Heat conduction in a three dimensional anharmonic crystal

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.