Abstract
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 semiclassical analogue of the notion introduced in [Z4].
Original language | English |
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Pages (from-to) | 867-885 |
Number of pages | 19 |
Journal | Journal of the Mathematical Society of Japan |
Volume | 51 |
Issue number | 4 |
DOIs | |
Publication status | Published - 1999 |
Keywords
- Quantum ergodicity
- Reduction
- Semi-classical limit
ASJC Scopus subject areas
- Mathematics(all)