A point particle model of lightly bound skyrmions

Abstract

A simple model of the dynamics of lightly bound skyrmions is developed in which skyrmions are replaced by point particles, each carrying an internal orientation. The model accounts well for the static energy minimizers of baryon number $1\leq B\leq 8$ obtained by numerical simulation of the full field theory. For $9\leq B\leq 23$, a large number of static solutions of the point particle model are found, all closely resembling size $B$ subsets of a face centred cubic lattice, with the particle orientations dictated by a simple colouring rule. Rigid body quantization of these solutions is performed, and the spin and isospin of the corresponding ground states extracted. As part of the quantization scheme, an algorithm to compute the symmetry group of an oriented point cloud, and to determine its corresponding Finkelstein-Rubinstein constraints, is devised.Comment: 33 page

Oscillons in a perturbed signum-Gordon model

“…Although the structure of static Skyrmions is fairly well understood both numerically and analytically (especially in the minimal Skyrme model [20,21], the loosely bound Skyrme models [11][12][13][14][15]22] and the BPS Skyrme model [4,5]), the time dependent solutions are much more difficult to obtain and to analyse. On the other hand, time-dependent configurations are needed in many physical applications of Skyrmions -especially in the (vibrational) quantization procedure.…”

“…Of course, this part is minimized by rational maps of a finite degree B leading to E u = 4π|B|. Therefore, we finally arrive at the following reduced model 12) where µ = (0, 1) and x 0 = t, x 1 = r and where we have introduced a new target space coordinateη = 1 − cos ξ. It should be underlined that solitonic solutions of this reduced theory interpolating between ξ = 0 and ξ = π give rise to three dimensional solitons (Skyrmion type solutions of the first BPS submodel) with the topological baryon charge equal to the degree of the rational map.…”

“…They are given by the formula 12) where v(x) = −x for L 1 and v(x) = 1 − x for R 1 . The remaining solutions have the general form 13) where the functions F (x+t) and G(x−t) are obtained from the matching conditions at the surfaces of the light cones.…”

Skyrme and Faddeev models in the low-energy limit of 4d Yang–Mills–Higgs theories

“…Topological solitons of the Skyrme model have a point-like core and are supposed to describe baryons and nuclei (see e.g. [3] for a review and [4,5,6] for some recent works). On the other hand, solitons in the Faddeev model take the form of stable knotted strings characterized by the Hopf charge (homotopy class of maps S 3 → S 2 ).…”

Rolling Skyrmions and the nuclear spin-orbit force

“…It successfully accounts for phenomena such as the stability of the alpha-particle, the long-range forces between nuclei, and quantum numbers of excited states of very light nuclei. Some of the recent successes of the model include reproducing the excited states of oxygen-16 [1] and carbon-12 [2], nuclear binding energies of the correct magnitude [3], accurately modelling neutron stars [4] and a geometric explanation for certain magic nuclei [5].…”