Composite structure of vortices in two-component Bose-Einstein condensate

In contrast to one-component Bose-Einstein condensate case, the vortices in two-component condensate can have various complicated structures. The vortices in a space-homogeneous Bose-Einstein condensate have been studied in this paper. It is shown that the vortex structure is described by three dimensionless parameters. This is totally different from the usual one-component condensate case, where an isolated vortex is described by a parameter-less dimensionless equation. The two-component vortex structure strongly depends on the sign of "interaction" constant of the components. A few types of vortices with different qualitative structure are explored. We show that the super-density vortices can exist, when the "interaction" constant is positive. The super-density vortices have the near-axis density greater than the equilibrium density of a homogeneous space Bose-Einstein condensate. We also show that the vortices with opposite direction of the condensate component rotation near the axis and far off the axis can exist.Comment: LaTeX, 13 pages, 4 figures, UJP styl

On Properties of the Intrinsic Geometry of Submanifolds in a Riemannian Manifold

In the paper we study the properties of a metric function which is the extension by continuity of the intrinsic metric of the interior of a submanifold to its boundary. This approach is the development of the classical intrinsic geometry of surfaces studied by A.D. Alexandrov and his school