Dynamical instability of a boson–fermion mixture at low dimensions

Abstract

We examine theoretically the dynamical response of a homogeneous mixture of condensed bosons and spin-polarized fermions confined inside a quasi-two-dimensional or a quasi-one-dimensional geometry, considering quasi-three-dimensional boson–boson and boson–fermion interactions. We focus on the effects of low dimensions on the density response functions in the crossover from weak to strong boson–fermion coupling up to the onset of instability. The dynamical condition is found to be in agreement with a linear stability analysis at equilibrium.