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

¹ Department of Physics and Center for Computational Science and Engineering National University of Singapore - Singapore 117542, Republic of Singapore
² Department of Physics, Nanjing Normal University Nanjing, Jiangsu 210097, PRC
³ Laboratory of Modern Acoustics and Institute of Acoustics, Nanjing University 210093, PRC
⁴ NUS Graduate School for Integrative Sciences and Engineering Singapore 117597, Republic of Singapore

Corresponding author: phylibw@nus.edu.sg

Received: 10 March 2006
Accepted: 11 May 2006

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 model etc.