Simulation of heat transport in low-dimensional oscillator lattices

TL;DR

This paper reviews numerical simulation methods for heat transport in low-dimensional oscillator lattices, revealing dimension-dependent divergence behaviors and introducing a diffusion approach to connect energy diffusion with heat conduction.

Contribution

It introduces a novel diffusion method linking energy diffusion to heat conduction and provides detailed simulation results across different dimensions.

Findings

1D lattices show power-law divergent thermal conductivity.

2D lattices exhibit logarithmic divergence.

3D lattices have finite thermal conductivity.

Abstract

The study of heat transport in low-dimensional oscillator lattices presents a formidable challenge. Theoretical efforts have been made trying to reveal the underlying mechanism of diversified heat transport behaviors. In lack of a unified rigorous treatment, approximate theories often may embody controversial predictions. It is therefore of ultimate importance that one can rely on numerical simulations in the investigation of heat transfer processes in low-dimensional lattices. The simulation of heat transport using the non-equilibrium heat bath method and the Green-Kubo method will be introduced. It is found that one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) momentum-conserving nonlinear lattices display power-law divergent, logarithmic divergent and constant thermal conductivities, respectively. Next, a novel diffusion method is also introduced. The heat diffusion theory connects the energy diffusion and heat conduction in a straightforward manner. This enables one to use the diffusion method to investigate the objective of heat transport. In addition, it contains fundamental information about the heat transport process which cannot readily be gathered otherwise.