Phonon Spectrum and Dynamical Stability of a Dilute Quantum Degenerate Bose-Fermi Mixture

We calculate the phonon excitation spectrum in a zero-temperature dilute boson-fermion gaseous mixture. We show how the sound velocity changes due to the boson-fermion interaction, and we determine the dynamical stability regime of a homogeneous mixture. We identify a resonant phonon-exchange interaction between the fermions as the physical mechanism leading to the instability.