Novel Vistas in Thermal Transport: Relaxons, Viscosities and Coherences

First, we examine the emergence of correlated transport phenomena in systems described by the linearized Boltzmann transport equation (LBTE), with examples centered around heat transport. We show how phonons are only a high-temperature approximation to the exact carriers, that we term relaxons, and that the thermal conductivity can be mapped exactly into a kinetic theory of the relaxon gas. We also calculate the viscosity of this gas, and coarse-grain the LBTE into coupled viscous equations that describe the hydrodynamic regime of heat propagation. Then, we discuss thermal transport in materials with low conductivity (thermoelectrics, thermal barrier coatings, glasses), highlighting the importance of a broader formulation - in the form of a Wigner transport equation - that includes also the tunnelling of phonon wavepackets.