Normal Heat Conductivity in a strongly pinned chain of anharmonic oscillators

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 $\kappa \sim \frac{1}{{\lambda }^2{T}^2}$, for $\lambda$ the anharmonic coupling strength.

Introduction and conclusion modified