Collision and coalescence dynamics of bosonic quantum Hall droplets

Recently bosonic quantum Hall droplets have been observed in rapidly rotating two-dimensional Bose-Einstein condensates (BECs), which exhibit robust dynamical stability. Inspired by this, we systematically investigate the collision and coalescence dynamics of these droplets within the Gross-Pitaevskii framework. For two-droplet collisions, we find two distinct collision outcomes, namely merging and separation, that are controlled by the initial relative velocity. The critical velocity exhibits a universal scaling law with the interaction and the particle number as $v_c \propto (gN)^{1/4}$, which can be interpreted from a simplified analytical model, revealing the essential role of the collision time. It differs fundamentally from the mechanism governing the conventional Lee-Huang-Yang stabilized quantum droplets. Furthermore, while the collision can change the shape of the droplet significantly, the center of mass trajectory remains nearly unaffected, owing to the conservation of angular momentum. For overlapping stationary droplets, vortex arrays can emerge through Kelvin-Helmholtz instability driven by phase-induced shear flow. Although two droplets may merge into a larger one, extended states cannot be constructed from multiple overlapping droplets. Instead, the system dynamically reorganizes into new isolated droplets, revealing the localized property in the bulk region. Our results reveal the unique nonequilibrium dynamics of quantum Hall droplets and suggest new pathways for manipulating strongly correlated rotating quantum fluids.