Thermal diffusion of envelope solitons on anharmonic atomic chains
Physikalisches Institut, TP 1, Universität Bayreuth, 95440 Bayreuth, Germany
2 Bogolyubov Institute for Theoretical Physics, 03143 Kiev, Ukraine
Corresponding author: a Christian.Brunhuber@uni-bayreuth.de
Published online: 26 November 2004
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 which predicts a stronger than linear time dependence of (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.
PACS: 05.10.Gg – Stochastic analysis methods / 05.45.Yv – Solitons / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.50.+q – Lattice theory and statistics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004