The Variational Principle and the Phonon Boltzmann Equation

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Amelia Carolina Sparavigna (2017). The Variational Principle and the Phonon Boltzmann Equation. Mechanics, Materials Science & Engineering, Vol 8. doi:10.2412/mmse.11.97.135

Authors: Amelia Carolina Sparavigna

ABSTRACT. The thermal transport in a solid happens when the material is subjected to a thermal gradient. If free electrons are absent, the thermal transport is due to the phonons, the quasiparticles corresponding to the vibrations of the atoms of the crystal. The equation that describes this transport is the phonon Boltzmann equation. Here we show how to solve it by means of the variational principle.

Keywords: Boltzmann equation, thermal conductivity, variational method, phonons, rare gas solids

DOI 10.2412/mmse.11.97.135

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