Phonon diffusion with frequency down‐conversion

Abstract

Abstract In most of the experiments with heat pulses the frequency spectrum of the nonequilibrium phonons does not differ very much from the equilibrium one. In this case nonequilibrity evolves only due to propagation in space (ballistic propagation, diffusion, second sound). But if the injected non‐equilibrium phonons are superthermal (i.e. have frequencies much higher than the bath temperature T ), nonequilibrity also evolves in the frequency domain – the spectral distribution due to the phonon decay shifts toward lower frequencies. The frequency down‐conversion influences the propagation, since all the scattering rates strongly depend on frequency. A theory of phonon diffusion accompanied by spontaneous phonon decay is presented. The phonon occupation numbers are supposed to be small and the bath temperature is supposed to be zero.