93 research outputs found
Nonconcentration in partially rectangular billiards
In specific types of partially rectangular billiards we estimate the mass of
an eigenfunction of energy in the region outside the rectangular set in the
high-energy limit. We use the adiabatic ansatz to compare the Dirichlet energy
form with a second quadratic form for which separation of variables applies.
This allows us to use sharp one-dimensional control estimates and to derive the
bound assuming that is not resonating with the Dirichlet spectrum of the
rectangular part.Comment: 28 pages, 1 figure; Typos corrected, error in final proof corrected
and techniques strengthene
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