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Ergodic properties of fractional Langevin motion with spatial correlated noise

  • H. -G. Duan
  • X. -T. LiangEmail author
Regular Article

Abstract

In this paper, using fractional Langevin equation, we investigate the diffusion behavior of particles in the potential with spatial correlated noise (random disorder). Weak ergodicity breaking is revealed by plotting time averaged mean square displacement and ergodicity breaking parameter. The results are consistent with continuous time random walk (CTRW) and also in agreement with the properties of ones obtained with experiments.

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    J. Mattson et al., Nature 462, 83 (2009)ADSCrossRefGoogle Scholar
  2. 2.
    R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000)MathSciNetADSzbMATHCrossRefGoogle Scholar
  3. 3.
    I. Golding, E.C. Cox, Phys. Rev. Lett. 96, 098102 (2006) ADSCrossRefGoogle Scholar
  4. 4.
    G. Migliorini, V.G. Rostiashvili, T.A. Vilgis, Eur. Phys. J. B 33, 61 (2003)ADSCrossRefGoogle Scholar
  5. 5.
    I.M. Tolic-Norrelykke et al., Phys. Rev. Lett. 93, 078102 (2004) ADSCrossRefGoogle Scholar
  6. 6.
    T. Akimoto, E. Yamamoto, K. Yasuoka, Y. Hirano, M. Yasui, Phys. Rev. Lett. 107, 178103 (2011) ADSCrossRefGoogle Scholar
  7. 7.
    A.V. Weigel, B. Simon, M.M. Tamkun, D. Krapf, Proc. Natl. Acad. Sci. USA 108, 6438 (2011) ADSCrossRefGoogle Scholar
  8. 8.
    J.-H. Jeon et al., Phys. Rev. Lett. 106, 048103 (2011) ADSCrossRefGoogle Scholar
  9. 9.
    J.-H. Jeon, R. Metzler, Phys. Rev. E 85, 021147 (2012) ADSCrossRefGoogle Scholar
  10. 10.
    S.C. Weber, A.J. Spakowitz, J.A. Theriot, Phys. Rev. Lett. 104, 238102 (2010) ADSCrossRefGoogle Scholar
  11. 11.
    E. Kepten, I. Bronshtein, Y. Garini, Phys. Rev. E 83, 041919 (2011) ADSCrossRefGoogle Scholar
  12. 12.
    H. Yang et al., Science 302, 262 (2003) ADSCrossRefGoogle Scholar
  13. 13.
    I. Goychuk, Chem. Phys. 375, 450 (2010) ADSCrossRefGoogle Scholar
  14. 14.
    I. Goychuk, P. Hanggi, Phys. Rev. Lett. 99, 200601 (2007) ADSCrossRefGoogle Scholar
  15. 15.
    J.-H. Jeon, R. Metzler, Phys. Rev. E 81, 021103 (2010) MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    M.A. Desposito, A.D. Vinales, Phys. Rev. E 80, 021111 (2009) ADSCrossRefGoogle Scholar
  17. 17.
    M. Khoury, A.M. Lacasta, J.M. Sancho, K. Lindenberg, Phys. Rev. Lett. 106, 090602 (2011) ADSCrossRefGoogle Scholar
  18. 18.
    W.T. Coffey, Y.P. Kalmykov, J.T. Walsron, The Langevin Equation (World Scientific, New Jersey, 2004) Google Scholar
  19. 19.
    A.H. Romero, J.M. Sancho, J. Comput. Phys. 156, 1 (1999)ADSzbMATHCrossRefGoogle Scholar
  20. 20.
    D. Banerjee, B.C. Bag, S.K. Banik D.S. Ray, J. Chem. Phys. 120, 8960 (2004) ADSCrossRefGoogle Scholar
  21. 21.
    H.-G. Duan, X.-T. Liang, Phys. Rev. A 83, 032316 (2011) ADSCrossRefGoogle Scholar
  22. 22.
    I. Goychuk, Phys. Rev. E 80, 046125 (2009) ADSCrossRefGoogle Scholar
  23. 23.
    I. Goychuk, P. Hanggi, Fractional Dynamics: Recent Advances (World Scientific, Singapore, 2011), Chap. 13, pp. 307–329Google Scholar
  24. 24.
    P. Reimann, R. Eichhorn, Phys. Rev. Lett. 101, 180601 (2008) ADSCrossRefGoogle Scholar
  25. 25.
    S. Burov, E. Barkai, Phys. Rev. Lett. 100, 070601 (2008) ADSCrossRefGoogle Scholar
  26. 26.
    Y. Deng, J. Bechhoefer, N.R. Forde, J. Opt. A Pure Appl. Opt. 9, S256 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    S. Burov, J.-H. Jeon, R. Metzler, E. Barkai, Phys. Chem. Chem. Phys. 13, 1800 (2011) CrossRefGoogle Scholar
  28. 28.
    S. Burov, R. Metzler, E. Barkai, Proc. Natl. Acad. Sci. 107, 13228 (2010) MathSciNetADSzbMATHCrossRefGoogle Scholar
  29. 29.
    Y. He, S. Burov, R. Metzler, E. Barkai, Phys. Rev. Lett. 101, 058101 (2008) ADSCrossRefGoogle Scholar
  30. 30.
    W.-H. Deng, E. Barkai, Phys. Rev. E 79, 011112 (2009)MathSciNetADSCrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.Department of Physics and Institute of Modern PhysicsNingBo UniversityNingBoP.R. China

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