Variational model for vortex quantum droplets

Quantum droplets represent a novel state of matter achieved by tailoring a binary Bose–Einstein condensate, where the collapse driven by self-attraction is arrested by quantum effects. This opens the possibility of producing interesting novel physical phenomena, which require accurate mathematical models for its correct description. In this work, we apply variational procedures to the mean field equation governing two-dimensional symmetric quantum droplets, to find simple yet very precise formulae for the droplet profile and the relationships between its main parameters, such as internal and external radii of the bright rings, the chemical potential or the number of atoms of the droplets. The comparison with direct numerical calculations demonstrates that our model provides a highly accurate description of the self-trapped eigenstates with flat-top profiles. These results should aid in the exploration of additional effects in liquid-like solitons and vortex states endowed with angular momentum.