Jones, Patrick; (1990) Dense skyrmion structures. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The Skyrme Model is used to investigate dense baryonic matter. A general review of skyrmionic crystalline arrays thus far investigated, reveals the existence of a universal delocalising phase transition as the density of baryonic matter is increased. At low densities the skyrmions localise on the lattice points, while at high densities they become delocalised and an array of half skyrmions remains. This phase transition is believed to represent the restoration of chiral symmetry of high densities. Numerical solutions of static arrays with fcc, bcc and intermediate symmetries are considered as a function of density. The fcc array is found at high densities to be the most stable of all the arrays so far considered. As the density is decreased the fcc array becomes unstable against deformations to arrays with intermediary symmetries. This instability occurs at a critical density slightly greater than that of the delocalising phase transition. A single skyrmion on a three sphere has an analogous delocalising phase transition as the volume of the sphere increases. Generalising this simple model of a skyrmion on a three sphere, to a skyrmion on an elliptical three surface, we identify that varying the shape of this sphere is analogous to deforming the fcc array. It is shown that the deformation transition occurs at the same critical volume as the delocalising phase transition. Beyond this density there are a large number of unstable modes, suggestive of a solid to liquid phase transition. There also exists a first order phase transition, corresponding to a phase separation. The relevance of The Chiral Bag Model to dense crystalline skyrmionic matter is discussed and its possible future application is outlined.

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