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Ergodic properties of fractional Langevin motion with spatial correlated noise

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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.

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References

  1. J. Mattson et al., Nature 462, 83 (2009)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. I. Golding, E.C. Cox, Phys. Rev. Lett. 96, 098102 (2006)

    Article  ADS  Google Scholar 

  4. G. Migliorini, V.G. Rostiashvili, T.A. Vilgis, Eur. Phys. J. B 33, 61 (2003)

    Article  ADS  Google Scholar 

  5. I.M. Tolic-Norrelykke et al., Phys. Rev. Lett. 93, 078102 (2004)

    Article  ADS  Google Scholar 

  6. T. Akimoto, E. Yamamoto, K. Yasuoka, Y. Hirano, M. Yasui, Phys. Rev. Lett. 107, 178103 (2011)

    Article  ADS  Google Scholar 

  7. A.V. Weigel, B. Simon, M.M. Tamkun, D. Krapf, Proc. Natl. Acad. Sci. USA 108, 6438 (2011)

    Article  ADS  Google Scholar 

  8. J.-H. Jeon et al., Phys. Rev. Lett. 106, 048103 (2011)

    Article  ADS  Google Scholar 

  9. J.-H. Jeon, R. Metzler, Phys. Rev. E 85, 021147 (2012)

    Article  ADS  Google Scholar 

  10. S.C. Weber, A.J. Spakowitz, J.A. Theriot, Phys. Rev. Lett. 104, 238102 (2010)

    Article  ADS  Google Scholar 

  11. E. Kepten, I. Bronshtein, Y. Garini, Phys. Rev. E 83, 041919 (2011)

    Article  ADS  Google Scholar 

  12. H. Yang et al., Science 302, 262 (2003)

    Article  ADS  Google Scholar 

  13. I. Goychuk, Chem. Phys. 375, 450 (2010)

    Article  ADS  Google Scholar 

  14. I. Goychuk, P. Hanggi, Phys. Rev. Lett. 99, 200601 (2007)

    Article  ADS  Google Scholar 

  15. J.-H. Jeon, R. Metzler, Phys. Rev. E 81, 021103 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  16. M.A. Desposito, A.D. Vinales, Phys. Rev. E 80, 021111 (2009)

    Article  ADS  Google Scholar 

  17. M. Khoury, A.M. Lacasta, J.M. Sancho, K. Lindenberg, Phys. Rev. Lett. 106, 090602 (2011)

    Article  ADS  Google Scholar 

  18. W.T. Coffey, Y.P. Kalmykov, J.T. Walsron, The Langevin Equation (World Scientific, New Jersey, 2004)

  19. A.H. Romero, J.M. Sancho, J. Comput. Phys. 156, 1 (1999)

    Article  ADS  MATH  Google Scholar 

  20. D. Banerjee, B.C. Bag, S.K. Banik D.S. Ray, J. Chem. Phys. 120, 8960 (2004)

    Article  ADS  Google Scholar 

  21. H.-G. Duan, X.-T. Liang, Phys. Rev. A 83, 032316 (2011)

    Article  ADS  Google Scholar 

  22. I. Goychuk, Phys. Rev. E 80, 046125 (2009)

    Article  ADS  Google Scholar 

  23. I. Goychuk, P. Hanggi, Fractional Dynamics: Recent Advances (World Scientific, Singapore, 2011), Chap. 13, pp. 307–329

  24. P. Reimann, R. Eichhorn, Phys. Rev. Lett. 101, 180601 (2008)

    Article  ADS  Google Scholar 

  25. S. Burov, E. Barkai, Phys. Rev. Lett. 100, 070601 (2008)

    Article  ADS  Google Scholar 

  26. Y. Deng, J. Bechhoefer, N.R. Forde, J. Opt. A Pure Appl. Opt. 9, S256 (2007)

    Article  ADS  Google Scholar 

  27. S. Burov, J.-H. Jeon, R. Metzler, E. Barkai, Phys. Chem. Chem. Phys. 13, 1800 (2011)

    Article  Google Scholar 

  28. S. Burov, R. Metzler, E. Barkai, Proc. Natl. Acad. Sci. 107, 13228 (2010)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  29. Y. He, S. Burov, R. Metzler, E. Barkai, Phys. Rev. Lett. 101, 058101 (2008)

    Article  ADS  Google Scholar 

  30. W.-H. Deng, E. Barkai, Phys. Rev. E 79, 011112 (2009)

    Article  MathSciNet  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Physics and Institute of Modern Physics, NingBo University, NingBo, 315211, P.R. China

    H. -G. Duan & X. -T. Liang

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  1. H. -G. Duan
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  2. X. -T. Liang
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Correspondence to X. -T. Liang.

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Duan, H.G., Liang, X.T. Ergodic properties of fractional Langevin motion with spatial correlated noise. Eur. Phys. J. B 85, 209 (2012). https://doi.org/10.1140/epjb/e2012-30002-x

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  • DOI: https://doi.org/10.1140/epjb/e2012-30002-x

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