Heat transport in nonlinear lattices free from the Umklapp process

We construct one-dimensional nonlinear lattices having the special property such that the Umklapp process vanishes and only the normal processes are included in the potential functions. We study heat transport in these lattices by non-equilibrium molecular dynamics simulation. It is shown that the ballistic heat transport occurs, i.e., the scaling law $kappapropto N$ holds between the thermal conductivity $kappa$ and the lattice size $N$. This result directly validates Peierlss hypothesis that only the Umklapp processes can cause the thermal resistance while the normal one do not.