Stationary ring solitons in field theory - knots and vortons
By Eugen Radu, M. Volkov. 2008
167 citations recorded by the source corpus.
We review the current status of the problem of constructing classical field theory solutions describing stationary vortex rings in Minkowski space in 3+1 dimensions. We describe the known up to date solutions of this type, such as the static knot solitons stabilized by the topological Hopf charge, the attempts to gauge them, the anomalous solitons stabilized by the Chern-Simons number, as well as the non-Abelian monopole and sphaleron rings. Passing to the rotating solutions, we first discuss the conditions insuring that they do not radiate, and then describe the spinning $Q$-balls, their twisted and gauged generalizations reported here for the first time, spinning skyrmions, and rotating monopole-antimonopole pairs. We then present the first explicit construction of global vortons as solutions of the elliptic boundary value problem, which demonstrates their non-radiating character. Finally, we describe the analogs of vortons in the Bose-Einstein condensates, analogs of spinning $Q$-balls in the non-linear optics, and also moving vortex rings in superfluid helium and in ferromagnetics.
Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/13f3d11a8413d487a75fee6b710cca5b89e4afd7
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In Astronomy and Astrophysics
In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- (INVITED) Vortex solitons: Old results and new perspectives (2019, background): “In addition to physics of nuclear matter and the classical field theory, which are the origin of the Skyrme model and diverse 3D states generated by it [30–32, 43–45], these complex 3D modes find important realizations in ferromagnets [46, 47], semiconductors [37, 38], superconductors [42], and in v”
- Tying quantum knots (2015, background): “This ring is surrounded by an infinite number of similar rings, each linked with all of the others to generate a knotted field structure [22].”
- A new form of liquid matter: Quantum droplets (2020, background): “On the one hand, 2D and 3D solitons offer many options inaccessible in 1D – in particular, the creation of 2D and 3D self-trapped states with the topological charge, that represents intrinsic vorticity [5], and more sophisticated 3D states, such as monopoles [6], skyrmions or hopfions with two indep”