Revisiting a stability problem of two-component droplets

TL;DR

This paper revisits the stability of two-component droplets, providing a more general analysis that accounts for arbitrary energy densities and physical constraints, revealing limitations on component densities.

Contribution

It offers a comprehensive stability analysis for two-component droplets beyond the standard mean field approach, including approximate solutions for Bose-Bose droplets.

Findings

Component densities are limited by interaction strength.

The stability range differs from the standard solution.

Generalized analysis applies to arbitrary energy densities.

Abstract

We study the problem of the stability of a two-component droplet. The standard solution known from the literature is based on a particular form of the mean field energy functional, in particular on distinction of hard mode and soft mode contributions. By imposing the constraint on densities of the two species which minimizes the hard mode energy, the problem is reduced to a stability analysis of a one component system. As opposed to this, we address the issue in full generality. Our analysis is valid for arbitrary forms of energy density. We formulate constraints which correspond to the physically relevant situation of a system which has unconstrained volume and may evaporate particles. For the specific case of a two component Bose-Bose droplet we find approximate analytic solutions and compare them to the standard result. We show that the densities of both components of a stable droplet are limited to a range depending on interaction strength, in contrast to the original unique solution.