Thermal conductivity of anharmonic lattices: Effective phonons and quantum corrections

TL;DR

This paper compares two effective phonon theories to analyze heat conduction in anharmonic lattices, providing analytical and simulation results on thermal conductivity, including quantum corrections that align with experimental observations.

Contribution

It demonstrates the equivalence of two phonon theories in modeling heat conduction and extends the analysis with quantum corrections for better experimental relevance.

Findings

Analytical calculation of thermal conductivity minimum and scaling behavior.

Agreement between theory and nonequilibrium simulation results.

Quantum corrections show low-temperature vanishing and umklapp peak consistent with experiments.

Abstract

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.