One dimensional Quantum Droplets under the effect of curved space-time

In this paper, we study quantum droplets in one dimension under the influence of space-time curvature by redefining the momentum operator ˆ P = −i(1 +αx^2)∂/∂x, resulting in a maximum length and a minimum momentum, consistent with anti-de Sitter space (AdS). By analyzing this effect through the α parameter on the exact solution of free quantum droplets, we find that the relationship between the number of atoms and the chemical potential deviates from the ordinary case. Additionally, we observe that the characteristic f lat-top shape of quantum droplets can disappear, transforming into a Gaussian profile in the presence of the maximum length (minimum momentum). Furthermore, our findings reveal that the interaction of quantum droplets with space-time curvature results in an increase in their size. Finally, by studying this effect on the variational solution using a Gaussian ansatz for small droplets, we conclude that α reduces the stability and self-localization of the quantum droplets.