https://doi.org/10.1140/epjb/e2004-00361-0
Thermal diffusion of envelope solitons on anharmonic atomic chains
1
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
Received:
28
June
2004
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
