Broken baby Skyrmions

Jäykkä, Juha; Speight, J.M.; Sutcliffe, Paul

doi:10.1098/rspa.2011.0543

Cited by 40 publications

(28 citation statements)

References 23 publications

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“…To overcome the computational difficulties and learn something about the electromagnetic properties of BPS Skyrme type solitons, one can analyze lower-dimensional analogs, as has been done successfully already in many occasions. In fact, there exists a (2 + 1) dimensional version of the Skyrme model, usually referred to as the baby Skyrme model, which supports solitonic solutions (baby skyrmions) [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38] (for the gauged version see [39,40]). This field theory also possesses its BPS limit, whose Lagrangian consists of the (2+1) dimensional version of the Skyrme term and a potential [41][42][43].…”

Section: Jhep11(2014)095mentioning

confidence: 99%

Magnetothermodynamics of BPS baby skyrmions

Adam

Romańczukiewicz

Sánchez-Guillén

et al. 2014

J. High Energ. Phys.

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The magnetothermodynamics of skyrmion type matter described by the gauged BPS baby Skyrme model at zero temperature is investigated. We prove that the BPS property of the model is preserved also for boundary conditions corresponding to an asymptotically constant magnetic field. The BPS bound and the corresponding BPS equations saturating the bound are found. Further, we show that one may introduce pressure in the gauged model by a redefinition of the superpotential. Interestingly, this is related to non-extremal type solutions in the so-called fake supersymmetry method. Finally, we compute the equation of state of magnetized BSP baby skyrmions inserted into an external constant magnetic field H and under external pressure P , i.e., V = V (P, H), where V is the "volume" (area) occupied by the skyrmions. We show that the BPS baby skyrmions form a ferromagnetic medium.

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Section: Jhep11(2014)095mentioning

confidence: 99%

Magnetothermodynamics of BPS baby skyrmions

Adam

Romańczukiewicz

Sánchez-Guillén

et al. 2014

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…This result was already derived, via a slightly different argument, in [10]. So, given an E minimizer ϕ which is conformal on average and satisfies E 0 = E 4 , we know that E is critical with respect to variations of the period lattice.…”

Section: Baby Skyrmion Crystalsmentioning

confidence: 83%

“…It follows that the baby skyrmion lattices found in [10], for example, for which the conditions (3.5), (3.8) were checked numerically, are soliton crystals according to our definition. These were defined on equianharmonic tori, that is tori with Λ generated by L and Le iπ/3 .…”

Section: Baby Skyrmion Crystalsmentioning

confidence: 97%

“…The terms coming from E 0 + E 2 + E 6 (that is, all but the second and last terms in the formula above) were obtained previously [10]. It remains to show that…”

Section: Skyrmion Crystalsmentioning

confidence: 99%

“…Under what circumstances is ϕ a soliton lattice, as defined in section 2? The stress tensor of ϕ is easily computed [10],…”

Section: Baby Skyrmion Crystalsmentioning

confidence: 99%

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Solitons on Tori and Soliton Crystals

Speight

2014

Commun. Math. Phys.

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Necessary conditions for a soliton on a torus M = R m /Λ to be a soliton crystal, that is, a spatially periodic array of topological solitons in stable equilibrium, are derived. The stress tensor of the soliton must be L 2 orthogonal to E, the space of parallel symmetric bilinear forms on T M , and, further, a certain symmetric bilinear form on E, called the hessian, must be positive. It is shown that, for baby Skyrme models, the first condition actually implies the second. It is also shown that, for any choice of period lattice Λ, there is a baby Skyrme model which supports a soliton crystal of periodicity Λ. For the three-dimensional Skyrme model, it is shown that any soliton solution on a cubic lattice which satisfies a virial constraint and is equivariant with respect to (a subgroup of) the lattice symmetries automatically satisfies both tests. This verifies in particular that the celebrated Skyrme crystal of Castillejo et al., and Kugler and Shtrikman, passes both tests.

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Classical Skyrmions—static solutions and dynamics

Manton

2012

Math Methods in App Sciences

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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.

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Broken baby Skyrmions

Cited by 40 publications

References 23 publications

Magnetothermodynamics of BPS baby skyrmions

Magnetothermodynamics of BPS baby skyrmions

Solitons on Tori and Soliton Crystals

Classical Skyrmions—static solutions and dynamics

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