# Comprehensive classification for Bose-Fermi mixtures

## TL;DR

This paper analytically classifies all possible ground states of a zero-temperature boson-fermion mixture, revealing various density configurations and stability conditions for different interaction regimes.

## Contribution

It provides a comprehensive analytical framework for classifying ground states of Bose-Fermi mixtures, including stability and density shape conditions, applicable to binary bosonic mixtures.

## Key findings

- Derived analytic conditions for density configurations under various interactions.
- Proved all configurations are energy minima.
- Provided a full classification of ground states in the interpenetrative regime.

## Abstract

We present analytical studies of a boson-fermion mixture at zero temperature with spin-polarized fermions. Using the Thomas-Fermi approximation for bosons and the local-density approximation for fermions, we find a large variety of different density shapes. In the case of continuous density, we obtain analytic conditions for each configuration for attractive as well as repulsive boson-fermion interaction. Furthermore, we analytically show that all the scenarios we describe are minima of the grand-canonical energy functional. Finally, we provide a full classification of all possible ground states in the interpenetrative regime. Our results also apply to binary mixtures of bosons.