Three-Dimensional Skyrmions with Arbitrary Topological Number in a Ferromagnetic Spin-1 Bose-Einstein Condensate

We propose a new scheme for creating three-dimensional Skyrmions in a ferromagnetic spin-1 Bose-Einstein condensate by manipulating a multipole magnetic field and a pair of counter-propagating laser beams. The result shows that a three-dimensional Skyrmion with topological number Q = 2 can be created by a sextupole magnetic field and the laser beams. Meanwhile, the vortex ring and knot structure in the Skyrmion are found. The topological number can be calculated analytically in our model, which implies that the method can be extended to create Skyrmions with arbitrary topological number. As the examples, three-dimensional Skyrmions with Q = 3, 4 are also demonstrated and are distinguishable by the density distributions with a specific quantization axis. These topological objects have the potential to be realized in ferromagnetic spin-1 Bose-Einstein condensates experimentally.

QUANTUM STATE OF A FREE SPIN-½ PARTICLE AND THE INEXTRICABLE DEPENDENCE OF SPIN AND MOMENTUM UNDER LORENTZ TRANSFORMATIONS

We revise the Dirac equation for a free particle and investigate Lorentz transformations on spinors. We study how the spin quantization axis changes under Lorentz transformations, and evince the interplay between spin and momentum in this context.

HYPERON POLARIZATION IN QUARK-DIQUARK CASCADE MODEL

We relate the hyperon polarizations in proton-proton and proton-nucleus collisions to the leading particle effect and use the constituent quark-diquark cascade model with SU(6) wave function. We assume that the quantization axis is characterized by the production normal of the leading baryon of the most massive cascade chain and the incident valence diquark tends to pick up a spin down sea quark or conversely a sea diquark preferentially combines with the spin up incident valence quark to form a leading baryon as compared with the spin down valence quark.