Dynamics of Vortices in Two-Dimensional Bose-einstein condensates

We derive the asymptotic motion equations of vortices for the time-dependent Gross–Pitaevskii equation with a harmonic trap potential. The asymptotic motion equations form a system of ordinary differential equations which can be regarded as a perturbation of the standard Kirchhoff problem. From the numerical simulation on the asymptotic motion equations, we observe that the bounded and collisionless trajectories of three vortices form chaotic, quasi 2or quasi 3-periodic orbits. Furthermore, a new phenomenon of 1:1-topological synchronization is observed in the chaotic trajectories of two vortices.