Phonon spectrum and dynamical stability of a quantum degenerate Bose-Fermi mixture

Abstract

We calculate the phonon excitation spectrum in a zero-temperature boson-fermion 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.