Here are movies of the 336 odd-symmetry eigenmodes in wavenumber range [90,100], computed using the scaling method. The mode number is around 1700. Only the right-half of the mushroom is shown:
Raw eigenmodes, with mode number j increasing in time.
The intensity |φj|2 is shown, with white
zero and larger values darker.
`Migrating scars' are actually visible in this movie, but only when you
know what to look for. They are mush clearer in the following.
Local density of states over the same wavenumber interval. This is essentially the previous movie smoothed in wavenumber by a Gaussian of width 0.12. Look for the migrating scars moving down the middle of the left-hand wall (the symmetry axis). You may want to set your movie player on loop.
This material is based upon work supported by the National Science Foundation under Grant No. DMS-0507614
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