Normal Heat Conduction in a Chain with Weak Interparticle Anharmonic Potential

TL;DR

This paper analytically investigates heat conduction in a one-dimensional chain with weak interparticle anharmonic potential, revealing a temperature-dependent phase transition where Fourier's law applies only at high temperatures.

Contribution

It provides a perturbative analytical expression for thermal conductivity in a chain with weak anharmonic interactions, highlighting a temperature-driven phase transition in heat conduction behavior.

Findings

Fourier's law holds only at high temperatures.

Thermal conductivity depends on temperature regimes.

A phase transition occurs as interior heat bath couplings are turned off.

Abstract

We analytically study heat conduction in a chain with interparticle interaction V(x)=lambda[1-cos(x)] and harmonic on-site potential. We start with each site of the system connected to a Langevin heat bath, and investigate the case of small coupling for the interior sites in order to understand the behavior of the system with thermal reservoirs at the boundaries only. We study, in a perturbative analysis, the heat current in the steady state of the one-dimensional system with weak interparticle potential. We obtain an expression for the thermal conductivity, compare the low and high temperature regimes, and show that, as we turn off the couplings with the interior heat baths, there is a "phase transition:'' the Fourier's law holds only at high temperatures.