We have studied the dependence of the thermal conductivity $\kappa$ on the strength of the interparticle potential $\lambda$ and the strength of the external potential $\beta$ in the Frenkel-Kontorova model. We found that the functional relation can be expressed in a scaling form, $\kappa \propto \frac{{\lambda }^{3∕2}}{{\beta }^2}$. 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 $\kappa$ is therefore a decreasing functon of $\beta$ and an increasing function of $\lambda$.

• Received 15 July 2008

DOI:https://doi.org/10.1103/PhysRevE.78.061130