The B = 2 Skyrmion's vibrational modes

Each mode's symmetry is denoted as dI, it has a degeneracy d, and transforms as an irrep I of the Skyrmion's symmetry group. We use the notation of Cotton. Character tables may be found here.

The zero modes are translations, rotations and isorotations. These decompose as 2E1u + 1A2u, 2E1g + 1A2g and 2E2u + 1A2g respectively. Note that, for the toroidal configuration, a rotation about the z-axis is equivalent to a isorotation about the white/black axis.

Freq. Symmetry Description/Notes Visualization
0.37 2E2g
The torus splits into two individual Skyrmions.
0.99 2E1u
Two halves of the torus isorotate in different directions, around the white/black axis. This may also be interpreted as two individual Skyrmions breathing out of phase.
1.03 1A1g
The breathing mode.
1.08 1A2u
The equator of the color wheel moves up and down.

Notes

Hover over an image (or if you're on a tablet/phone: tap on an image) to make it come to life. The hover-over text tells you the Cartesian realization of the element of the irrep you are looking at.