Aging phenomena in nonlinear dissipative chains

  • F. GobetEmail author
  • S. Ciliberto
  • T. Dauxois
Original Paper


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.


Correlation Function Strong Dependence Localize Mode Master Curve Energy Relaxation 
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  1. 1.
    A.M. Kosevich, Zh. Eksp. Teor. Fiz. 67, 1793 (1974)Google Scholar
  2. 2.
    A.J. Sievers, S. Takeno, Phys. Rev. Lett. 61, 970 (1988)CrossRefGoogle Scholar
  3. 3.
    T. Dauxois, M. Peyrard, Phys. Rev. Lett. 70, 3935 (1993)CrossRefGoogle Scholar
  4. 4.
    R. MacKay, S. Aubry, Nonlinearity 7, 1623 (1994)CrossRefMathSciNetzbMATHGoogle Scholar
  5. 5.
    B.I. Swanson , Phys. Rev. Lett. 82, 3288 (1999)CrossRefGoogle Scholar
  6. 6.
    U.T. Schwarz, L.Q. English, A.J. Sievers, Phys. Rev. Lett. 83, 223 (1999)CrossRefGoogle Scholar
  7. 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)CrossRefGoogle Scholar
  8. 8.
    G.P. Tsironis, S. Aubry, Phys. Rev. Lett. 77, 5225 (1996)CrossRefGoogle Scholar
  9. 9.
    R. Reigada, A. Sarmiento, K. Lindenberg, Phys. Rev. E 64, 066608 (2001)CrossRefGoogle Scholar
  10. 10.
    M. Peyrard, J. Farago, Physica A 288, 199 (2000)CrossRefGoogle Scholar
  11. 11.
    G. Kopidakis, S. Aubry, Physica B 296, 237 (2001)CrossRefGoogle Scholar
  12. 12.
    S. Aubry, G. Kopidakis, e-print cond-mat/0102162Google Scholar
  13. 13.
    J.L. Marin, F. Falo, P.J. Martinez, L.M. Floria, Phys. Rev. E 63, 066603 (2001)CrossRefGoogle Scholar
  14. 14.
    G.J. Martyna, M.L. Klein, M. Tuckerman, J. Chem. Phys. 97, 2635 (1992)CrossRefGoogle Scholar
  15. 15.
    N. Theodorakopoulos, T. Dauxois, M. Peyrard, Phys. Rev. Lett. 85, 6 (2000)CrossRefGoogle Scholar
  16. 16.
    T. Dauxois, N. Theodorakopoulos, M. Peyrard, J. Stat. Phys. 107, 869 (2002)CrossRefzbMATHGoogle Scholar
  17. 17.
    K.Y. Tsang, K.L. Ngai, Phys. Rev. E 54, R3067 (1996)Google Scholar
  18. 18.
    A. Bibaki, N.K. Voulgarakis, S. Aubry, G.P. Tsironis, Phys. Rev. E 59, 1234 (1999)CrossRefGoogle Scholar
  19. 19.
    R. Kohlrausch, Pogg. Ann. Physik 12, 393 (1847)Google Scholar
  20. 20.
    Spin Glasses and Random Fields, Series on Direction in Condensed Matter Physics, Vol. 12, edited by A.P. Young (World Scientific, Singapore, 1998)Google Scholar
  21. 21.
    W. Kob, J.L. Barrat, Phys. Rev. Lett. 78, 4581 (1997)CrossRefGoogle Scholar
  22. 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)Google Scholar
  23. 23.
    L. Cipelletti, S. Manley, R.C. Ball, D.A. Weitz, Phys. Rev. Lett. 84, 2275 (2000)CrossRefGoogle Scholar
  24. 24.
    M. Kroon, G.H. Wegdam, R. Sprik, Phys. Rev. E 54, 6541 (1996)CrossRefGoogle Scholar
  25. 25.
    A. Knaebel , Europhys. Lett. 52, 73 (2000)Google Scholar
  26. 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]Google Scholar
  27. 27.
    A. Barrat, Phys. Rev. E 57, 3629 (1998)CrossRefGoogle Scholar
  28. 28.
    J.L. Barrat, W. Kob, Europhys. Lett. 46, 637 (1999)Google Scholar
  29. 29.
    L. Berthier, L.F. Cugliandolo, J.L. Iguain, Phys. Rev. E 63, 051302 (2001)CrossRefGoogle Scholar
  30. 30.
    L. Bellon, S. Ciliberto, C. Laroche, Europhys. Lett. 54, 511 (2001)Google Scholar
  31. 31.
    T.S. Grigera, N.E. Israeloff, Phys. Rev. Lett. 83, 5038 (1999)CrossRefGoogle Scholar
  32. 32.
    D. Herisson, M. Ocio, Phys. Rev. Lett. 88, 257202 (2002)CrossRefGoogle Scholar
  33. 33.
    L. Buisson, L. Bellon, S. Ciliberto, J. Condens. Matter A, to appear (2003): cond-mat/0210490Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Laboratoire de PhysiqueUMR-CNRS 5672Lyon Cedex 07France

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