Knotted Solitons in a Charged Two-Condensate Bose System

TL;DR

This paper introduces a topological framework for understanding vortex lines and knotted solitons in a charged two-condensate Bose system, revealing their topological charges and invariants using advanced mathematical methods.

Contribution

It presents a novel topological analysis of vortex lines and knotted solitons in a charged two-condensate Bose system using (1) gauge potential decomposition and  mapping techniques.

Findings

Vortex lines characterized by Hopf indices and Brower degrees.

Existence of two classes of knotted solitons with nontrivial Hopf invariants.

Topological charges described by BF action.

Abstract

By making use of the decomposition of U(1) gauge potential theory and the \phi mapping method, we propose that a charged two-condensate Bose system possesses vortex lines and two classes of knotted solitons. The topological charges of the vortex lines are characterized by the Hopf indices and the Brower degrees of \phi-mapping, and the knotted solitons are described by the nontrivial Hopf invariant and the BF action, respectively.