Bose-Einstein condensation and density collapse in a weakly coupled boson-fermion mixture

TL;DR

This paper studies the conditions under which a weakly coupled boson-fermion mixture undergoes Bose-Einstein condensation and density collapse, focusing on the effects of interactions and mixture composition.

Contribution

It provides a theoretical analysis of the mechanical instability and BEC transition temperatures in a boson-fermion mixture with specific interactions, using a diagrammatic approach.

Findings

Identifies the conditions for density collapse due to induced boson-boson attraction.

Calculates the onset temperature for mechanical instability.

Determines the BEC transition temperature based on interaction parameters.

Abstract

We investigate the mechanical instability toward density collapse and the transition temperature of Bose-Einstein condensation in the weakly coupled boson-fermion many-body mixture of single-component boson and fermion gases, in the case of the repulsive boson-boson and attractive boson-fermion interactions; no fermion-fermion interaction is assumed due to the Pauli exclusion because of the diluteness of the mixture. The mechanical instability occurs in the part of bosonic gas in the case where the induced boson-boson attraction mediated by the fermion polarization overcomes the boson-boson repulsive interaction at low temperatures. We calculate the onset temperature of the mechanical instability and the BEC transition temperature for the interaction strength and the boson-fermion number ratio. We also discuss the relation between the mechanical instability and the BEC transition using a diagrammatic method.