Phonon-phonon interactions in liquid helium

Abstract

This is a short review of recent experimental and theoretical studies of phonon interactions in superfluid helium. Phonon-phonon scattering in helium is strongly influenced by the conservation laws and by the peculiarities of the phonon dispersion relation. Theory predicts that because of these factors the spontaneous decay rate varies dramatically with phonon energy, and experiments have confirmed this prediction. The conservation laws can also be used to show that phonon-phonon collisions are predominatly small-angle scattering. We discuss the influence of this special property of phonon collisions on the hydrodynamics of the phonon gas, and we consider the solutions of the hydrodynamic equations in several situations of experimental interest.