Topological Solitons

Manton, N. S.; Sutcliffe, Paul

doi:10.1017/cbo9780511617034

Cited by 1,498 publications

(2,311 citation statements)

References 0 publications

Supporting

Mentioning

2,208

Contrasting

Unclassified

Order By: Relevance

“…The B = 7 Skyrmion has icosahedral symmetry. This is a beautiful and surprising result mathematically, and consistent with the existence of a BPS monopole, a rational map and an SU (2) instanton, all with topological charge 7 and the same symmetry [44,54] [45]. It is formed by merging a B = 4 and a B = 3 Skyrmion along a common diagonal, preserving C 3 symmetry.…”

Section: The Skyrme Model and Skyrmionssupporting

confidence: 61%

“…The conserved topological charge of the solitons is identified with the physically conserved baryon number, B. The most important solutions are the static solutions of minimal energy for each baryon number, which are known as Skyrmions [44]. These can be in translational or rotational motion, and can rotate in isospace, the internal symmetry space of the three pion fields.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Classical Skyrmions—static solutions and dynamics

Manton

2012

Math Methods in App Sciences

View full text Add to dashboard Cite

Skyrmions with a realistic value of the pion mass parameter are expected to be quite compact structures, but beyond baryon number B = 8 only a few examples are known. The largest of these is the cubically symmetric B = 32 Skyrmion which is a truncated piece of the Skyrme crystal. Here it is proposed that many more such Skyrmions could be found, without any restriction on the baryon number, as pieces of the Skyrme crystal. Particular attention is given to the possibility of reducing B by 1 by chopping a corner off a cubic crystal chunk.Nuclei are modelled by Skyrmions with quantised spin and isospin. Here it is argued that these quantised states can be approximated by classically spinning Skyrmions. The orientations of the spinning Skyrmions corresponding to polarised protons, neutrons and deuterons are identified. Nuclear collisions and the nuclear spin-orbit force are discussed in terms of classically spinning Skyrmions. Going beyond the rigid collective motions of Skyrmions, there are spatially modulated collective motions, which are oscillatory in time. They are argued to describe not just vibrational excitations of nuclei, but also giant resonance states.

show abstract

Section: The Skyrme Model and Skyrmionssupporting

confidence: 61%

Section: Introductionmentioning

confidence: 99%

Classical Skyrmions—static solutions and dynamics

Manton

2012

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…The ansatz for the Higgs field is chosen to be invariant under subgroup of this symmetry which is the SO(2) rotational transformation with a particular choice of U(1) gauge transformation, that cancels the two-dimensional rotation. It is guaranteed that the solutions of the effective equations of motion, derived by using this ansatz, are also the solutions of the full equation of motions [17]. Using these ansatz, the static energy, proportional to the static action, can be simply written as…”

Section: Jhep02(2016)117mentioning

confidence: 99%

“…Now let us see if the vortices have finite energy using the Derrick's Theorem [16,17]. We can write the scaled static energy of (2.3) to be…”

Section: Jhep02(2016)117 4 Static Energymentioning

confidence: 99%

More on Bogomol’nyi equations of three-dimensional generalized Maxwell-Higgs model using on-shell method

Atmaja

Ramadhan

Hora

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

Abstract:We use a recent on-shell method, developed in [1], to construct Bogomol'nyi equations of the three-dimensional generalized Maxwell-Higgs model [2]. The resulting Bogomol'nyi equations are parametrized by a constant C 0 and they can be classified into two types determined by the value of C 0 = 0 and C 0 = 0. We identify that the Bogomol'nyi equations obtained by Bazeia et al. [2] are of the (C 0 = 0)-type Bogomol'nyi equations. We show that the Bogomol'nyi equations of this type do not admit the Prasad-Sommerfield limit in its spectrum. As a resolution, the vacuum energy must be lifted up by adding some constant to the potential. Some possible solutions whose energy equal to the vacuum are discussed briefly. The on-shell method also reveals a new (C 0 = 0)-type Bogomol'nyi equations. This non-zero C 0 is related to a non-trivial function f C 0 defined as a difference between energy density of the scalar potential term and of the gauge kinetic term. It turns out that these Bogomol'nyi equations correspond to vortices with locally non-zero pressures, while their average pressure P remain zero globally by the finite energy constraint.

show abstract

“…The study of kinks (also known as topological solitons [13]) and domain walls in classical and quantum field theories [14,15], in theories of gravity and cosmology [16,17] and even in the nonlinear field theories of fluid * Electronic address: khare@iiserpune.ac.in † Electronic address: christov@lanl.gov ‡ Electronic address: avadh@lanl.gov mechanics [18] remains a topic of active research. Similarly, Ginzburg-Landau theories [19,20] have been very successful in explaining superconducting, superfluid and many other transitions as well as in modeling topological defects (e.g., vortices and domain walls) in a variety of functional materials, through the inclusion of the gradient of the relevant order parameter in the free energy.…”

Section: Introductionmentioning

confidence: 99%

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

2014

View full text Add to dashboard Cite

We obtain exact solutions for kinks in φ 8 , φ 10 and φ 12 field theories with degenerate minima, which can describe a second-order phase transition followed by a first-order one, a succession of two first-order phase transitions and a second-order phase transition followed by two first-order phase transitions, respectively. Such phase transitions are known to occur in ferroelastic and ferroelectric crystals and in meson physics. In particular, we find that the higher-order field theories have kink solutions with algebraically-decaying tails and also asymmetric cases with mixed exponentialalgebraic tail decay, unlike the lower-order φ 4 and φ 6 theories. Additionally, we construct distinct kinks with equal energies in all three field theories considered, and we show the co-existence of up to three distinct kinks (for a φ 12 potential with six degenerate minima). We also summarize phonon dispersion relations for these systems, showing that the higher-order field theories have specific cases in which only nonlinear phonons are allowed. For the φ 10 field theory, which is a quasi-exactly solvable (QES) model akin to φ 6 , we are also able to obtain three analytical solutions for the classical free energy as well as the probability distribution function in the thermodynamic limit.

show abstract

Topological Solitons

Cited by 1,498 publications

References 0 publications

Classical Skyrmions—static solutions and dynamics

Classical Skyrmions—static solutions and dynamics

More on Bogomol’nyi equations of three-dimensional generalized Maxwell-Higgs model using on-shell method

Successive phase transitions and kink solutions inϕ8,ϕ10, andϕ12field theories

Contact Info

Product

Resources

About