Scaling and the thermal conductivity of the Frenkel-Kontorova model

We have studied the dependence of the thermal conductivity κ on the strength of the interparticle potential λ and the strength of the external potential β in the Frenkel-Kontorova model. We found that the functional relation can be expressed in a scaling form, κ∝λ3∕2β². This result is first obtained by nonequilibrium molecular dynamics. It is then confirmed by two analytical methods, the self-consistent phonon theory and the self-consistent stochastic reservoirs method. The thermal conductivity κ is therefore a decreasing functon of β and an increasing function of λ.