Thermodynamic stability, compressibility matrices, and effects of mediated interactions in a strongly interacting Bose-Fermi mixture

We theoretically investigate the thermodynamic stability of a normal-state Bose-Fermi mixture, with tunable pairing interaction $-U_{\rm BF}<0$ associated hetero-nuclear Feshbach resonance, as well weak repulsive Bose-Bose $U_{\rm BB}\ge 0$. Including strong hetero-pairing fluctuations former within self-consistent $T$-matrix approximation, latter mean-field level, we calculate compressibility matrix, to assess this system against density fluctuations. In weak- and intermediate-coupling regime respect BF}$, show that an effective attractive between bosons mediated by in Fermi component makes unstable below certain temperature $T_{\rm clp}$ (leading collapse). When BB}=0$, is always higher than Bose-Einstein condensation (BEC) c}$. BB}>0$, collapse suppressed, BEC transition becomes possible. It also suppressed formation tightly bound molecules when BF}$ strong; however, since may be viewed molecular gas case, does not occur. Since quantum gases involving Bose atoms are known sensitive inter-particle correlations, our results would useful for study many-body properties mixture stable manner, without facing unwanted collapse.