Related papers: Understanding the 1-Skyrmion
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…
In the continuum a skyrmion is a topological nontrivial map between Riemannian manifolds, and a stationary point of a particular energy functional. This paper describes lattice analogues of the aforementioned skyrmions, namely a natural way…
Intricate spin textures in helimagnets, identified as stable topological Skyrmions, were observed experimentally, where Skyrme lattice was supposed to exhibit symmetric structures in the ground state. We show the possibility of asymmetric…
Resolutions of identity for certain non-Hermitian Hamiltonians constructed from biorthogonal sets of their eigen- and associated functions are given for the spectral problem defined on entire axis. Non-Hermitian Hamiltonians under…
We obtain the rotational spectrum of strange multibaryon states by performing the SU(3) collective coordinate quantization of the static multi-Skyrmions. These background configurations are given in terms of rational maps, which are very…
An analytical solution to the the three-dimensional telegraph equation is presented. This equation has recently received some attention but so far the treatment has been one-dimensional. By using the structural similarity to the…
We consider a first order operator with a periodic 3x3 matrix potential on the real line. This operator appears in the problem of the periodic vector NLS equation. The spectrum of the operator covers the real line, it is union of the…
Using the field theory method and coherent spin state approach, we investigate properties of magnetic solitons in spacetime while focussing on 1D kinks, 2D and 3D skyrmions. We also study the case of a rigid skyrmion dissolved in a magnetic…
Starting from approximate Skyrmion solutions obtained using the rational map ansatz, improved approximate Skyrmions are constructed using scaling arguments. Although the energy improvement is small, the change of shape clarifies whether the…
Using the shape invariance property we obtain exact solutions of the (1+1)dimensional Klein-Gordon equation for certain types of scalar and vector potentials. We also discuss the possibility of obtaining real energy spectrum with…
We construct analytic (3+1)-dimensional Skyrmions living at finite Baryon density in the SU(N) Skyrme model that are not trivial embeddings of SU(2) into SU(N). We used Euler angles decomposition for arbitrary N and the generalized hedgehog…
The band structure of the Lam\'e equation, viewed as a one-dimensional Schr\"odinger equation with a periodic potential, is studied. At integer values of the degree parameter l, the dispersion relation is reduced to the l=1 dispersion…
We introduce a new method of symmetrization of mappings on the $n$-sphere ($n\geq 2$). They are applied to estimate solutions of quasilinear elliptic partial differential equations of $p$-Laplacian type, with combinations of Dirac measures…
Magnetic skyrmions have so far been treated as two-dimensional spin structures characterized by a topological winding number describing the rotation of spins across the skyrmion. However, in real systems with a finite thickness of the…
We construct a decomposition of the identity operator on a Riemannian manifold $M$ as a sum of smooth orthogonal projections subordinate to an open cover of $M$. This extends a decomposition of the real line by smooth orthogonal projection…
Llarull's Theorem states that any Riemannian metric on the $n$-sphere which has scalar curv{\-}ature greater than or equal to $n(n-1)$, and whose distance function is bounded below by the unit sphere's, is isometric to the unit sphere.…
We prove a new classification result for (CR) rational maps from the unit sphere in some ${\mathbb C}^n$ to the unit sphere in ${\mathbb C}^N$. To so so, we work at the level of Hermitian forms, and we introduce ancestors and descendants.
A quantal model description of a discrete localized skyrmion singularity embedded in a ferromagnetic environment is proposed. It allows discussing the importance of various parameters in the appearance of a quantal skyrmion singularity.…
Skyrmions are the magnetic defects in an ultrathin magnetic film, similar to the bubble domains in the thicker films. Even weak uniaxial anisotropy determines its radius unambiguously. We consider the dynamics of the skyrmion decay. We show…
We investigate the existence, and lack of unicity, of a holomorphic fibration by discs transversal to a rational curve in a complex surface.