Nonlinear superposition law and Skyrme crystals

Jun 30, 2013
8 pages
Published in:
  • Phys.Rev.D 88 (2013) 6, 065028
  • Published: Sep 25, 2013
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Abstract: (APS)
Exact configurations of the four-dimensional Skyrme model are presented. The static configurations have the profile. Which behaves as a kink and, consequently, the corresponding energy-momentum tensor describes a domain wall. Furthermore, a class of exact time-periodic Skyrmions is discovered. Within such a class, it is possible to disclose a remarkable phenomenon that is a genuine effect of the Skyrme term. For a special value of the frequency the Skyrmions admit a nonlinear superposition principle. One can combine two or more exact “elementary” Skyrmions (which may depend in a nontrivial way on all the spacelike coordinates) into a new exact composite Skyrmion. Because of such a superposition law, despite the explicit presence of nonlinear effects in the energy-momentum tensor, the interaction energy between the elementary Skyrmions can be computed exactly. The relations with the appearance of Skyrme crystals are discussed.
Note:
  • 13 pages, no figure. A discussion of the domain-wall behaviour of the static configurations has been included. A detailed analysis of the boundary conditions has been added. Version accepted for publication on Phys. Rev. D
  • 12.39.Dc
  • 05.45.Yv
  • 11.10.Lm
  • 11.27.+d
  • effect: nonlinear
  • tensor: energy-momentum
  • energy: interaction
  • dimension: 4
  • Skyrmion
  • crystal