A generalized decay law for particle- and wave-like thermal phonons

Our direct atomic simulations reveal that a thermally activated phonon mode involves a large population of elastic wavepackets. These excitations are characterized by a wide distribution of lifetimes and coherence times expressing particle- and wave-like 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 in relaxation times and thermal conductivity. This work opens new horizons in the understanding of the origin and the treatment of thermal phonons.