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Thermal diffusion of envelope solitons on anharmonic atomic chains

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  • C. Brunhuber
  • F. Mertens
  • Y. Gaididei

Abstract

We study the motion of envelope solitons on anharmonic atomic chains in the presence of dissipation and thermal fluctuations. We consider the continuum limit of the discrete system and apply an adiabatic perturbation theory which yields a system of stochastic integro-differential equations for the collective variables of the ansatz for the perturbed envelope soliton. We derive the Fokker-Planck equation of this system and search for a statistically equivalent system of Langevin equations, which shares the same Fokker-Planck equation. We undertake an analytical analysis of the Langevin system and derive an expression for the variance of the soliton position Var[x s ] which predicts a stronger than linear time dependence of Var[x s ] (superdiffusion). We compare these results with simulations for the discrete system and find they agree well. We refer to recent studies where the diffusion of pulse solitons were found to exhibit a superdiffusive behaviour on longer time scales. Copyright Springer-Verlag Berlin/Heidelberg 2004

Suggested Citation

  • C. Brunhuber & F. Mertens & Y. Gaididei, 2004. "Thermal diffusion of envelope solitons on anharmonic atomic chains," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 42(1), pages 103-112, November.
  • Handle: RePEc:spr:eurphb:v:42:y:2004:i:1:p:103-112
    DOI: 10.1140/epjb/e2004-00361-0
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    Cited by:

    1. Arnaud Debussche & Eric Gautier, 2005. "Small Noise Asymptotic of the Timing Jitter in Soliton Transmission," Working Papers 2005-20, Center for Research in Economics and Statistics.

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