### Quasimodes of Seba billiards

Winn, B *(Loughborough)*

Tuesday 15 July 2008, 16:00-16:45

Seminar Room 1, Newton Institute

#### Abstract

We construct quasimodes for the Seba billiard and related systems. The Seba billiard is a rectangle billiard with a delta-function potential. By making further assumptions on the spectrum of the rectangle billiard, we are able to prove that the quasimodes, in fact, approximate a sequence of true eigenmodes. The additional hypothesis required is related to the Berry-Tabor conjecture for energy levels of integrable quantum systems

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