Effective phonons in anharmonic lattices: anomalous vs normal heat conduction

TL;DR

This paper develops an effective phonon theory to explain heat conduction behaviors in 1D anharmonic lattices, distinguishing between anomalous and normal conduction based on the presence of on-site potential.

Contribution

It introduces a unified formalism using effective phonons and power spectrum weighting to explain different heat conduction regimes in momentum conserved and non-conserved lattices.

Findings

Effective phonon modes oscillate quasi-periodically.

The formalism explains both anomalous and normal heat conduction.

Results align well with numerical models like FPU, Frenkel-Kontorova, and φ^4.

Abstract

We study heat conduction in one dimensional (1D) anharmonic lattices analytically and numerically by using an effective phonon theory. It is found that every effective phonon mode oscillates quasi-periodically. By weighting the power spectrum of the total heat flux in the Debye formula, we obtain a unified formalism that can explain anomalous heat conduction in momentum conserved lattices without on-site potential and normal heat conduction in lattices with on-site potential. Our results agree very well with numerical ones for existing models such as the Fermi-Pasta-Ulam model, the Frenkel-Kontorova model and the $\phi^4$ model etc.