Hyperspherical approach to dipolar Bose-Einstein condensates

Recently a number of interesting phenomena have been observed in ultracold dipolar Bose gasses, such as droplets and supersolids. Typical theoretical descriptions of dipolar Bose-Einstein condensates (BECs) require use of the nonlinear Gross-Pitaevskii equation. Here we apply a hyperspherical approach to dipolar BECs, giving an entirely linear 2D Schrodinger equation. We use this to generate excited states of dipolar droplets and pancakes, and explore dynamics in this linear regime. We additionally show a general correspondence between hyperspherical methods and the Gaussian ansatz to the Gross-Pitaevskii equation in the limit of a large number of particles.