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

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Abstract
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.