Quantum ergodicity at a finite energy level
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The purpose of this paper is to formulate the notion of quantum ergodicity at a finite energy level for certain quantum mechanics, by using the method of Sunada [Sul]. Under some assumptions on the corresponding classical mechanics, we obtain a necessary and sufficient condition in terms of semi-classical asymptotic behaviour of eigenfunctions of a quantum Hamiltonian so that the classical mechanics is ergodic. We also obtain a result on quantum weak mixing at a finite energy level which is a semi-classical analogue of the notion introduced in [Z4].
- Tokyo Sugaku Kaisya Zasshi
Tokyo Sugaku Kaisya Zasshi 51(4), 867-885, 1999-10-01
The Mathematical Society of Japan