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We show that eigenfunctions of the Laplacian on certain non-compact domains with finite area may localize at infinity - provided there is no extreme level clustering - and thus rule out quantum unique ergodicity for such systems. The construction is elementary and based on 'bouncing ball' quasimodes whose discrepancy is proved to be significantly smaller than the mean level spacing.
Bibliographical notePublisher: Springer
Other identifier: IDS number 034FT
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