Thermal diffusion of envelope solitons on anharmonic atomic chains

Brunhuber, C.; Mertens, F. G.; Gaididei, Y.
November 2004
European Physical Journal B -- Condensed Matter;Nov2004, Vol. 42 Issue 1, p103
Academic Journal
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 positionVar[xs] which predicts a stronger than linear time dependence ofVar[xs] (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.


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