Anomalous Heat Conduction in Three-Dimensional Nonlinear Lattices

Abstract

Heat conduction in three-dimenisional nonlinear lattice models is studied using nonequilibrium molecular dynamics simulations. We employ the FPU model, in which there exists a nonlinearity in the interaction of biquadratic form. It is confirmed that the thermal conductivity, the ratio of the energy flux to the temperature gradient, diverges in systems up to 128x128x256 lattice sites. This size corresponds to nanoscopic to mesoscopic scales of several tens of nanometers. From these results, we conjecture that the energy transport in insulators with perfect crystalline order exhibits anomalous behavior. The effects of lattice structure, random impurities, and natural length in interactions are also examined. We find that face-centered cubic (fcc) lattices display stronger divergence than simple cubic lattices. When impurity sites of infinitely large mass, which are hence fixed, are randomly distributed, such divergence vanishes.

10pages, 10 figures, Fig. 1 is replaced and some minor corrections were made

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• Anomalous Heat Conduction and Anomalous Diffusion in Low Dimensional Nanoscale Systems
• Heat transport and phonon localization in mass-disordered harmonic crystals
• Heat conduction in a three dimensional anharmonic crystal
• Nonstationary heat conduction in one-dimensional models with substrate potential
• Anomalous energy diffusion in two-dimensional nonlinear lattices
• Thermal rectification in three-dimensional mass-graded anharmonic oscillator lattices
• Heat conduction in a chain of dissociating particles: effect of dimensionality
• Heat conductivity in the beta-FPU lattice. Solitons and breathers as energy carriers