  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.
