Q-lump scattering Sutcliffe, Paul
The journal of high energy physics,
06/2023, Volume:
2023, Issue:
6
Journal Article
Peer reviewed
Open access
A
bstract
Q-lumps are spinning planar topological solitons with stationary solutions that satisfy first-order Bogomolny equations. Q-lump scattering has previously been studied only in the charge two ...sector, by approximating time evolution by motion in the moduli space of stationary solutions. In this paper, higher charge scattering is studied via motion on families of 4-dimensional submanifolds of moduli space, obtained by imposing cyclic symmetries. The results are shown to be in good agreement with field theory simulations, which are then applied to study more complicated Q-lump scattering processes, including examples where the moduli space approximation is not applicable. A variety of exotic scattering events are presented.
A
bstract
The geodesic approximation is a powerful method for studying the dynamics of BPS solitons. However, there are systems, such as BPS monopoles in three-dimensional hyperbolic space, where ...this approach is not applicable because the moduli space metric defined by the kinetic energy is not finite. In the case of hyperbolic monopoles, an alternative metric has been defined using the abelian connection on the sphere at infinity, but its relation to the dynamics of hyperbolic monopoles is unclear. Here this metric is placed in a more general context of boundary metrics on soliton moduli spaces. Examples are studied in systems in one and two space dimensions, where it is much easier to compare the results with simulations of the full nonlinear field theory dynamics. It is found that geodesics of the boundary metric provide a reasonable description of soliton dynamics.
A
bstract
The Atiyah-Hitchin manifold is the moduli space of parity inversion symmetric charge two SU(2) monopoles in Euclidean space. Here a hyperbolic analogue is presented, by calculating the ...boundary metric on the moduli space of parity inversion symmetric charge two SU(2) monopoles in hyperbolic space. The calculation of the metric is performed using a twistor description of the moduli space and the result is presented in terms of standard elliptic integrals.
Knots in the Skyrme–Faddeev model Sutcliffe, Paul
Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences,
11/2007, Volume:
463, Issue:
2087
Journal Article
Peer reviewed
Open access
The Skyrme-Faddeev model is a modified sigma model in three-dimensional space, which has string-like topological solitons classified by the integer-valued Hopf charge. Numerical simulations are ...performed to compute soliton solutions for Hopf charges up to 16, with initial conditions provided by families of rational maps from the three-sphere into the complex projective line. A large number of new solutions are presented, including a variety of torus knots for a range of Hopf charges. Often these knots are only local energy minima, with the global minimum being a linked solution, but for some values of the Hopf charge they are good candidates for the global minimum energy solution. The computed energies are in agreement with Ward's conjectured energy bound.
Full text
Available for:
BFBNIB, NMLJ, NUK, PNG, SAZU, UL, UM, UPUK
A
bstract
A problem with the standard Skyrme model is that Skyrmion binding energies are around 15%, being much larger than the order 1% binding energies of the nuclei that they aim to describe. Here ...we consider theories that extend the standard Skyrme model of pions by including rho mesons, via dimensional deconstruction of Yang-Mills theory with an extra dimension. We report the first results of parallel numerical computations of multi-Skyrmions in theories of this type, including a model that reduces Skyrmion energies below those of the standard Skyrme model whilst retaining exactly the same Faddeev-Bogomolny energy bound. We compute all Skyrmions with baryons numbers up to 12 and find that the inclusion of rho mesons reduces binding energies to less than 4%, and therefore moves Skyrmion theory closer to experimental data. Furthermore, we find that this dramatic reduction in binding energies is obtained without changing the qualitative features of the Skyrmions, such as their symmetries.
A magnetic Skyrmion is a stable two-dimensional nanoparticle describing a localized winding of the magnetization in certain magnetic materials. Skyrmions are the subject of intense experimental and ...theoretical investigation and have potential technological spintronic applications. Here we show that numerical computations of frustrated magnets predict that Skyrmions can be tied into knots to form new stable three-dimensional nanoparticles. These stable equilibria of twisted loops of Skyrmion strings have an integer-valued topological charge, known as the Hopf charge, that counts the number of particles. Rings are formed for low values of this charge, but for higher values it is energetically favorable to form links and then knots. This computational study provides a novel impetus for future experimental work on these nanoknots and an exploration of the potential technological applications of three-dimensional nanoparticles encoding knotted magnetization.
Full text
Available for:
CMK, CTK, FMFMET, IJS, NUK, PNG, UM
Hopfions in chiral magnets Sutcliffe, Paul
Journal of physics. A, Mathematical and theoretical,
09/2018, Volume:
51, Issue:
37
Journal Article
Peer reviewed
Open access
A magnetic Hopfion is a three-dimensional topological soliton that consists of a closed loop of a twisted magnetic Skyrmion string. The results of numerical simulations are presented that demonstrate ...the existence of a stable Hopfion in a nanocylinder of a chiral magnet and an explicit analytic expression is shown to provide a reasonable approximation to the numerically computed Hopfion. A mechanism is suggested to create the Hopfion from a target Skyrmion by introducing an interfacial perpendicular magnetic anisotropy.
Knot theory in modern chemistry Horner, Kate E; Miller, Mark A; Steed, Jonathan W ...
Chemical Society reviews,
11/2016, Volume:
45, Issue:
23
Journal Article
Peer reviewed
Open access
Knot theory is a branch of pure mathematics, but it is increasingly being applied in a variety of sciences. Knots appear in chemistry, not only in synthetic molecular design, but also in an array of ...materials and media, including some not traditionally associated with knots. Mathematics and chemistry can now be used synergistically to identify, characterise and create knots, as well as to understand and predict their physical properties. This tutorial review provides a brief introduction to the mathematics of knots and related topological concepts in the context of the chemical sciences. We then survey the broad range of applications of the theory to contemporary research in the field.
This tutorial review provides an introduction to the mathematics of knots and topological concepts in the context of the chemical sciences.
Among topological solitons, magnetic skyrmions are two-dimensional particle-like objects with a continuous winding of the magnetization, and magnetic Hopfions are three-dimensional objects that can ...be formed from a closed loop of twisted skyrmion strings. Theoretical models suggest that magnetic Hopfions can be stabilized in frustrated or chiral magnetic systems, and target skymions can be transformed into Hopfions by adapting their perpendicular magnetic anisotropy, but their experimental verification has been elusive so far. Here, we present an experimental study of magnetic Hopfions that are created in Ir/Co/Pt multilayers shaped into nanoscale disks, known to host target skyrmions. To characterize three-dimensional spin textures that distinguish Hopfions from target skyrmions magnetic images are recorded with surface-sensitive X-ray photoemission electron microscopy and bulk-sensitive soft X-ray transmission microscopy using element-specific X-ray magnetic circular dichroism effects as magnetic contrast. These results could stimulate further investigations of Hopfions and their potential application in three-dimensional spintronics devices.
PDF
