Phonon Heat Transport Seen in Pulses

The ballistic to diffusive crossover, that occurs when quasiparticles transport heat or charge, is important in small systems. Propagation of energy from an initial localized pulse provides a useful picture of the process. This paper looks at the simplest example, vibrational pulses on a one-dimensional harmonic chain of atoms. Pure ballistic propagation occurs in ordered chains, and a crossover toward diffusive propagation can be seen in disordered chains. A full analysis is inhibited by non-perturbative effects, especially Anderson localization. A partial analysis using Boltzmann theory is given.