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 1B2 + 2E, 1A2 + 2E and 1A2 + 2E respectively.
We have found it is helpful to view the B=5 Skyrmion from above when describing these modes, and hence have plotted the viewpoint from above as well as our standard angle.
Note: it is also helpful to interpret the top and bottom edges of the B=5 Skyrmion as single Skyrmions and the central equator as a torus. We will refer to these concepts throughout the descriptions.
| Freq. | Symmetry | Description/Notes | Visualization |
|---|---|---|---|
| 0.10 | 2E | The top edge shears away from the rest of the Skyrmion, which moves to preserve the center of mass. The bottom edge remains stationary. |
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| 0.23 | 1B1 | The top and bottom edges twist in opposite directions. |
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| 0.42 | 1A1 | The entire Skyrmion elongates. Asymptotically, it becomes a chain of five individual Skyrmions. |
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| 0.43 | 1B2 | The Skyrmion splits in half, four of its holes lying in the incision plane. |
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| 0.45 | 2E | A B=2 torus emerges from the top of the Skyrmion. Asymptotically, the Skyrmion splits into B=2 and B=3 clusters. |
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| 0.49 | 1B2 | The top edge detaches from the rest, leaving a B=4 core. In the other direction, the bottom edge detaches instead. |
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| 0.51 | 2E | A B=1 Skyrmion detaches from the equatorial torus, along the x-axis. |
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| 0.57 | 1A1 | The Skyrmion elongates while also pushing outwards. The asymptotic configuration looks like a riding saddle with D2d symmetry. |
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| 0.61 | 1B1 | The equator, interpreted as a B=2 Skyrmion, performs 1+1 90 degree scattering. |
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| 0.77 | 1A2 | The top and bottom halves of the Skyrmion twist in different directions. |
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| 0.8 | 2E | One of the four long faces (containing two holes) inflates while the opposite one deflates. The remaining two remain unchanged. |
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| 0.81 | 1A1 | The top and bottom edges break away from the equator, which deforms into a square-like object. |
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| 0.84 | 1B1 | The top half isorotates clockwise around the black/white axis while the bottom half isorotates in the other direction. |
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| 0.89 | 1B2 | The top half inflates while the bottom half deflates. |
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| 0.95 | 1B2 | Similar to the 0.43 mode, but physically due to breathing. |
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| 0.95 | 2E | Similar to the 0.45 mode, but physically due to breathing. |
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| 1.00 | 1A1 | The breathing mode. |
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| 1.04 | 1A2 | The top and bottom half isorotate in the same direction, but the equator remains unchanged. This is similar to the 0.84 mode but in phase. |
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| 1.09 | 1A1 | Similar to the 0.57 mode, but physically due to breathing. |
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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.