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 1A2u + 2Eu, 1A2g + 2Eg and 1A1u + 1B2u + 1B2g respectively.
There are several ways to describe the B=8 which are useful here. One is to view it as two B=4 cubes; another is as four B=2 tori. One can also identify it as central cube surrounded by two tori.
| Freq. | Symmetry | Description/Notes | Visualization |
|---|---|---|---|
| 0.18 | 1A1u | The cubes rotate
around their common C4 symmetry axis, out of phase. |
|
| 0.19 | 1A2g | The cubes isorotate around the red iso-axis, out of phase. |
|
| 0.22 | 2Eu | The cubes rotate towards each other forming a bent-arm. |
|
| 0.25 | 1A1g | The cubes move away from each other. |
|
| 0.33 | 1B1g | The cubes isorotate around the white/black iso-axis, out of phase. |
|
| 0.35 | 1B1u | Each cube vibrates like the B=4, 0.48 mode out of phase. |
|
| 0.38 | 2Eg | Similar to the 0.22 mode, but the rotation is in phase yielding a shear mode of the two cubes. |
|
| 0.43 | 1A2u | The cubes each vibrate like the B=4, 0.46 mode out of phase. The outgoing tori lie in the plane perpendicular to the common C4 symmetry axis. |
|
| 0.44 | 1A1g | The central cube vibrates like the B=4, 0.46 mode. |
|
| 0.44 | 2Eu | Each cube vibrates like the B=4, 0.48 mode out of phase. |
|
| 0.45 | 1B2u | Each cube vibrates like the B=4, 0.46 mode out of phase. |
|
| 0.46 | 1B1g | Each cube vibrates like the B=4, 0.46 mode in phase. |
|
| 0.47 | 1B2g | The outer tori vibrate like the B=2, 0.37 mode in phase. |
|
| 0.48 | 1B2g | The central cube vibrates like the B=4, 0.48 mode. |
|
| 0.48 | 2Eg | Each cube vibrates like the B=4, 0.48 mode, in phase. |
|
| 0.52 | 1B1u | Each cube vibrates like the B=4, 0.52 mode, in phase. |
|
| 0.59 | 2Eg | Each cube vibrates like the B=4, 0.62 mode out of phase realized in such a way that the central cube's deformation is small. |
|
| 0.62 | 1B2u | Each cube vibrates like the B=4, 0.62 mode in phase realized in such a way that the central cube significantly deforms. |
|
| 0.72 | 1A1g | The center cube breathes. |
|
| 0.72 | 2Eu | Each cube vibrates like the B=4, 0.94 mode, realized such that two edges of the central cube pull away from each other. |
|
| 0.81 | 1B1g | The central cube vibrates like the B=4, 0.87 mode while the top and bottom tori vibrate like the B=2, 0.37 mode. All motion is due to breathing. |
|
| 0.83 | 1B2g | Each cube vibrates like the B=4, 0.94 mode in phase. |
|
| 0.84 | 1B1u | The central cube vibrates like the B=4, 0.87 mode. |
|
| 0.85 | 1A2u | One cube inflates while the other deflates. The central cube moves back and forth between the two tori. |
|
| 0.86 | 2Eu | Two neighboring faces inflate while the opposite faces deflate. The faces in between move their positions to compensate. |
|
| 0.88 | 2Eg | Each cube vibrates like the B=4, 0.87 mode out of phase. |
|
| 0.91 | 1A1g | Both cubes breathe in phase. |
|
| 0.94 | 2Eu | Similar to the 0.22 mode but physically due to isorotation. |
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| 0.98 | 1A2u | The top and bottom tori inflate and deflate out of phase. |
|
| 1.03 | 2Eg | Each cube vibrates like the B=4, 0.94 mode out of phase. |
|
| 1.05 | 1B1g | Similar to the 0.46 mode but physically due to a breathing motion. |
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| 1.06 | 1B1u | Similar to the 0.35 mode but physically due to a breathing motion. |
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| 1.08 | 1B2u | Similar to the 0.45 mode but physically due to a breathing motion. |
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| 1.10 | 2Eu | The two cubes vibrate like the B=4, 1.14 mode in phase. |
|
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.