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica e Tecnologie Relative, Group of Interdisciplinary Physics, Università di Palermo and CNISM-INFM, Unità di Palermo, Viale delle Scienze, Edificio 18, I-90128, Palermo, Italy

    G. Augello, D. Valenti & B. Spagnolo

Authors
  1. G. Augello
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Valenti
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. Spagnolo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Valenti.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Augello, G., Valenti, D. & Spagnolo, B. Non-Gaussian noise effects in the dynamics of a short overdamped Josephson junction. Eur. Phys. J. B 78, 225–234 (2010). https://doi.org/10.1140/epjb/e2010-10106-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2010-10106-1

Keywords

Search

Navigation