Transport Waves as Crystal Excitations

We introduce the concept of transport waves by showing that the linearized Boltzmann transport equation admits excitations in the form of waves that have well defined dispersion relations and decay times. Crucially, these waves do not represent single-particle excitations, but are collective excitations of the equilibrium distribution functions. We study in detail the case of thermal transport, where relaxons are found in the long-wavelength limit, and second sound is reinterpreted as the excitation of one or several temperature waves at finite frequencies. Graphene is studied numerically, finding decay times of the order of microseconds. The derivation, obtained by a spectral representation of the Boltzmann equation, holds in principle for any crystal or semiclassical transport theory and is particularly relevant when transport takes place in the hydrodynamic regime.