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Skyrmions, fullerenes and rational maps

Battye, Richard A., Sutcliffe, Paul M. (2002) Skyrmions, fullerenes and rational maps. Reviews in Mathematical Physics, 14 (1). pp. 29-85. ISSN 0129-055X. (doi:10.1142/S0129055X02001065) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:7977)

The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided.
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We apply two very different approaches to calculate Skyrmions with baryon number B less than or equal to 22. The first employs the rational map ansatz, where approximate charge B Skyrmions are constructed from a degree B rational map between Riemann spheres. We use a simulated annealing algorithm to search for the minimal energy rational map of a given degree B. The second involves the numerical solution of the full non-linear time dependent equations of motion, with initial conditions consisting of a number of well separated Skyrmion clusters. In general, we find a good agreement between the two approaches. For B greater than or equal to 7 almost all the solutions are of fullerene type, that is, the baryon density isosurface consists of twelve pentagons and 2B-14 hexagons arranged in a trivalent polyhedron. There are exceptional cases where this structure is modified, which we discuss in detail. We find that for a given value of B there are often many Skyrmions, with different symmetries, whose energies are very close to the minimal value, some of which we discuss. We present rational maps which are good approximations to these Skyrmions and accurately compute their energy by relaxation using the full non-linear dynamics.

Item Type: Article
DOI/Identification number: 10.1142/S0129055X02001065
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Judith Broom
Date Deposited: 14 Sep 2008 14:32 UTC
Last Modified: 16 Nov 2021 09:45 UTC
Resource URI: (The current URI for this page, for reference purposes)

University of Kent Author Information

Sutcliffe, Paul M..

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