# Supercurrent coupling destabilizes knot solitons

@article{Speight2011SupercurrentCD, title={Supercurrent coupling destabilizes knot solitons}, author={James Martin Speight and Juha Jaykka}, journal={Physical Review D}, year={2011}, volume={84}, pages={125035} }

In an influential paper of 2002, Babaev, Faddeev and Niemi conjectured that two-component Ginzburg-Landau (TCGL) theory in three dimensions should support knot solitons, where the projective equivalence class of the pair of complex condensate fields [psi_1,psi_2]:R^3 -> CP^1 has non-zero Hopf degree. The conjecture was motivated by a certain truncation of the TCGL model which reduced it to the Faddeev-Skyrme model, long known to support knot solitons. Physically, the truncation amounts to…

## 6 Citations

### Isospinning hopfions

- Physics
- 2013

The problem of constructing internally rotating solitons of fixed angular frequency ω in the Faddeev–Skyrme model is reformulated as a variational problem for an energy-like functional, called…

### Stable Hopf-Skyrme topological excitations in the superconducting state

- PhysicsPhysical Review B
- 2019

At large scales, magnetostatics of superconductors is described by a massive vector field theory: the London model. The magnetic field cannot penetrate into the bulk unless quantum vortices are…

### Skyrmions and Hopfions in 3D Frustrated Magnets

- Physics
- 2021

A model of an inversion-symmetric frustrated spin system is introduced which hosts three-dimensional extensions of magnetic Skyrmions. In the continuum approximation this model reduces to a…

### Kelvin knots in superconducting state

- Physics
- 2018

The failed “vortex-atoms” theory of matter by Kelvin and Tait [1, 2] had a profound impact on mathematics and physics. Building on the under-standing of vorticity by Helmholtz, and observ-ing…

### Dynamics of dipoles and vortices in nonlinearly coupled three-dimensional field oscillators.

- PhysicsPhysical review. E
- 2016

The dynamics of a pair of harmonic oscillators represented by three-dimensional fields coupled with a repulsive cubic nonlinearity is investigated through direct simulations of the respective field…

## References

SHOWING 1-10 OF 19 REFERENCES

### Topologically nontrivial configurations associated with Hopf charges investigated in the two-component Ginzburg-Landau model

- Physics, Mathematics
- 2008

We study the stability of Hopfions embedded in the Ginzburg-Landau (GL) model of two oppositely charged components. It has been shown by Babaev et al. [Phys. Rev. B 65, 100512 (2002)] that this model…

### Investigation of the stability of Hopfions in the two-component Ginzburg-Landau model

- Physics, Mathematics
- 2006

We study the stability of Hopﬁons embedded in the Ginzburg-Landau (GL) model of two oppositely charged components. It has been shown by Babaev et al. [Phys. Rev. B 65 , 100512 (2002)] that this model…

### Knots in the Skyrme–Faddeev model

- PhysicsProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2007

The Skyrme–Faddeev model is a modified sigma model in three-dimensional space, which has string-like topological solitons classified by the integer-valued Hopf charge. Numerical simulations are…

### Stability of topological solitons in modified two-component Ginzburg-Landau model

- Physics, Mathematics
- 2009

We study the stability of Hopfions embedded in a certain modification Ginzburg-Landau model of two equally charged condensates. It has been shown by Ward [Phys. Rev. D66, 041701(R) (2002)] that…

### Stabilizing textures with magnetic fields

- Physics
- 2002

The best-known way of stabilizing textures is by Skyrme-like terms, but another possibility is to use gauge fields. The semilocal vortex may be viewed as an example of this, in two spatial…

### Hidden symmetry and knot solitons in a charged two-condensate Bose system

- Physics
- 2002

We show that a charged two-condensate Ginzburg-Landau model or equivalently a Gross-Pitaevskii functional for two charged Bose condensates, can be mapped onto a version of the nonlinear O(3) sigma ...

### Ground state in the Faddeev-Skyrme model

- Physics
- 2000

Helsinki Institute of Physics and Laboratory of Physics, Helsinki University of Technology, P.O. Box 1100, FIN-02015 HUT,Espoo, Finland~Received 4 January 2000; published 18 September 2000!New…

### Stable skyrmions in two-component Bose-Einstein condensates.

- PhysicsPhysical review letters
- 2002

It is shown that stable Skyrmions exist in two-component atomic Bose-Einstein condensates, in the regime of phase separation, and the salient features of an experimental setup in which they might realized are suggested.