Zero-temperature phase diagram of binary boson-fermion mixtures

We calculate the phase diagram for dilute mixtures of bosoms and fermions at zero temperature. The linear stability conditions are derived and related to the effective boson-induced interaction between the fermions. We show that in equilibrium there are three possibilities: (a) a single uniform phase, (b) a purely fermionic phase coexisting with a purely bosonic one, and (c) a purely fermionic phase coexisting with a mixed phase.