05-119 Jens Marklof

Quantum Leaks (42K, latex) Mar 28, 05

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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.

Files: 05-119.src( 05-119.keywords , escape.tex )