Upper Bounds on the Rate of Quantum Ergodicity |
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Authors: | Roman Schubert |
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Institution: | (1) School of Mathematics, University of Bristol, Bristol, BS8 1TW, United Kingdom |
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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
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.
Communicated by Jens Marklof
Submitted: March 16, 2005 Accepted: February 2, 2006 |
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Keywords: | |
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