Theoretical confirmation of Feynman's hypothesis on the creation of circular vortices in Bose-Einstein condensates: III.

In two preceding papers (Infeld and Senatorski 2003 J. Phys.: Condens. Matter 15 5865, Senatorski and Infeld 2004 J. Phys.: Condens. Matter 16 6589) the authors confirmed Feynman's hypothesis on how circular vortices can be created from oppositely polarized pairs of linear vortices (first paper), and then gave examples of the creation of several different circular vortices from one linear pair (second paper). Here, in part III, we give two classes of examples of how the vortices can interact. The first confirms the intuition that the reconnection processes which join two interacting vortex lines into one, and thus increase the degree of entanglement of the vortex system, practically do not occur. The second shows that new circular vortices can also be created from pairs of oppositely polarized coaxial circular vortices. This seems to contradict the results for such pairs given in Koplik and Levine (1996 Phys. Rev. Lett. 76 4745).