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.

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.