Energy Density Contours for Oblate Configurations
These two graphs represent the energy density in the x-y plane
for two of the textures simulated. In each case the configuration
was obtained by starting with a configuration that had a spherically
symmetric energy density, and shrinking along the x-axis by 50%.
The results are axially symmetric (the full energy density profile
is obtained by rotation around the x-axis).
The energy density in SO(4)/SO(3), in which the initial (pre-deformation)
configuration was truly spherically symmetric, is simply distorted along
with the coordinates. In the SO(3)/SO(2) model the original configuration
was not truly symmetric; there is a preferred direction associated with
the map from three-dimensional space to the vacuum manifold S^2. This
is manifested in the energy density of the squeezed configuration,
in which the maximum energy density describes a ring in the y-z plane.
The difference in the behavior of the energies when a configuration
is deformed is related to the instability to nonspherical collapse,
as discussed in the page on
quadrupole moments.
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