Dynamics of baby Skyrmions

Abstract

Baby Skyrmions are topological solitons in a (2+1)-dimensional field theory which resembles the Skyrme model in important respects. We apply some of the techniques and approximations commonly used in discussions of the Skyrme model to the dynamics of baby Skyrmions and directly test them against numerical simulations. Specifically we study the effect of spin on the shape of a single baby Skyrmion, the dependence of the forces between two baby Skyrmions on the baby Skyrmions' relative orientation and the forces between two baby Skyrmions when one of them is spinning.

Some aspects of self-duality and generalised BPS theories

“…And, indeed, field theories based on versions of the above energy functional [7]- [15] are known to support both Bogomolnyi bounds and topological BPS solitons [10]- [15]. Among these BPS theories there are BPS submodels of some well-known and relevant non-linear field theories like, e.g., the Skyrme [16][17][18] and baby Skyrme [19][20][21][22][23] models or the abelian Higgs model, which makes them all the more interesting also from a phenomenological perspective (see, e.g., [24,25]). Given these results, one rather obvious question then arises -as to whether a version of the "deformation procedure" mentioned above generalises to the higher-dimensional theories, and whether this procedure can be used also in these cases to find soliton solutions of many different theories starting from a soliton of a certain "seed" theory.…”

Interaction of noncommutative solitons with defects

“…The effects of medium disorders and impurities can be added to the equation of motion as perturbative terms [7,8]. These effects also can be taken into account by making some parameters of the equation of motion to be function of space or time [9,10].…”

Recent mathematical developments in the Skyrme model

“…Now the condition that the map is an isometry is given by a n y of the following statements: (104) If any one of these equations is true, they are all true. Equations (101) and (104) require that is invertible to make sense.…”

“…Equations (101) and (104) require that is invertible to make sense. As we will see, it is not necessary for to be invertible, hence (102) and (103) are more fundamental.…”

“…Interactions which depend on the relative orientation of rapidly spinning bodies are common in the classical or semi-classical treatment of soliton systems. A similar numerical example is presented by Piette et al [104] in the case of \baby-Skyrmions" (Skyrmions in a two dimensional space), where classical trajectories and scattering of spinning solitons is studied. They too exhibit an \oscillatory" interaction which nonetheless generates a net force between the particles and non-trivial scattering.…”