Bose-Einstein condensation in a mixture of interacting Bose and Fermi particles

TL;DR

This paper develops a self-consistent model for Bose-Fermi mixtures, analyzing how fermions influence Bose-Einstein condensation, revealing that fermions lower the transition temperature and smooth thermodynamic features.

Contribution

It introduces a novel self-consistent field model for Bose-Fermi mixtures with delta-like interactions, providing insights into the thermodynamics and phase transition behavior.

Findings

Fermion admixture reduces Bose-Einstein condensation temperature.

Thermodynamic quantities become smoother at the transition with fermions.

Nonanalytic dependence of thermodynamic potential on interaction strength.

Abstract

A self-consistent field model for a mixture of Bose and Fermi particles is formulated. There is explored in detail the case of a delta-like interaction, for which the thermodynamic functions are obtained, and Bose-Einstein condensation of interacting particles in the presence of the admixture of fermions is studied. It is shown that the admixture of Fermi particles leads to reducing of the temperature of Bose-Einstein condensation and smoothing of features of thermodynamic quantities at the transition temperature. As in the case of a pure Bose system, in the state of a mixture with condensate the dependence of the thermodynamic potential on the interaction constant between Bose particles has a nonanalytic character, so that it proves impossible to develop the perturbation theory in the magnitude of interaction of Bose particles.