Nondissipative diffusion of lattice solitons out of thermal equilibrium

We perform Langevin dynamics simulations for pulse solitons on atomic chains with anharmonic nearest-neighbor interactions. After switching off noise and damping after a sufficiently long time, the solitons are only influenced by the thermal phonon bath which had been created by the noise. The soliton diffusion constant D is considerably smaller than before the switch-off, and it is proportional to the square of the temperature T , in contrast to the diffusion due to the noise which is proportional to T . We derive a diffusion equation for a soliton which is scattered elastically in an ensemble of phonons and derive general expressions for D and for the drift velocity v(d) . These expressions can be evaluated for the case of the Toda lattice for which the soliton shift due to the phonon scattering is known explicitly. D is indeed proportional to T2 and agrees well with the simulation results, while v(d) is much smaller than the soliton velocity and cannot be measured in the simulations due to the large fluctuations of the soliton position. We express D in terms of soliton characteristics which are known also for solitons on other anharmonic chains in the continuum limit: namely, velocity, amplitude, and width. The results agree well with the simulations if the soliton shape is the same as in the Toda case. If the shape is different, only an estimate of the order of magnitude can be given.