Quantum Leaks
arXiv:math-ph/0503066 · doi:10.1007/s00220-005-1467-6
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.
References in corpus (6)
- Scarred eigenstates for quantum cat maps of minimal periods
- On the maximal scarring for quantum cat map eigenstates
- More ergodic billiards with an infinite cusp
- Semi-dispersing billiards with an infinite cusp
- Eigenfunctions for partially rectangular billiards
- Localization in infinite billiards: a comparison between quantum and classical ergodicity