Europhys. Lett.
Volume 75, Number 1, July 2006
Page(s) 49 - 55
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 02 June 2006
Europhys. Lett., 75 (1), pp. 49-55 (2006)
DOI: 10.1209/epl/i2006-10079-7

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

Nianbei 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 $\phi^4$ model etc.

44.10.+i - Heat conduction.
63.20.-e - Phonons in crystal lattices.
44.05.+e - Analytical and numerical techniques.

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