Abstract
We introduce a variation of the Bose-Einstein condensate(BEC)-Skyrme model, with an altered potential for miscible BECs that gives rise to two physical vortex strings. In the ground state of each topological sector, the vortices are linked exactly $B$ times, due to a recently formulated theorem, with $B$ being the baryon number of the solution. The model also possesses metastable states, where the vortices are degenerate and do not lend the interpretation of the baryon number as the linking number of the vortices.
Highlights
More than a century ago, Lord Kelvin imagined that atoms were made of knotted vortices [1], but this idea has not been successful so far
In Refs. [22,23,24] we introduced a potential inspired by twocomponent Bose-Einstein condensates (BECs), V ∼ M2jφ1j2jφ2j2, which deforms the Skyrmions into a twisted vortex ring by explicitly breaking the SU(2) isospin symmetry normally possessed by Skyrmion solutions
We have considered the miscible BECSkyrme model, which is the generalized Skyrme model with fourth-order and sixth-order derivative terms augmented by the BEC-inspired potential, but with the opposite overall sign of the potential compared with the previously considered immiscible BEC-Skyrme model
Summary
More than a century ago, Lord Kelvin imagined that atoms were made of knotted vortices [1], but this idea has not been successful so far. [2] we have circumvented the issue by introducing a rotation of the 2-sphere, making it possible to find points which are regular and giving rise to nondegenerate vortices that provide the linking number Q 1⁄4 B. One may consider such a rotation a bit arbitrary and wonder about the physical implication thereof. This notion takes a very physical form in the presence of the miscible BEC-inspired potential, as the degenerate vortex links generally give rise to higher-energy (metastable) states and the nondegenerate vortex links yield stable (ground) states.
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