Note on converse quantum ergodicity

Gutkin, Boris

doi:10.1090/S0002-9939-09-09849-9

Note on converse quantum ergodicity
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by Boris Gutkin

Proc. Amer. Math. Soc. 137 (2009), 2795-2800

DOI: https://doi.org/10.1090/S0002-9939-09-09849-9

Published electronically: March 5, 2009

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Abstract:

Quantum ergodicity asserts that eigenstates of a system with classical ergodic dynamics must be “equidistributed” in the phase space. In the present note we show that the converse is not true. We provide an example of billiards which are quantum ergodic but not classically ergodic.

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