Title: Axial collective mode of a dipolar quantum droplet

Abstract: In this work, we investigate the ground state properties and collective excitations of a dipolar Bose-Einstein condensate that self-binds into a quantum droplet, stabilized by quantum fluctuations. We demonstrate that a sum rule approach can accurately determine the frequency of the low energy axial excitation, using properties of the droplet obtained from the ground state solutions. This excitation corresponds to an oscillation in the length of the filament-shaped droplet. Additionally, we evaluate the static polarizabilities, which quantify change in the droplet dimensions in response to a change in harmonic confinement.