Abstract
We investigate how the Rayleigh-Plateau instability of a filament made of a $^{41}\mathrm{K}\text{\ensuremath{-}}^{87}\mathrm{Rb}$ self-bound mixture may lead to an array of identical quantum droplets, with typical breaking times which are shorter than the lifetime of the mixture. If the filament is laterally confined, as it happens in a toroidal trap, and atoms of one species are in excess with respect to the optimal equilibrium ratio, the droplets are immersed into a superfluid background made by the excess species which provides global phase coherence to the system, suggesting that the droplet array in the unbalanced system may display supersolid character. This possibility is investigated by computing the nonclassical translational inertia coefficient. The filament may be a reasonable representation of a self-bound mixture subject to toroidal confinement when the bigger circle radius of the torus is much larger than the filament radius.
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