Equation of Motion of a Quantum Vortex.

Iwo Białynicki‐Birula, Zofia Białynicka-Birula, Cezary Śliwa

Exact analytic solutions of the time-dependent Schr\"odinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are identified. Vortex creation and annihilation and vortex interactions are illustrated in the special cases of the free motion, the motion in the harmonic potential, and in the constant magnetic field. Similar analysis of the vortex motions is carried out also for a relativistic wave equation.

Lara Thompson, Philip C. E. Stamp

Richard J. Creswick, Harry L. Morrison

Sergey K. Nemirovskii

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.

Andreas J. Wallraff, Alexander V. Lukashenko, Jürgen Lisenfeld +4 more

T. Winiecki, Charles S. Adams

We simulate the motion of a massive object through a dilute Bose-Einstein condensate by numerical solution of the Gross-Pitaevskii equation coupled to an equation of motion for the object. Under a constant applied force, the object accelerates up to a maximum velocity where a vortex ring is formed which slows the object down. If the applied force is less than a critical value, the object becomes trapped within the vortex core. We show that the motion follows the time-independent solutions, and use these solutions to predict the conditions required for vortex detachment.