Jens Marklof
Quantum Leaks
(42K, latex)

ABSTRACT.  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.