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 crossover from one dimensional to three dimensional behavior of the thermal conductivity κ. We find that for large N, the crossover 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 nondiverging κ and thus provides the first verification of Fourier's law in a system without pinning.