Quantum vortices in the Bose–Einstein condensate. Reconnection and motion equations

The paper describes several features of vortex filaments in a weakly non-ideal Bose-Einstein condensate (BEC) with a counterflow. The study focuses on a process of reconnection and equations of motion. A primary motivation of this study is a fact that quantum vortex dynamics for superfluid helium was obtained previously at a phenomenological level. But some critical problems can be solved through a study of a corresponding problem in BEC. By considering a vortex filament as a crossing line for surfaces where the real and imaginary parts of a macroscopic wave function ψ ( r , t ) turn into zero, we derived the equations of motion for a vortex filament. It is remarkable that the equation structure coincides completely with a structure of equation for vortex filament dynamics in superfluid helium that has been obtained from other (phenomenological) foundations.