Approximate theories for binary magnetic quantum droplets

We develop two approximate theories to describe the miscible and immiscible droplets that can occur in a binary mixture of highly magnetic bosonic atoms. In addition allowing simpler calculations, provide insight into role quantum fluctuations regimes. Results are validated by comparison those from extended Gross-Pitaevskii equation. As an application, we solve for ground-state crossing miscible-immiscible transition as function short-ranged interspecies interaction parameter. consider regimes where occurs suddenly or smooth cross-over. Using dynamical show character is revealed number domains produced when ramping droplet regime.