Non-Meissner electrodynamics and knotted solitons in two-component superconductors

I consider electrodynamics and the problem of knotted solitons in two-component superconductors. Possible existence of knotted solitons in multicomponent superconductors was predicted several years ago. However their basic properties and stability in these systems remains an outstandingly difficult question both for analytical and numerical treatment. Here I propose a new perturbative approach to treat self-consistently all the degrees of freedom in the problem. I show that there exists a length scale for a Hopfion texture where the electrodynamics of a two-component superconductor is dominated by a self-induced Faddeev term, which is a stark contrast to the Meissner electrodynamics of single-component systems. I also show that at certain short length scales knotted solitons in two-component Ginzburg-Landau model are not described by a Faddeev-Skyrme-type model and are unstable. However these solitons can be stable at some intermediate length scales. I argue that configurations with a high topological charge may be more stable in this system than low-topological-charge configurations. In the second part of the paper I discuss qualitatively different physics of the stability of knotted solitons in a more general Ginzburg-Landau model and point out the physically relevant terms which enhance or suppress stability of the knotted solitons. With this argument it is demonstrated that the generalized Ginburg-Landau model possesses stable knotted solitons.Comment: In print in Phys. Rev. B. v2: a typo (missing factor) fixed. v3: discussion of some aspects made more detailed following a referee reques

Solitons, Links and Knots

Using numerical simulations of the full nonlinear equations of motion we investigate topological solitons of a modified O(3) sigma model in three space dimensions, in which the solitons are stabilized by the Hopf charge. We find that for solitons up to charge five the solutions have the structure of closed strings, which become increasingly twisted as the charge increases. However, for higher charge the solutions are more exotic and comprise linked loops and knots. We discuss the structure and formation of these solitons and demonstrate that the key property responsible for producing such a rich variety of solitons is that of string reconnection.Comment: 24 pages plus 14 figures in GIF forma

Knot Solitons

The existence of ring-like and knotted solitons in O(3) non-linear sigma model is analysed. The role of isotopy of knots/links in classifying such solitons is pointed out. Appearance of torus knot solitons is seen.Comment: Latex 9 pages + 2 eps figure

Hopf Soliton Solutions from Low Energy Effective Action of SU(2) Yang-Mills Theory

The Skyrme-Faddeev-Niemi (SFN) model which is an O(3) $\sigma$ model in three dimensional space up to fourth-order in the first derivative is regarded as a low-energy effective theory of SU(2) Yang-Mills theory. One can show from the Wilsonian renormalization group argument that the effective action of Yang-Mills theory recovers the SFN in the infrared region. However, the theory contains another fourth-order term which destabilizes the soliton solution. In this paper we derive an extended action including second derivative terms and obtain soliton solutions numerically. A new topological lower bound formula is infered for the extended action.Comment: 18 pages, 7 figure

Hopf solitons in the Nicole model

The Nicole model is a conformal field theory in a three-dimensional space. It has topological soliton solutions classified by the integer-valued Hopf charge, and all currently known solitons are axially symmetric. A volume-preserving flow is used to construct soliton solutions numerically for all Hopf charges from 1 to 8. It is found that the known axially symmetric solutions are unstable for Hopf charges greater than 2 and new lower energy solutions are obtained that include knots and links. A comparison with the Skyrme–Faddeev model suggests many universal features, though there are some differences in the link types obtained in the two theories

Toroidal Soliton Solutions in O(3)^N Nonlinear Sigma Model

A set of N three component unit scalar fields in (3+1) Minkowski space-time is investigated. The highly nonlinear coupling between them is chosen to omit the scaling instabilities. The multi-soliton static configurations with arbitrary Hopf numbers are found. Moreover, the generalized version of the Vakulenko-Kapitansky inequality is obtained. The possibility of attractive, repulsing and noninteracting channels is discussed.Comment: to be published in Mod. Phys. Lett.

Glueball mass from quantized knot solitons and gauge-invariant gluon mass

We propose an approach which enables one to obtain simultaneously the glueball mass and the gluon mass in the gauge-invariant way to shed new light on the mass gap problem in Yang-Mills theory. First, we point out that the Faddeev (Skyrme--Faddeev-Niemi) model can be induced through the gauge-invariant vacuum condensate of mass dimension two from SU(2) Yang-Mills theory. Second, we obtain the glueball mass spectrum by performing the collective coordinate quantization of the topological knot soliton in the Faddeev model. Third, we demonstrate that a relationship between the glueball mass and the gluon mass is obtained, since the gauge-invariant gluon mass is also induced from the relevant vacuum condensate. Finally, we determine physical values of two parameters in the Faddeev model and give an estimate of the relevant vacuum condensation in Yang-Mills theory. Our results indicate that the Faddeev model can play the role of a low-energy effective theory of the quantum SU(2) Yang-Mills theory.Comment: 17 pages, 2 figures, 3 tables; a version accepted for publication in J. Phys. A: Math. Gen.; Sect. 2 and sect. 5 (old sect. 4) are modified. Sect. 4, Tables 1 and Table 3 are adde

Soliton in Gravitating Gas. Hoag's Object

We explore the possibility of creating of solitons in gravitating gas. It is shown that the virial arguments does not put an obstacle for the existence of localized static solutions. The simplest toroidal soliton of gravitating gas could be the explanation of the peculiar galaxy named Hoag's object.Comment: 14 pages, 1 Figur