Normal Heat Conductivity in a strongly pinned chain of anharmonic oscillators

TL;DR

This paper derives a finite heat conductivity in a strongly pinned anharmonic oscillator chain under non-equilibrium forcing, using a Gaussian approximation to analyze the stationary state and collision operator.

Contribution

It introduces a novel analytical approach to compute heat conductivity in a strongly pinned anharmonic chain using a Gaussian approximation and Boltzmann equation.

Findings

Finite heat conductivity proportional to 1/λ²T²

Gaussian approximation effectively models non-equilibrium stationary states

Resonance localization aids in inverting the collision operator

Abstract

We consider a chain of coupled and strongly pinned anharmonic oscillators subject to a non-equilibrium random forcing. Assuming that the stationary state is approximately Gaussian, we first derive a stationary Boltzmann equation. By localizing the involved resonances, we next invert the linearized collision operator and compute the heat conductivity. In particular, we show that the Gaussian approximation yields a finite conductivity $\kappa\sim\frac{1}{\lambda^2T^2}$, for $\lambda$ the anharmonic coupling strength.