Faddeev-Hopf knots: Dynamics of linked un-knots

Abstract

We have studied numerically Faddeev-Hopf knots, which are defined as those unit-vector fields in $R^3$ that have a nontrivial Hopf charge and minimize Faddeev's Lagrangian. A given initial configuration was allowed to relax into a (local) minimum using the first order dissipative dynamics corresponding to the steepest descent method. A linked combination of two un-knots was seen to relax into different minimum energy configurations depending on their charges and their relative handedness and direction. In order to visualize the results we plot certain gauge-invariant iso-surfaces.

11 pages with 6 figures (3 in color)

References in corpus (1)

• To be or knot to be?

Cited by in corpus (94)

• Hidden symmetry and knot solitons in a charged two-condensate Bose system
• Stationary ring solitons in field theory - knots and vortons
• Skyrmion knots in frustrated magnets
• Hopfions in chiral magnets
• Current-Driven Dynamics of Magnetic Hopfions
• Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions
• Dual neutral variables and knot solitons in triplet superconductors
• Topological Transformation and Free-Space Transport of Photonic Hopfions
• Exact static soliton solutions of 3+1 dimensional integrable theory with nonzero Hopf numbers
• Three-dimensional dynamics of magnetic hopfion driven by spin transfer torque
• Aspects of Electric and Magnetic Variables in SU(2) Yang-Mills Theory
• Knots in the Skyrme-Faddeev model
• Spin-Charge Separation, Conformal Covariance and the SU(2) Yang-Mills Theory
• Glueballs, closed fluxtubes and eta(1440)
• Magnetic Geometry and the Confinement of Electrically Conducting Plasmas
• Non-Meissner electrodynamics and knotted solitons in two-component superconductors
• Optical excitations of Skyrmions, knotted solitons, and defects in atoms
• The Interaction of Two Hopf Solitons
• Andreev-Bashkin effect and knot solitons in interacting mixture of a charged and a neutral superfuids with possible releveance for neutron stars
• Sphalerons in the Skyrme model
• A model of glueballs
• Exact vortex solutions in a CP^N Skyrme-Faddeev type model
• Relaxation of twisted vortices in the Faddeev-Skyrme model
• Fermionic quantization of Hopf solitons
• Estimation of the Lin-Yang bound of the least static energy of the Faddeev model
• Unwinding in Hopfion vortex bunches
• Glueball mass from quantized knot solitons and gauge-invariant gluon mass
• Classically Isospinning Hopf Solitons
• Investigation of the stability of Hopfions in the two-component Ginzburg-Landau model
• A Skyrme-like model with an exact BPS bound
• Formation and Controlling of Optical Hopfions in High Harmonic Generation
• Knots in interaction
• Compact Q-balls and Q-shells in the CPN type models
• Kelvin knots in superconducting state
• Toroidal Solitons in Nicole-type Models
• Scattering of knotted vortices (Hopfions) in the Faddeev-Skyrme model
• The tight knot spectrum in QCD
• T-Duality for Coset Models
• On a low energy bound in a class of chiral field theories with solitons
• Stabilizing textures with magnetic fields
• Hopf solitons and elastic rods
• Integrability and Hopf Solitons in Models with Explicitly Broken O(3) Symmetry
• Generalized Eikonal Knots and New Integrable Dynamical Systems
• Hopf solitons and Hopf Q-balls on S^3
• Hopfion Dynamics in Chiral Magnets
• Aspects of Duality and Confining Strings
• Vortices in the extended Skyrme-Faddeev model
• Instantons, Monopoles and the Flux Quantization in the Faddeev-Niemi Decomposition
• $SU(3)$ Knot Solitons: Hopfions in the $F_2$ Skyrme-Faddeev-Niemi model
• Emergent magnetic field and vector potential of the toroidal magnetic hopfions
• Skyrmions and Faddeev-Hopf Solitons
• Static Hopfions in the extended Skyrme-Faddeev model
• Potentials and the vortex solutions in the $C{P}^N$ Skyrme-Faddeev model
• Elliptic solutions of the Skyrme model
• Energy Bounds of Linked Vortex States
• Some properties of (3+1) dimensional vortex solutions in the extended CP^N Skyrme-Faddeev model
• Leapfrogging vortex rings in the Landau-Lifshitz equation
• Class of exact solutions of the Skyrme and the Faddeev model
• Hopf solitons in the Nicole model
• Infrared Yang-Mills theory as a spin system. A lattice approach
• Exploring instantons with spin-lattice systems
• Effective sigma models and lattice Ward identities
• Fractional Hopfions in the Faddeev-Skyrme model with a symmetry breaking potential
• Approximate vortex solution of Faddeev model
• Hopfions interaction from the viewpoint of the product ansatz
• Cabling in the Skyrme-Faddeev model
• Magnetic Hopfions in the Faddeev-Skyrme-Maxwell model
• Emergent Magnetic Field and Nonzero Gyrovector of the Toroidal Magnetic Hopfion
• Strongly coupled Skyrme-Faddeev-Niemi hopfions
• Hopf Solitons from Instanton Holonomy
• Reduction of static field equation of Faddeev model
• Generalized Skyrme Crystals
• Stability of topological solitons in modified two-component Ginzburg-Landau model
• Hopf Soliton Solutions from Low Energy Effective Action of SU(2) Yang-Mills Theory
• Knotted Configurations with Arbitrary Hopf Index from the Eikonal Equation
• Twisted Vortices in a Gauge Field Theory
• A first integration of some knot soliton models
• Topological interfaces crossed by defects and textures of continuous and discrete point group symmetries in spin-2 Bose-Einstein condensates
• Collective coordinate quantization and spin statistics of the solitons in the $\mathbb{C}{P}^N$ Skyrme-Faddeev model
• Converting Classical Theories to Quantum Theories by Solutions of the Hamilton-Jacobi Equation
• Chirality and fermion number in a knotted soliton background
• Nonlinear sigma models solvable by the Aratyn-Ferreira-Zimerman ansatz
• Topological transition from a hopfion to a toron via flexoelectric self-polarization in chiral liquid crystals
• Non-abelian color dielectric - towards the effective model of the low energy QCD
• Structures of Order Parameters in Inhomogeneous Phase States of Strongly Correlated Systems
• Hopf Solitons on the Lattice
• Waves in the Skyrme--Faddeev model and integrable reductions
• Skyrme-Faddeev model from 5d super-Yang-Mills
• Nontrivial Causal Structures Engendered by Knotted Solitons
• Knot solitons in modified Ginzburg-Landau model
• New Faddeev-Niemi type variables for static SU(3) Yang-Mills theory
• Some vortex solutions in the extended Skyrme-Faddeev model
• Soliton solutions in an effective action for SU(2) Yang-Mills theory: including effects of higher-derivative term
• Solitonic solutions of Faddeev model