Generalized decay law for particlelike and wavelike thermal phonons

Our direct atomic simulations reveal that a thermally activated phonon mode involves a large population of elastic wave packets. These excitations are characterized by a wide distribution of lifetimes and coherence times expressing particlelike and wavelike natures. In agreement with direct simulations, our theoretical derivation yields a generalized law for the decay of the phonon number taking into account coherent effects. Before the conventional exponential decay due to phonon-phonon scattering, this law introduces a delay proportional to the square of the coherence time. This additional regime leads to a moderate increase of the relaxation times and to a different dependence of phonon relaxation to those. This work opens new horizons in the understanding of the origin and the treatment of thermal phonons.