Vortex motion in trapped Bose–Einstein condensate

We have studied the motion of a vortex-antivortex pair together with a single vortex in trapped Bose-Einstein condensate (BEC) by numerically solving the twodimensional Gross-Pitaevskii equation, and found that the path of the vortices depends on the initial separation distance and dissipation. This motion was periodic and it was found that sound waves appear due to the cyclical movement, whose intensity was stronger when the initial separation distance was smaller. The sound energy was the difference between the kinetic energy and the vortex energy. The simulations was made in inhomogeneous Bose-Einstein condensate without and with dissipation. With no dissipation the vortices followed the same path with a slight oscillation due to the sound waves. From the density plot it was observed that for a smaller initial separation distance d0, the sound production was more intensive, with a rapid change in the density than for larger separation distance. The period, frequency, translation speed and different energies were measured for different initial separation distances d0:s and for different dissipations γ:s. For one vortex the connection between the dissipation γ and the friction coefficients α and α ′ was studied as well. By fitting results, we found the desired connection between the friction coefficients α and α ′ , which have their origin from vortex dynamics and the dissipations γ:s, which have their origin from a model of thermal cloud. In that case we saw how the vortex spiralling out of the condensate. Later, to create turbulence, we put randomly eight pairs of vortex-antivortex in the condensate with initial separation distance d0= 1.800 between them. In that case, we have studied the decay rate of the total energy, kinetic energy, quantum energy, trap energy and the z-component of the angular momentum together with the increase rate of the intern energy. We have finished our investigation about putting randomly vortex-antivortex pairs with a study about the decrease of the number of vortices Nv(t)/Nv(0) with time t and found that the decrease is exponential.