Hyperbolic Bending of Vortex Lines with Finite Number and Length in Rotating Trapped Bose--Einstein Condensates

The minimal energy configurations of hyperbolic bending vortex lines in the rotating trapped Bose--Einstein condensates are investigated by using a variational ansatz and numerical simulation. The theoretical calculation of the energy of the vortex lines as a function of the rotation frequency gives self-consistently vortex number, curvature and configuration. The numerical results show that bending is more stable than straight vortex line along the z-axis, and the vortex configuration in the xy-plane has a little expansion by increasing z.