Skip to main content
SpringerLink
Log in

Propagation dynamics on the Fermi-Pasta-Ulam lattices

  • Research article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

The spatiotemporal propagation of a momentum excitation on the finite Fermi-Pasta-Ulam lattices is investigated. The competition between the solitary wave and phonons gives rise to interesting propagation behaviors. For a moderate nonlinearity, the initially excited pulse may propagate coherently along the lattice for a long time in a solitary wave manner accompanied by phonon tails. The lifetime of the long-transient propagation state exhibits a sensitivity to the nonlinear parameter. The solitary wave decays exponentially during the final loss of stability, and the decay rate varying with the nonlinear parameter exhibits two different scaling laws. This decay is found to be related to the largest Lyapunov exponent of the corresponding Hamiltonian system, which manifests a transition from weak to strong chaos. The mean-free-path of the solitary waves is estimated in the strong chaos regime, which may be helpful to understand the origin of anomalous conductivity in the Fermi-Pasta-Ulam lattice.

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. S. Lepri, R. Livi, and A. Politi, Phys. Rev. Lett., 1997, 78(10): 1896

    Article  ADS  Google Scholar 

  2. K. Aoki and D. Kusnezov, Phys. Rev. Lett., 2001, 86(18): 4029

    Article  ADS  Google Scholar 

  3. S. Lepri, R. Livi, and A. Politi, Phys. Rep., 2003, 377(1): 1

    Article  MathSciNet  ADS  Google Scholar 

  4. A. Dhar, Adv. Phys., 2008, 57(5): 457

    Article  ADS  Google Scholar 

  5. N. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, and B. Li,, Rev. Mod. Phys., 2012, 84(3): 1045

    Article  ADS  Google Scholar 

  6. M. Terraneo, M. Peyrard, and G. Casati, Phys. Rev. Lett., 2002, 88(9): 094302

    Article  ADS  Google Scholar 

  7. B. Li, L. Wang, and G. Casati, Phys. Rev. Lett., 2004, 93(18): 184301

    Article  ADS  Google Scholar 

  8. C. W. Chang, D. Okawa, H. Garcia, A. Majumdar, and A. Zettl, Phys. Rev. Lett., 2007, 99(4): 045901

    Article  ADS  Google Scholar 

  9. L. Wang and B. Li, Phys. Rev. Lett., 2007, 99(17): 177208

    Article  ADS  Google Scholar 

  10. L. Wang and B. Li, Phys. Rev. Lett., 2008, 101(26): 267203

    Article  ADS  Google Scholar 

  11. L. Wang and B. Li, Phys. World, 2008, 21: 27

    Google Scholar 

  12. C. W. Chang, D. Okawa, A. Majumdar, and A. Zettl, Science, 2006, 314(5802): 1121

    Article  ADS  Google Scholar 

  13. W. Kobayashi, Y. Teraoka, and I. Terasaki, Appl. Phys. Lett., 2009, 95(17): 171905

    Article  ADS  Google Scholar 

  14. J. Ren and B. Li, Phys. Rev. E, 2010, 81(2): 021111

    Article  ADS  Google Scholar 

  15. G. S. Zavt, M. Wagner, and A. Lütze,, Phys. Rev. E, 1993, 47(6): 4108

    Article  ADS  Google Scholar 

  16. A. Sarmiento, R. Reigada, A. H. Romero, and K. Lindenberg, Phys. Rev. E, 1999, 60(5): 5317

    Article  ADS  Google Scholar 

  17. A. Rosas and K. Lindenberg, Phys. Rev. E, 2004, 69(1): 016615

    Article  ADS  Google Scholar 

  18. E. Fermi, J. Pasta, and S. Ulam, Los Alamos Document No. LA-1940, 1955

    Google Scholar 

  19. N. J. Zabusky and M. D. Kruskal, Phys. Rev. Lett., 1965, 15(6): 240

    Article  ADS  MATH  Google Scholar 

  20. A. J. Sievers and S. Takeno, Phys. Rev. Lett., 1988, 61(8): 970

    Article  ADS  Google Scholar 

  21. S. Flach, M. V. Ivanchenko, and O. I. Kanakov, Phys. Rev. Lett., 2005, 95(6): 064102

    Article  ADS  Google Scholar 

  22. P. Villain and M. Lewenstein, Phys. Rev. A, 2000, 62(4): 043601

    Article  ADS  Google Scholar 

  23. G. Miloshevich, R. Khomeriki, and S. Ruffo, Phys. Rev. Lett., 2009, 102(2): 020602

    Article  ADS  Google Scholar 

  24. B. Li, J. H. Lan, and L. Wang, Phys. Rev. Lett., 2005, 95(10): 104302

    Article  ADS  Google Scholar 

  25. T. Mai, A. Dhar, and O. Narayan, Phys. Rev. Lett., 2007, 98(18): 184301

    Article  ADS  Google Scholar 

  26. A. Dhar and K. Saito, Phys. Rev. E, 2008, 78(6): 061136

    Article  ADS  Google Scholar 

  27. N. Li, B. Li, and S. Flach, Phys. Rev. Lett., 2010, 105(5): 054102

    Article  ADS  Google Scholar 

  28. C. Antonopoulos and T. Bountis, Phys. Rev. E, 2006, 73(5): 056206

    Article  MathSciNet  ADS  Google Scholar 

  29. J. A. D. Wattis, J. Phys. A, 1993, 26(5): 1193

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. G. Friesecke and J. Wattis, Commun. Math. Phys., 1994, 161(2): 391

    Article  MathSciNet  ADS  MATH  Google Scholar 

  31. F. Zhang, D. J. Isbister, and D. J. Evans, Phys. Rev. E, 2000, 61(4): 3541

    Article  ADS  Google Scholar 

  32. F. Zhang, D. J. Isbister, and D. J. Evans, Phys. Rev. E, 2001, 64(2): 021102

    Article  ADS  Google Scholar 

  33. S. R. Forrest and T. A. Jr. Witten, J. Phys. A, 1979, 12(5): L109

    Article  ADS  Google Scholar 

  34. G. Gallavotti (Ed.), The Fermi-Pasta-Ulam Problem, Springer-Verlag, 2008

    MATH  Google Scholar 

  35. L. Casetti, R. Livi, and M. Pettini, Phys. Rev. Lett., 1995, 74(3): 375

    Article  ADS  Google Scholar 

  36. L. Casetti, C. Clementi, and M. Pettini, Phys. Rev. E, 1996, 54(6): 5969

    Article  MathSciNet  ADS  Google Scholar 

  37. N. Li and B. Li, Europhys. Lett., 2007, 78(3): 34001

    Article  ADS  Google Scholar 

  38. H. Zhao, Phys. Rev. Lett., 2006, 96(14): 140602

    Article  ADS  Google Scholar 

  39. N. Li, P. Tong, and B. Li, Europhys. Lett., 2006, 75(1): 49

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing, 100875, China

    Zong-Qiang Yuan & Zhi-Gang Zheng

Authors
  1. Zong-Qiang Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi-Gang Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Gang Zheng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yuan, ZQ., Zheng, ZG. Propagation dynamics on the Fermi-Pasta-Ulam lattices. Front. Phys. 8, 349–355 (2013). https://doi.org/10.1007/s11467-013-0333-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11467-013-0333-9

Keywords

Search

Navigation