Quantum ergodicity at a finite energy level

Tatsuya Tate

doi:10.2969/jmsj/05140867

Quantum ergodicity at a finite energy level

Tatsuya Tate

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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
Pages (from-to)	867-885
Number of pages	19
Journal	Journal of the Mathematical Society of Japan
Volume	51
Issue number	4
DOIs	https://doi.org/10.2969/jmsj/05140867
Publication status	Published - 1999

Keywords

Quantum ergodicity
Reduction
Semi-classical limit

ASJC Scopus subject areas

Mathematics(all)

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10.2969/jmsj/05140867

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KW - Semi-classical limit

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