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

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• Thermal conductivities of one-dimensional anharmonic/nonlinear lattices: renormalized phonons and effective phonon theory
• Fourier's law based on microscopic dynamics
• Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions
• Heat conductivity from molecular chaos hypothesis in locally confined billiard systems
• Kinetic theory of phonons in weakly anharmonic particle chains
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• Hot scatterers and tracers for the transfer of heat in collisional dynamics
• On the derivation of Fourier's law for coupled anharmonic oscillators
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