Advertisement

The European Physical Journal Special Topics

, Volume 216, Issue 1, pp 31–35 | Cite as

Time characteristics of Lévy flights in a steep potential well

  • A.A. DubkovEmail author
  • B. Spagnolo
Regular Article

Abstract

Using the method previously developed for ordinary Brownian diffusion, we derive a new formula to calculate the correlation time of stationary Lévy flights in a steep potential well. For the symmetric quartic potential, we obtain the exact expression of the correlation time of steady-state Lévy flights with index α = 1. The correlation time of stationary Lévy flights decreases with an increasing noise intensity and steepness of potential well.

Keywords

Correlation Time European Physical Journal Special Topic Noise Intensity Kolmogorov Equation Stationary Probability Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A.V. Chechkin, et al., J. Stat. Phys. 115, 1505 (2004)CrossRefzbMATHADSGoogle Scholar
  2. 2.
    A.A. Dubkov, B. Spagnolo, Fluct. Noise Lett. 5, L267 (2005)CrossRefMathSciNetGoogle Scholar
  3. 3.
    A.V. Chechkin, et al., Phys. Rev. E 75, 041101 (2007)CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    A.A. Dubkov, B. Spagnolo, Acta Phys. Pol. B 38, 1745 (2007)ADSMathSciNetGoogle Scholar
  5. 5.
    A.A. Dubkov, A. La Cognata, B. Spagnolo, J. Stat. Mech-Theory E., P01002 (2009)Google Scholar
  6. 6.
    R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)CrossRefzbMATHADSMathSciNetGoogle Scholar
  7. 7.
    A.V. Chechkin, et al., Adv. Chem. Phys. 133, 439 (2006)Google Scholar
  8. 8.
    A.A. Dubkov, B. Spagnolo, V.V. Uchaikin, Int. J. Bifurc. Chaos 18, 2649 (2008)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    A.A. Dubkov, A.N. Malakhov, A.I. Saichev, Radiophys. Quant. Electr. 43, 335 (2000)CrossRefADSMathSciNetGoogle Scholar
  10. 10.
    S. Yu. Medvedev, Radiophys. Quant. Electr. 20, 863 (1977)CrossRefADSGoogle Scholar
  11. 11.
    A.I. Saichev, Radiophys. Quant. Electr. 17, 657 (1974)CrossRefADSGoogle Scholar
  12. 12.
    A.N. Malakhov, Chaos 7, 488 (1997)CrossRefzbMATHADSMathSciNetGoogle Scholar
  13. 13.
    A.V. Chechkin, et al., Chem. Phys. 284, 233 (2002)CrossRefADSGoogle Scholar
  14. 14.
    A.V. Chechkin, et al., J. Phys. A: Math. Gen. 36, L537 (2003)CrossRefzbMATHADSMathSciNetGoogle Scholar
  15. 15.
    A.V. Chechkin, et al., Europhys. Lett. 72, 348 (2005)CrossRefADSMathSciNetGoogle Scholar
  16. 16.
    G. Augello, D. Valenti, B. Spagnolo, Eur. Phys. J. B 78, 225 (2010)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences and Springer 2013

Authors and Affiliations

  1. 1.Lobachevsky State University, Radiophysics FacultyNizhni NovgorodRussia
  2. 2.Università di Palermo, Dipartimento di Fisica, Group of Interdisciplinary Physics and CNISMPalermoItaly

Personalised recommendations