Phonon Viscosity

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Abstract
The Boltzmann equation for thermal phonons in a dielectric crystal in the presence of a slowly varying but otherwise arbitrary, strain field is solved formally by expanding the phonon distribution function in terms of eigenfunctions of the collision operator. The macroscopic stress is then calculated in terms of the macroscopic strain and the phonon distribution function by using the quasiharmonic approximation. The resulting equation for the stress is of the same form as that given by thermoelasticity, except for the presence of an extra term which is linear in the strain rate. The coefficient of the strain rate in this term is identified with the phonon viscosity tensor, and a formal expression for this tensor is obtained.