Broken baby Skyrmions

The baby Skyrme model is a (2+1)-dimensional analogue of the Skyrme model, in which baryons are described by topological solitons. We introduce a version of the baby Skyrme model in which the global O (3) symmetry is broken to the dihedral group D N . It is found that the single soliton in this theory is composed of N partons that are topologically confined. The case N =3 is studied in some detail and multi-soliton solutions are computed and related to polyiamonds, which are plane figures composed of equilateral triangles joined by common edges. It is shown that the solitons may be viewed as pieces of a doubly periodic soliton lattice. It is proved, for a general baby Skyrme model on a general torus, that the condition that the energy of a soliton lattice is critical with respect to variations of the torus is equivalent to the field satisfying a virial relation and being, in a precise sense, conformal on average. An alternative model with D 3 symmetry is also introduced, which has an exact explicit soliton lattice solution. Soliton solutions are computed and compared in the two D 3 theories. Some comments are made regarding the extension of these ideas to the Skyrme model.

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Compactons and topological solitons of the Drinfel'd–Sokolov system

Nonlinear Analysis Modelling and Control ◽

10.15388/na.2014.2.5 ◽

2014 ◽

Vol 19 (2) ◽

pp. 209-224

Author(s):

Mustafa Inc ◽

Eda Fendoglu ◽

Houria Triki ◽

Anjan Biswas

Keyword(s):

Elliptic Function ◽

Function Method ◽

Soliton Solutions ◽

Ansatz Method ◽

Topological Soliton ◽

Topological Solitons ◽

Wave Solutions

This paper presents the Drinfel’d–Sokolov system (shortly D(m, n)) in a detailed fashion. The Jacobi’s elliptic function method is employed to extract the cnoidal and snoidal wave solutions. The compacton and solitary pattern solutions are also retrieved. The ansatz method is applied to extract the topological 1-soliton solutions of the D(m, n) with generalized evolution. There are a couple of constraint conditions that will fall out in order to exist the topological soliton solutions.

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Soliton lattice and single soliton solutions of the associated Lamé and Lamé potentials

Journal of Mathematical Physics ◽

10.1063/1.1738952 ◽

2004 ◽

Vol 45 (6) ◽

pp. 2323-2337 ◽

Cited By ~ 1

Author(s):

Ioana Bena ◽

Avinash Khare ◽

Avadh Saxena

Keyword(s):

Soliton Solutions ◽

Soliton Lattice

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NUCLEI AS SUPERPOSITION OF TOPOLOGICAL SOLITONS

International Journal of Modern Physics E ◽

10.1142/s0218301308009719 ◽

2008 ◽

Vol 17 (01) ◽

pp. 212-216

Author(s):

A. ACUS ◽

E. NORVAIŠAS ◽

D. O RISKA

Keyword(s):

Form Factor ◽

Degrees Of Freedom ◽

Canonical Quantization ◽

Baryon Number ◽

Skyrme Model ◽

Light Nuclei ◽

Electric Form Factor ◽

Fundamental Representation ◽

Rational Map ◽

Topological Solitons

The rational map approximation provides an opportunity to describe light nuclei as classical solitons with baryon number B > 1 in the framework of the Skyrme model. The rational map ansatz yields a possibility of factorization of S3 baryon charge into S1 and S2 parts, the phenomenology of the model being strongly affected by the chosen factorization. Moreover, in the fundamental representation superposition of two different soliton factorizations can be used as solution ansatz. The canonical quantization procedure applied to collective degrees of freedom of the classical soliton leads to anomalous breaking of the chiral symmetry and exponential falloff of the energy density of the soliton at large distance, without explicit symmetry breaking terms included. The evolution of the shape of electric form factor as a function of two different factorization soliton mix ratio is investigated. Numerical results are presented.

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The skyrmion-bubble transition in a ferromagnetic thin film

SciPost Physics ◽

10.21468/scipostphys.4.5.027 ◽

2018 ◽

Vol 4 (5) ◽

Cited By ~ 25

Author(s):

Anne Bernand-Mantel ◽

Lorenzo Camosi ◽

Alexis Wartelle ◽

Nicolas Rougemaille ◽

Michaël Darques ◽

...

Keyword(s):

Magnetic Field ◽

Soliton Solutions ◽

Perpendicular Magnetic Anisotropy ◽

Characteristic Size ◽

Continuous Transformation ◽

Topological Soliton ◽

Topological Solitons ◽

Ferromagnetic Thin Films ◽

Magnetic Skyrmions ◽

The Magnetic Field

Magnetic skyrmions and bubbles, observed in ferromagnetic thin films with perpendicular magnetic anisotropy, are topological solitons which differ by their characteristic size and the balance in the energies at the origin of their stabilisation. However, these two spin textures have the same topology and a continuous transformation between them is allowed. In the present work, we derive an analytical model to explore the skyrmion-bubble transition. We evidence a region in the parameter space where both topological soliton solutions coexist and close to which transformations between skyrmion and bubbles are observed as a function of the magnetic field. Above a critical point, at which the energy barrier separating both solutions vanishes, only one topological soliton solution remains, which size can be continuously tuned from micrometer to nanometer with applied magnetic field.

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Coordinating Visual and Analytic Strategies: A Study of Students' Understanding of the Group D4

Journal for Research in Mathematics Education ◽

10.5951/jresematheduc.27.4.0435 ◽

1996 ◽

Vol 27 (4) ◽

pp. 435-457

Author(s):

Rina Zazkis ◽

Ed Dubinsky ◽

Jennie Dautermann

Keyword(s):

Alternative Model ◽

Dihedral Group ◽

Classification Scheme ◽

Mathematical Thinking ◽

Mathematical Problem ◽

Mathematical Problem Solving ◽

Analytic Thinking ◽

Clinical Interviews ◽

Visual Approach ◽

Group D

This study contributes to the ongoing discussion of visualization and analysis in mathematical thinking. On the basis of data gathered from clinical interviews with 32 students in their first abstract algebra course, we consider the tasks of listing the elements of the dihedral group D4 and finding the product of two such elements. These problems can be solved either using a “visual” approach of transforming a square or an “analytic” approach of multiplying permutations. Rather than clearly preferring either a visual or analytic strategy, most students in our study used some combination of these approaches. Our results suggest that the conventional analyzer/visualizer dichotomy may not be an appropriate classification scheme for describing learning processes or for designing instruction. We propose an alternative model, the Visualizer/Analyzer or VA model, that assumes visualization and analysis to be mutually dependent in mathematical problem solving, rather than unrelated opposites. Our model provides one description of how this mutual dependence might function. We end by considering how pedagogical approaches might be designed in consonance with this model to help students coordinate visual and analytic thinking.

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MULTIBARYON SOLUTIONS OF A CHIRAL QUARK-MESON MODEL

International Journal of Modern Physics E ◽

10.1142/s0218301394000206 ◽

1994 ◽

Vol 03 (02) ◽

pp. 769-782 ◽

Cited By ~ 4

Author(s):

J. SEGAR ◽

M. SRIPRIYA ◽

M.S. SRIRAM

Keyword(s):

Soliton Solutions ◽

Skyrme Model ◽

Energy Distributions ◽

Model Calculations ◽

Soliton Model ◽

Nucleon Potential ◽

Model Based ◽

Cylindrically Symmetric ◽

Fixed Distance ◽

Energy Of Interaction

We consider multibaryon configurations in a SU(2) quark soliton model based on chiral invariant quark-meson couplings. We compute the energy of interaction between two nucleons by considering configurations which correspond to two B=1 solitons separated by a fixed distance. The gross features of the inter-nucleon potential are reproduced. We also find cylindrically symmetric, classically stable soliton solutions with B=2, 3 and 4. The energy distributions corresponding to these solutions are toroidal in nature. The results closely parallel the Skyrme-model calculations.

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Neutron stars within the Skyrme model

International Journal of Modern Physics E ◽

10.1142/s0218301319300066 ◽

2019 ◽

Vol 28 (08) ◽

pp. 1930006 ◽

Cited By ~ 2

Author(s):

Carlos Naya

Keyword(s):

Neutron Stars ◽

Effective Field Theory ◽

Lower Energy ◽

Degrees Of Freedom ◽

Effective Field ◽

Skyrme Model ◽

Collective Excitations ◽

Strong Interactions ◽

Topological Solitons ◽

Energy Bounds

The Skyrme model is a low energy effective field theory of strong interactions where nuclei and baryons appear as collective excitations of pionic degrees of freedom. In the last years, there has been a revival of Skyrme’s ideas and new related models, and some of them with BPS bounds (topological lower energy bounds) have been proposed. It is the aim of this paper to review how they can be applied to the study of neutron stars allowing for a description by means of topological solitons. We will focus on different aspects as the equation of state or the mass-radius relation, where we find that high maximal masses are supported.

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Gravitating Meron-like topological solitons in massive Yang–Mills theory and the Einstein–Skyrme model

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09444-7 ◽

2021 ◽

Vol 81 (7) ◽

Author(s):

Marcelo Ipinza ◽

Patricio Salgado-Rebolledo

Keyword(s):

Direct Product ◽

Skyrme Model ◽

Group Element ◽

Ricci Scalar ◽

Einstein Equations ◽

Lorentzian Manifolds ◽

Topological Solitons ◽

Yang Mills ◽

Mills Field ◽

Gauge Connection

AbstractWe show that Merons in D-dimensional Einstein–Massive–Yang–Mills theory can be mapped to solutions of the Einstein–Skyrme model. The identification of the solutions relies on the fact that, when considering the Meron ansatz for the gauge connection $$A=\lambda U^{-1}dU$$ A = λ U - 1 d U , the massive Yang–Mills equations reduce to the Skyrme equations for the corresponding group element U. In the same way, the energy–momentum tensors of both theories can be identified and therefore lead to the same Einstein equations. Subsequently, we focus on the SU(2) case and show that introducing a mass for the Yang–Mills field restricts Merons to live on geometries given by the direct product of $$S^3$$ S 3 (or $$S^2$$ S 2 ) and Lorentzian manifolds with constant Ricci scalar. We construct explicit examples for $$D=4$$ D = 4 and $$D=5$$ D = 5 . Finally, we comment on possible generalisations.

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