Ballistic and diffusive phonon heat transport studied by pulse propagation in one dimension

Several kinds of heat pulses are inserted into a one-dimensional lattice. Their propagation is studied in classical mechanics, which gives insight into ballistic versus diffusive behavior. The results are modeled using quasiparticle pictures, especially the phonon Boltzmann equation. Ballistic propagation is easily modeled, has interesting dependence on the shape of the initial insertion, and gives insight into new aspects of Boltzmann theories of systems inhomogeneous in space and time. Phonon scattering provides an approach to diffusive propagation. Scattering by impurities with altered mass give new features to the propagating pulse, as does anharmonic phonon-phonon coupling. The Boltzmann-predicted pulse shapes using relaxation-time approximation show a crossover toward diffusion, but do not agree closely with the simulations.