Exact Vortex Clusters of Two-Dimensional Quantum Fluid with Harmonic Confinement

A family of exact analytical solutions of vortices in quantum fluid governed by a two-dimensional time-dependent Schr?dinger equation is presented, which describes different kinds of vortex structures. The dynamics of different vortex clusters, such as the single vortex, vortex pair, vortex dipole and vortex trimer in a two-dimensional quantum fluid are analytically studied based on these exact solutions. The time evolutions of the wave of such vortices are demonstrated, and the orbits of motion of singular points in the vortices are also explored. The interactions of vortices in many-vortex clusters are discussed. A repulsive interaction between vortices with the same topological charge, and inter-annihilation and inter-creation of vortices with opposite topological charge, are shown.