Anomalous heat conduction in three-dimensional nonlinear lattices

Heat conduction in three-dimenisional nonlinear lattice models is studied using nonequilibrium molecular dynamics simulations. We employ the Fermi-Pasta-Ulam-β model, in which nonlinearity exists in the interaction of the biquadratic form. It is confirmed that the thermal conductivity, the ratio of the energy flux to the temperature gradient, diverges with increasing system size up to 128 x 128 x 256 lattice sites. This size corresponds to nanoscopic to mesoscopic scales of approximately 100 nm. From these results, we conjecture that the energy transport in insulators with perfect crystalline order exhibits anomalous behavior. The effects of the lattice structure, random impurities, and the natural length in interactions are also examined. We find that fcc lattices display stronger divergence than simple cubic lattices. When impurity sites of infinitely large mass, which are thus fixed, are randomly distributed, such divergence vanishes.