Skip to main content
SpringerLink
Log in

Aging phenomena in nonlinear dissipative chains

  • Original Paper
  • Published:
The European Physical Journal B - Condensed Matter and Complex Systems Aims and scope Submit manuscript

Abstract.

We study the energy relaxation in a one-dimensional nonlinear lattice with dissipative couplings. After thermalisation of this system, the extremities of the chain are put in contact with a zero-temperature reservoir, showing the existence of surprising quasi-stationary states with non zero energy, tough the dissipative coupling is high. This strange behavior, due to long-lived nonlinear localized modes, induces stretched exponential relaxation laws. Furthermore, we observe a strong dependence on the waiting time tw after the quench of the two-time intermediate correlation function C(t w +t, t w ). This function can be scaled onto a master curve, similar to the case of spin or Lennard-Jones glasses.

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. A.M. Kosevich, Zh. Eksp. Teor. Fiz. 67, 1793 (1974)

    Google Scholar 

  2. A.J. Sievers, S. Takeno, Phys. Rev. Lett. 61, 970 (1988)

    Article  Google Scholar 

  3. T. Dauxois, M. Peyrard, Phys. Rev. Lett. 70, 3935 (1993)

    Article  Google Scholar 

  4. R. MacKay, S. Aubry, Nonlinearity 7, 1623 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  5. B.I. Swanson , Phys. Rev. Lett. 82, 3288 (1999)

    Article  Google Scholar 

  6. U.T. Schwarz, L.Q. English, A.J. Sievers, Phys. Rev. Lett. 83, 223 (1999)

    Article  Google Scholar 

  7. E. Trias, J.J. Mazo, T.P. Orland, Phys. Rev. Lett. 84, 741 (2000) P. Binder, D. Abraimov, A.V. Ustinov, S. Flach, Y. Zoloraryuk, Phys. Rev. Lett. 84, 745 (2000)

    Article  Google Scholar 

  8. G.P. Tsironis, S. Aubry, Phys. Rev. Lett. 77, 5225 (1996)

    Article  Google Scholar 

  9. R. Reigada, A. Sarmiento, K. Lindenberg, Phys. Rev. E 64, 066608 (2001)

    Article  Google Scholar 

  10. M. Peyrard, J. Farago, Physica A 288, 199 (2000)

    Article  Google Scholar 

  11. G. Kopidakis, S. Aubry, Physica B 296, 237 (2001)

    Article  Google Scholar 

  12. S. Aubry, G. Kopidakis, e-print cond-mat/0102162

  13. J.L. Marin, F. Falo, P.J. Martinez, L.M. Floria, Phys. Rev. E 63, 066603 (2001)

    Article  Google Scholar 

  14. G.J. Martyna, M.L. Klein, M. Tuckerman, J. Chem. Phys. 97, 2635 (1992)

    Article  Google Scholar 

  15. N. Theodorakopoulos, T. Dauxois, M. Peyrard, Phys. Rev. Lett. 85, 6 (2000)

    Article  Google Scholar 

  16. T. Dauxois, N. Theodorakopoulos, M. Peyrard, J. Stat. Phys. 107, 869 (2002)

    Article  MATH  Google Scholar 

  17. K.Y. Tsang, K.L. Ngai, Phys. Rev. E 54, R3067 (1996)

  18. A. Bibaki, N.K. Voulgarakis, S. Aubry, G.P. Tsironis, Phys. Rev. E 59, 1234 (1999)

    Article  Google Scholar 

  19. R. Kohlrausch, Pogg. Ann. Physik 12, 393 (1847)

    Google Scholar 

  20. Spin Glasses and Random Fields, Series on Direction in Condensed Matter Physics, Vol. 12, edited by A.P. Young (World Scientific, Singapore, 1998)

  21. W. Kob, J.L. Barrat, Phys. Rev. Lett. 78, 4581 (1997)

    Article  Google Scholar 

  22. E. Vincent, J. Hammann, M. Ocio, J.P. Bouchaud, L.F. Cugliandolo, Slow dynamics and aging, edited by M. Rubi (Springer-Verlag, Berlin, 1997)

  23. L. Cipelletti, S. Manley, R.C. Ball, D.A. Weitz, Phys. Rev. Lett. 84, 2275 (2000)

    Article  Google Scholar 

  24. M. Kroon, G.H. Wegdam, R. Sprik, Phys. Rev. E 54, 6541 (1996)

    Article  Google Scholar 

  25. A. Knaebel , Europhys. Lett. 52, 73 (2000)

    Google Scholar 

  26. J.-P. Bouchaud, L.F. Cugliandolo, J. Kurchan, M. Mezard, Out of equilibrium dynamics in spin-glasses and other glassy systems, published in [20]

  27. A. Barrat, Phys. Rev. E 57, 3629 (1998)

    Article  Google Scholar 

  28. J.L. Barrat, W. Kob, Europhys. Lett. 46, 637 (1999)

    Google Scholar 

  29. L. Berthier, L.F. Cugliandolo, J.L. Iguain, Phys. Rev. E 63, 051302 (2001)

    Article  Google Scholar 

  30. L. Bellon, S. Ciliberto, C. Laroche, Europhys. Lett. 54, 511 (2001)

    Google Scholar 

  31. T.S. Grigera, N.E. Israeloff, Phys. Rev. Lett. 83, 5038 (1999)

    Article  Google Scholar 

  32. D. Herisson, M. Ocio, Phys. Rev. Lett. 88, 257202 (2002)

    Article  Google Scholar 

  33. L. Buisson, L. Bellon, S. Ciliberto, J. Condens. Matter A, to appear (2003): cond-mat/0210490

Download references

Author information

Authors and Affiliations

  1. Laboratoire de Physique, UMR-CNRS 5672, ENS Lyon, 46 Allée d'Italie, 69364, Lyon Cedex 07, France

    F. Gobet, S. Ciliberto & T. Dauxois

Authors
  1. F. Gobet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Ciliberto
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. T. Dauxois
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. Gobet.

Additional information

Received: 11 February 2003, Published online: 4 August 2003

PACS:

05.20.-y Classical statistical mechanics - 05.45.-a Nonlinear dynamics and nonlinear dynamical systems

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gobet, F., Ciliberto, S. & Dauxois, T. Aging phenomena in nonlinear dissipative chains. Eur. Phys. J. B 34, 193–199 (2003). https://doi.org/10.1140/epjb/e2003-00211-7

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjb/e2003-00211-7

Keywords

Search

Navigation