Suppression of capillary instability in a confined quantum liquid filament

Quantum Bose-Bose mixtures with large interspecies attraction can form self-bound, liquid-like droplets stabilized by quantum fluctuations. Despite equilibrium densities much lower than those of classical liquids, these droplets exhibit finite surface tension and liquid-like behaviors. Recent experiments have demonstrated Rayleigh-Plateau instability (a paradigmatic example of capillary instability) in elongated droplets confined in an optical waveguide. Here, we consider the case of an infinite filament and extend the theoretical description to include transverse harmonic confinement. By solving the Bogoliubov-de Gennes equations within a single-component framework, benchmarked against full Gross-Pitaevskii simulations, we show that increasing confinement progressively suppresses the instability, leading to complete stabilization beyond a critical trap frequency.