Bose-Fermi Pairs in a Mixture and the Luttinger Theorem within a Nozieres-Schmitt-Rink like Approach

TL;DR

This paper investigates Bose-Fermi pair correlations at zero temperature using a T-matrix approach, confirming the Luttinger theorem in a homogeneous mixture and relating findings to Fermi polarons.

Contribution

It demonstrates that the Luttinger theorem holds in a Nozieres-Schmitt-Rink like approach for Bose-Fermi mixtures and provides detailed calculations of occupation numbers and condensate depletion.

Findings

Luttinger theorem is respected in the model

Calculated occupation numbers and condensate depletion

Results align with Fermi polaron studies in imbalanced mixtures

Abstract

Bose-Fermion pair correlations in a mixture are considered at zero temperature in the T-matrix approximation. Special attention is paid to the Luttinger theorem. In a strict RPA variant of the Nozieres-Schmitt-Rink approach, it is shown that this theorem is respected also in the homogeneous infinite matter case. We calculate the corresponding occupation numbers of fermions and bosons and the condensate depletion. We also show that in the limit of very small boson density, our results are in good agreement with the results found in the literature for the Fermi polaron in strongly imbalanced Fermi-Fermi mixtures.