Related papers: Understanding Skyrmions using Rational Maps
There is a classical extension, of M\"obius automorphisms of the Riemann sphere into isometries of the hyperbolic space $\mathbb{H}^3$, which is called the Poincar\'e extension. In this paper, we construct extensions of rational maps on the…
A tri-linear rational map in dimension three is a rational map $\phi: (\mathbb{P}_\mathbb{C}^1)^3 \dashrightarrow \mathbb{P}_\mathbb{C}^3$ defined by four tri-linear polynomials without a common factor. If $\phi$ admits an inverse rational…
The skyrmion, which is characterised by a topological integer, is a structure that is topologically stable against local disturbances. The huge potential of skyrmions for use in magnetic storage systems has drawn considerable research…
Motivated by a demand for explicit genus 1 Belyi maps from theoretical physics, we give an efficient method of explicitly computing genus one Belyi maps by (1) composing covering maps from elliptic curves to the Riemann sphere with simpler…
Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the…
We elucidate magnetic effects in the skyrmion system to probe into the dense nuclear matter. We find a deformed $\pi^0$ dipole structure of a baryon induced by a magnetic field. We then extend our scope to stacked Skyrme crystal layers to…
We model quantum Hall skyrmions in graphene monolayer at quarter filling by a theory of CP3 fields and study the energy minimizing skyrmions in presence of valley pseudospin anisotropy and Zeeman coupling. We present a diagram of all types…
Static properties of multiskyrmions with baryon numbers up to 8 are calculated, including momenta of inertia and sigma-term. The calculations are based on the recently suggested SU(2) rational map ansaetze. Minimization with the help of…
We derive an effective Hamiltonian system describing the low energy dynamics of circular magnetic skyrmions and antiskyrmions. Using scaling and symmetry arguments we model (anti-)skyrmion dynamics through a finite set of coupled,…
Within the class of field theories with the field contents of the Skyrme model, one submodel can be found which consists of the square of the baryon current and a potential term only. For this submodel, a Bogomolny bound exists and the…
In this article, we show that all admissible rational maps with fixed or period two cluster cycles can be constructed by the mating of polynomials. We also investigate the polynomials which make up the matings that construct these rational…
We generalize the notion of calibrated submanifolds to smooth maps and show that the several examples of smooth maps appearing in the differential geometry become the examples of our situation. Moreover, we apply these notion to give the…
The present paper attempts to show an alternative approach with regards to rational Pythagorean-hodograph (PH) curves and especially more natural approach for rational PH helices (i.e. rational helices). It exploits geometric features of…
We study static solutions of the Skyrme model on the two-sphere of radius L, for various choices of potential. The high-density Skyrmion phase corresponds to the ratio beta=L/(size of Skyrmion) being small, whereas the low-density phase…
We construct discrete analogs of Skyrmions in nonlinear dynamical lattices. The Skyrmion is built as a vortex soliton of a complex field, coupled to a dark radial soliton of a real field. Adjusting the Skyrmion ansatz to the lattice setting…
We present a method for computing projective isomorphisms between rational surfaces that are given in terms of their parametrizations. The main idea is to reduce the computation of such projective isomorphisms to five base cases by…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
We numerically simulate the formation of $(2+1)$-dimensional baby Skyrmions and $(3+1)$-dimensional $SU(2)$ Skyrmions from domain wall collisions. It has been suggested that Skyrmion, anti-Skyrmion pairs can be produced from the interaction…
One of the most interesting open problems concerning the Skyrme model of nuclear physics is the regularity of its solutions. In this article, we study 2+1 dimensional equivariant Skyrme maps, for which we prove, using the method of…
We construct a spherical domain wall which has baryon charge distributed on a sphere of finite radius in a Skyrme model with a sixth order derivative term and a modified mass term. Its distribution of energy density likewise takes the form…