O the Theory of Point Vortices in Two-Dimensional Bose Liquids

Harry L. Morrison, Uwe K. Albertin, James Lindesay

V. P. Ruban

The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose–Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a few circulation quanta at each point, has been considered in a hydrodynamic approximation. A special class of density profiles has been chosen, so that it proves possible to calculate analytically the velocity field produced by point vortices. The equations of motion have been given in a noncanonical Hamiltonian form. The theory has been generalized to the case where the condensate forms a curved quasi-two-dimensional shell in the three-dimensional space.

Fanghua Lin, Tai‐Chia Lin

Jiamei Kong, Rukuan Wu

In this paper, we investigate the dynamics of the vortices in the homogeneous two-dimensional Bose–Einstein condensate by considering the condensate density variation. It is shown that the condensate density variation plays an important role when two vortices are close together. By the time-dependent Lagrangian functional method and the numerical simulation, we study how the interaction strength of the vortices varies with the distance between two vortices with the same or different topological charges, and generalize the results for the vortex pairs to the multi-vortex case. The numerical simulations demonstrate the validity of our theory.

Shuxing Chen, Shing–Tung Yau

Ivan Poparić, Leandra Vranješ Markić, Jordi Boronat

Using density functional theory, we have theoretically studied the formation and the stability of vortices in quantum liquid droplets composed of a mixture of hyperfine states of potassium. Following the experimental setup that produced quantum droplets for the first time, we work with squeezed drops that are compressed in one direction. By squeezing the drops even more, toward a quasi-two-dimensional geometry, we study the minimum atom number able to show a stable vortex and obtain that this number is significantly smaller than previous predictions for spherical droplets. The reduction of the critical atom number for forming a stable vortex could make their experimental observation in these droplets, which is still lacking, more feasible. Contrary to results obtained in heteronuclear mixtures, where the energetically preferred vortices are partially filled with the species not participating in the rotation, our results show a relevant stability island of fully empty vortices. Increasing the number of particles in the drop and the speed of rotation, we estimate the transition line between empty and filled vortices.