Angularly localized Skyrmions

Details Angularly localized Skyrmions Angularly localized Skyrmions

2005-07-14

arxiv.org/abs/nlin/0507028v1

J.Phys. A39 (2006) 1507-1520

Nonlinear Sciences

Pattern Formation and Solitons

22 pages

Scientific paper

10.1088/0305-4470/39/6/021

Quantized Skyrmions with baryon numbers $B=1,2$ and 4 are considered and angularly localized wavefunctions for them are found. By combining a few low angular momentum states, one can construct a quantum state whose spatial density is close to that of the classical Skyrmion, and has the same symmetries. For the B=1 case we find the best localized wavefunction among linear combinations of $j=1/2$ and $j=3/2$ angular momentum states. For B=2, we find that the $j=1$ ground state has toroidal symmetry and a somewhat reduced localization compared to the classical solution. For B=4, where the classical Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by combining the $j=0$ ground state with the lowest rotationally excited $j=4$ state. We use the rational map approximation to compare the classical and quantum baryon densities in the B=2 and B=4 cases.

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