The scattering of baby Skyrmions off potential obstructions, in a Landau-Lifshitz model

Abstract

The dynamics of baby skyrmions of the (2+1) new baby Skyrme model, in a Landau - Lifshitz model, was studied in the presence of various potential obstructions of varying geometries. The potential obstructions were created by introducing a localised inhomogeneity in the new baby Skyrme model's potential coefficient. The size and shape of the potential obstruction was varied and two systems were investigated, namely the symmetric and asymmetric systems. In the symmetric system the trajectory of the baby skyrmions, as they traverse the barrier, was deformed from the normal circular trajectory, during which time the skyrmions sped up. For critical values of the barrier height, the baby skyrmions no longer formed a bound state and were free to separate. In the case of a potential hole, the baby skyrmions no longer formed a bound state and moved asymptotically along the edge of the hole. In the asymmetric barrier system the baby skyrmions behaved the same as the skyrmions of the symmetric obstructions. Away from the obstruction the baby skyrmions orbited the boundary of the system. In the potential hole system the bound skyrmions moved along the edge of the hole. For critical values of the hole depth, the bound state between the skyrmions was broken, resulting in one of the skyrmions remaining stationary and the other traversing the edge of the hole. During our investigations into this system it was found that the definition of the angular momentum must be modified to ensure overall conservation. It was shown how these modifications arise and how they are calculated.