Heat transport in nonlinear lattices free from the Umklapp process

TL;DR

This paper constructs special one-dimensional nonlinear lattices where only normal phonon processes occur, and demonstrates through simulations that heat transport is ballistic, supporting the hypothesis that Umklapp processes are necessary for thermal resistance.

Contribution

The paper introduces a class of nonlinear lattices free from Umklapp processes and shows they exhibit ballistic heat transport, validating a key hypothesis in phonon scattering theory.

Findings

Heat transport in these lattices is ballistic, with thermal conductivity proportional to system size.

Normal processes alone do not cause thermal resistance in these lattices.

Results support the idea that Umklapp processes are essential for thermal resistance.

Abstract

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. These lattices have long-range quartic nonlinear and nearest neighbor harmonic interactions with/without harmonic on-site potential. We study heat transport in two cases of the lattices with and without harmonic on-site potential by non-equilibrium molecular dynamics simulation. It is shown that the ballistic heat transport occurs in both cases, i.e., the scaling law $\kappa\propto N$ holds between the thermal conductivity $\kappa$ and the lattice size $N$. This result directly validates Peierls's hypothesis that only the Umklapp processes can cause the thermal resistance while the normal one do not.