Thermal conductivity of anharmonic lattices: Effective phonons and quantum corrections

Details Thermal conductivity of anharmonic lattices: Effective phonons and quantum corrections Thermal conductivity of anharmonic lattices: Effective phonons and quantum corrections

2010-01-21

arxiv.org/abs/1001.3788v1

Phys. Rev. E 78, 061103 (2008)

Physics

Condensed Matter

Statistical Mechanics

19 pages, 8 figures

Scientific paper

10.1103/PhysRevE.78.061103

We compare two effective phonon theories, which have both been applied recently to study heat conduction in anharmonic lattices. In particular, we study the temperature dependence of the thermal conductivity of the Fermi-Pasta-Ulam model via the Debye formula, showing the equivalence of both approaches. The temperature for the minimum of the thermal conductivity and the corresponding scaling behavior are analytically calculated, which agree well with the result obtained from nonequilibrium simulations. We also give quantum corrections for the thermal conductivity from quantum self-consistent phonon theory. The vanishing behavior at the low temperature regime and the existence of an umklapp peak are qualitatively consistent with experimental studies.

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