Skip to main content
Article thumbnail
Location of Repository

Lattices of Generalized Skyrmions



Generalized Skyrme systems are those which include both the Skyrme and the Skyrme-Faddeev models through an interpolating parameter \alpha \in [0,1] the former corresponds to \alpha=0 and the latter to \alpha=1. Our numerical and analytical investigations centre around the \alpha=0 Skyrme crystal, its deformations, and its behaviour and symmetries as a function of \alpha, called the\ud generalized Skyrme crystal. We show that a double square lattice emerges when the Skyrme crystal is deformed in a certain limit; we compare its energy with the one corresponding to a double hexagonal lattice and show that it\ud has a lower energy-per-charge than its hexagonal counterpart. On the other hand, vortex-like structures with two 1-vortices (vortices of order 1) and two 1-antivortices, denoted V+AV+V+AV, appear when the Skyrme crystal is deformed in a different limit, as well as when the generalized Skyrme crystal is taken close to the Skyrme-Faddeev limit. This leads us to the study of generalized V+AV and V+AV+V+AV configurations, as a function of \alpha. We show that when these configurations are stacked in the axial direction, they exhibit some winding and linking properties as they are taken close to the Skyrme-Faddeev limit, where the V+AV+V+AV configurations appear to be\ud more stable than their V+AV counterparts. Finally, the study of such configurations led to the discovery of two crystalline solutions whose properties are investigated in some detail: a 2-vortex/2-antivortex pair, denoted 2V+2AV,\ud and a “multi-sheet” solution, both of which have a lower energy-per-charge than the V+AV+V+AV solution, in the Skyrme-Faddeev limit

Year: 2011
OAI identifier:
Provided by: Durham e-Theses

Suggested articles


  1. (1941). A classification of mappings of the three-dimensional complex into the two-dimensional sphere,
  2. (1927). A Course of Modern Analysis doi
  3. (1988). A new skyrmion crystal, doi
  4. (1961). A Nonlinear field theory, doi
  5. (1998). A Skyrme lattice with hexagonal symmetry, doi
  6. (2000). Aspects of duality and confining strings, doi
  7. (1987). Axial symmetry of bound baryon number two solution of the Skyrme Model, doi
  8. (1979). Baryons in the 1/N Expansion, doi
  9. (2001). Classical gauge vacua as knots, doi
  10. (1982). Closed vortex type solitons with Hopf index, J.Phys.A A15, doi
  11. (1964). Comments on nonlinear wave equations as models for elementary particles, doi
  12. (1983). Current Algebra, Baryons, and Quark Confinement, doi
  13. (2010). Deformed Skyrme Crystals, doi
  14. (1989). Dense skyrmion systems, doi
  15. (1994). Differential Models of Hysteresis (Springer-Verlag doi
  16. (1987). Exotic Skyrmions, doi
  17. (1999). Faddeev-Hopf knots: Dynamics of linked unknots, doi
  18. (2006). Fermionic quantization of Hopf solitons, doi
  19. (1987). Geometry of skyrmions, doi
  20. (2002). Hidden symmetry and knot solitons in a charged two-condensate Bose system, doi
  21. (1999). Hopf solitons on S(3) and R(3), doi
  22. (1987). Is the B=2 skyrmion axially symmetric?, doi
  23. (2007). Knots in the Skyrme-Faddeev model, doi
  24. (2011). Massive hopfions, doi
  25. (1985). Nuclear matter in the Skyrme Model, doi
  26. (2007). Numerical Mathematics and Computing (Thomson Brooks/Cole,
  27. (1975). Quantisation of solitons
  28. (2004). Relaxation of twisted vortices in the Faddeev-Skyrme model, doi
  29. Report on waves (1845),
  30. (1989). Skyrmion crystals and their symmetries, doi
  31. Skyrmion Multi-Walls, doi
  32. (2004). Skyrmions and Faddeev-Hopf solitons, doi
  33. (2005). Skyrmions and the pion mass, doi
  34. (2006). Skyrmions with massive pions, doi
  35. (2002). Skyrmions, fullerenes and rational maps, doi
  36. (2006). Soliton/exciton transport in proteins, doi
  37. (2001). Solitonic fullerenes, doi
  38. (1999). Solitons, links and knots, doi
  39. (1976). Some Comments on the Many Dimensional Solitons, doi
  40. (2005). Spinning skyrmions and the skyrme parameters, doi
  41. (1979). Stability of solitons in S(2) in the nonlinear sigma model,
  42. (1997). Stable knot-like structures in classical field theory, doi
  43. (1997). Static solitons with nonzero Hopf number, doi
  44. (2010). Supercurrent coupling in the Faddeev-Skyrme model, doi
  45. (1997). Symmetric skyrmions, doi
  46. (2000). The Interaction of two Hopf solitons, doi
  47. (2006). The Road to Reality (Vintage Books,
  48. (1984). The Skyrme Model with Pion Masses, doi
  49. (2004). Topological Solitons doi
  50. (2009). Unwinding in Hopfion vortex bunches, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.