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Skyrmions, Fullerenes and Rational Maps

Battye, R.A.; Sutcliffe, P.M.


R.A. Battye


We apply two very different approaches to calculate Skyrmions with baryon number B ≤ 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 ≥ 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.


Battye, R., & Sutcliffe, P. (2002). Skyrmions, Fullerenes and Rational Maps. Reviews in Mathematical Physics, 14(1), 29-85.

Journal Article Type Article
Publication Date Jan 1, 2002
Deposit Date Feb 15, 2008
Journal Reviews in Mathematical Physics
Print ISSN 0129-055X
Electronic ISSN 1793-6659
Publisher World Scientific Publishing
Peer Reviewed Peer Reviewed
Volume 14
Issue 1
Pages 29-85

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