Quantum Leaks

Details Quantum Leaks Quantum Leaks

2005-03-28

arxiv.org/abs/math-ph/0503066v1

Physics

Mathematical Physics

Scientific paper

10.1007/s00220-005-1467-6

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.

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