Effective phonons in anharmonic lattices: Anomalous vs. normal heat conduction

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 Prenkel-Kontorova model and the Φ4 model etc. © EDP Sciences.