Hydrodynamic heat transport in dielectric crystals in the collective limit and the drifting/driftless velocity conundrum
Lluc Sendra, Albert Beardo, J. Bafaluy, Pol Torres, F. X. Álvarez, J. Camacho
Abstract
We apply a recently developed method for solving the linearized phonon Boltzmann equation to study the hydrodynamic thermal transport in dielectrics in the collective limit, i.e., when normal collisions dominate resistive ones. The method recovers Guyer and Krumhansl results for a single Debye branch and extends them to general dispersion relations and branches. Specifically, we obtain explicit microscopic expressions for the phonon distribution and for the transport coefficients in this limit. We find that the phonon distribution differs from the commonly used displaced distribution in two terms: one accounting for viscous flow and another one which allows us to solve a long-standing issue on drifting and driftless second-sound velocities. Thus, the new method allows us to generalize previous results and fill some gaps on fundamental aspects of the collective limit through a simple mathematical formalism. We compare the hydrodynamic framework with previous models and discuss its limitations.