Abstract.
We study the semiclassical behaviour of eigenfunctions of quantum systems with ergodic classical limit. By the quantum ergodicity theorem almost all of these eigenfunctions become equidistributed in a weak sense. We give a simple derivation of an upper bound of order \( |{\rm ln{\hbar}}| ^{-1} \) on the rate of quantum ergodicity if the classical system is ergodic with a certain rate. In addition we obtain a similar bound on transition amplitudes if the classical system is weak mixing. Both results generalise previous ones by Zelditch.
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Communicated by Jens Marklof
Submitted: March 16, 2005 Accepted: February 2, 2006
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Schubert, R. Upper Bounds on the Rate of Quantum Ergodicity. Ann. Henri Poincaré 7, 1085–1098 (2006). https://doi.org/10.1007/s00023-006-0277-5
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DOI: https://doi.org/10.1007/s00023-006-0277-5