Energy Transport in Weakly Anharmonic Chains

TL;DR

This paper studies energy transport in a one-dimensional oscillator chain with weak anharmonicity, confirming Fourier's law through theoretical kinetic theory and molecular dynamics simulations, and identifying phonon collisions as key to finite heat conductivity.

Contribution

It provides a theoretical and numerical analysis of heat conduction in weakly anharmonic chains, demonstrating the role of phonon collisions in establishing finite thermal conductivity.

Findings

Fourier's law holds in weakly anharmonic chains.

Kinetic theory predictions agree with simulations at low temperatures.

Phonon collisions are responsible for finite heat conductivity.

Abstract

We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier's law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.