Heat conduction in a three dimensional anharmonic crystal

TL;DR

This study uses nonequilibrium simulations to investigate heat conduction in a 3D anharmonic lattice, confirming Fourier's law and the transition from 1D to 3D behavior with finite thermal conductivity.

Contribution

First numerical verification of Fourier's law in a 3D anharmonic crystal without pinning, demonstrating finite thermal conductivity and dimensional crossover.

Findings

Thermal conductivity becomes finite in 3D systems.

Crossover from 1D to 3D behavior occurs at small aspect ratios.

Fourier's law holds in the studied anharmonic lattice.

Abstract

We perform nonequilibrium simulations of heat conduction in a three dimensional anharmonic lattice. By studying slabs of length N and width W, we examine the cross-over from one-dimensional to three dimensional behavior of the thermal conductivity. We find that for large N, the cross-over takes place at a small value of the aspect ratio W/N. From our numerical data we conclude that the three dimensional system has a finite non-diverging thermal conductivity and thus provide the first verification of Fourier's law in a system without pinning.