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 2- or quasi 3-periodic orbits. Furthermore, a new phenomenon of 1:1-topological synchronization is observed in the chaotic trajectories of two vortices.
|Number of pages||26|
|Journal||International Journal of Bifurcation and Chaos in Applied Sciences and Engineering|
|State||Published - 1 Jan 2002|
- Bose-Einstein condensates
- Topological synchronization