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Quantum Leaks

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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.

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Authors and Affiliations

  1. School of Mathematics, University of Bristol, Bristol, BS8 1TW, U.K

    Jens Marklof

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  1. Jens Marklof
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Correspondence to Jens Marklof.

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Communicated by P. Sarnak

Research supported by an EPSRC Advanced Research Fellowship and EPSRC Research Grant GR/T28058/01.

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Marklof, J. Quantum Leaks. Commun. Math. Phys. 264, 303–316 (2006). https://doi.org/10.1007/s00220-005-1467-6

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