Dragging a defect in a droplet Bose-Einstein condensate

In the present work we consider models of quantum droplets within a weakly interacting mass-balanced binary Bose-Bose mixture in the presence of a defect in the form of a laser beam moving through the respective condensates including the Lee-Huang-Yang correction. Our analysis features separately an exploration of the existence, stability, bifurcations, and dynamics in one-, two-, and three-dimensional settings. In the absence of an explicit solution of the problem, we provide an analysis of the speed of sound and observe how the states traveling with the defect may feature a saddle-center bifurcation as the speed or the strength of the defect is modified. Relevant bifurcation diagrams are constructed systematically and the unstable states, as well as the dynamics past the existence of stable states, are monitored. The connection of the resulting states with dark solitonic patterns in one dimension, vortical states in two dimensions, and vortex rings in three dimensions is accordingly elucidated.