Temperature dependence of thermal conductivity in 1D nonlinear lattices

TL;DR

This paper investigates how the thermal conductivity of one-dimensional nonlinear lattices varies with temperature, revealing a non-universal behavior influenced by nonlinearity strength, supported by simulations and theoretical analysis.

Contribution

It introduces a correlation between nonlinearity strength and thermal conductivity, proposing a conjecture within effective phonon theory and validating it through simulations and analytical methods.

Findings

Thermal conductivity depends on temperature via nonlinearity strength.

The mean-free-path of effective phonons is inversely proportional to nonlinearity.

The temperature dependence of conductivity is not universal for small nonlinear perturbations.

Abstract

We examine the temperature dependence of thermal conductivity of one dimensional nonlinear (anharmonic) lattices with and without on-site potential. It is found from computer simulation that the heat conductivity depends on temperature via the strength of nonlinearity. Based on this correlation, we make a conjecture in the effective phonon theory that the mean-free-path of the effective phonon is inversely proportional to the strength of nonlinearity. We demonstrate analytically and numerically that the temperature behavior of the heat conductivity $\kappa\propto1/T$ is not universal for 1D harmonic lattices with a small nonlinear perturbation. The computer simulations of temperature dependence of heat conductivity in general 1D nonlinear lattices are in good agreements with our theoretic predictions. Possible experimental test is discussed.