# The stability of the low-dimensional mixtures of dilute quantum gases

## TL;DR

This paper investigates the stability of dilute Bose-Fermi and Bose-Bose mixtures with repulsive interactions in one and two dimensions using renormalization group analysis, providing stability conditions and critical temperature estimates.

## Contribution

It offers new stability criteria for dilute quantum gas mixtures and calculates the superfluid critical temperature in two dimensions.

## Key findings

- Bose-Fermi mixture is stable against de-mixing in the dilute limit.
- Stability conditions for Bose-Bose mixtures are established in the dilute limit.
- Critical temperature for superfluidity in 2D Bose-Fermi mixture is calculated.

## Abstract

We study the stability of the dilute Bose-Fermi and Bose-Bose mixtures with repulsive interactions in one and two dimensions in terms of the renormalization group. For the Bose-Fermi mixture, we show that the uniform mixture is stable against de-mixing in the dilute limit. For the Bose-Bose mixture, we give the stability conditions in the dilute limit. As a byproduct, we also calculate the critical temperature for the superfluid phase of the two-dimensional Bose-Fermi mixture in the extremely dilute limit.