Effective phonons in anharmonic lattices: Anomalous vs. normal heat conductionNianbei Li1, Peiqing Tong1, 2 and Baowen Li1, 3, 4
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
received 10 March 2006; accepted in final form 11 May 2006
published online 2 June 2006
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.
44.10.+i - Heat conduction.
63.20.-e - Phonons in crystal lattices.
44.05.+e - Analytical and numerical techniques.
© EDP Sciences 2006