Anomalous Heat Conduction in Three-Dimensional Nonlinear Lattices

TL;DR

This study uses molecular dynamics simulations to demonstrate that heat conduction in three-dimensional nonlinear lattices diverges with system size, indicating anomalous energy transport behavior in perfect crystals.

Contribution

It provides the first evidence of size-dependent divergence of thermal conductivity in 3D nonlinear lattices and explores effects of lattice structure and impurities.

Findings

Thermal conductivity diverges up to 128x128x256 lattice sites.

Face-centered cubic lattices show stronger divergence than simple cubic lattices.

Random impurities suppress divergence, leading to normal heat conduction.

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.