Lattices of Generalized Skyrmions
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9MbAbstractGeneralized Skyrme systems are those which include both the Skyrme and the Skyrme Faddeev models through an interpolating parameter [0,1] the former corresponds to =0 and the latter to =1. Our numerical and analytical investigations centre around the =0 Skyrme crystal, its deformations, and its behaviour and symmetries as a function of, called the generalized Skyrme crystal. We show that a double square lattice emerges when the Skyrme crystal is deformed in a certain limit; we compare its energy with the one corresponding to a double hexagonal lattice and show that it has a lower energy per charge than its hexagonal counterpart. On the other hand, vortex like structures with two 1 vortices (vortices of order 1) and two 1 antivortices, denoted V+AV+V+AV, appear when the Skyrme crystal is deformed in a different limit, as well as when the generalized Skyrme crystal is taken close to the Skyrme Faddeev limit. This leads us to the study of generalized V+AV and V+AV+V+AV configurations, as a function of. We show that when these configurations are stacked in the axial direction, they exhibit some winding and linking properties as they are taken close to the Skyrme Faddeev limit, where the V+AV+V+AV configurations appear to be more stable than their V+AV counterparts. Finally, the study of such configurations led to the discovery of two crystalline solutions whose properties are investigated in some detail: a 2 vortex/2 antivortex pair, denoted 2V+2AV, and a “multi sheet” solution, both of hermes mens gold belt replica
which have a lower energy per charge than the V+AV+V+AV solution, in the Skyrme Faddeev limit.