Quantum ergodicity at a finite energy level
type: Item
instance of: scholarly article
title: Quantum ergodicity at a finite energy level
zbMATH Open document ID: 0948.37052
author: Tatsuya Tate
published in: Journal of the Mathematical Society of Japan
publication date: 2000-04-09T00:00:00Z
review text: The author considers classical homogeneous Hamilton flows which commute with \(R_+\)-action on the cotangent bundle. A notion of quantum ergodicity at a finite energy level for the quantum mechanics corresponding to such systems is formulated. The relationship between quantum and classical ergodicity is investigated. Under some assumptions on the classical system the author obtains necessary and sufficient conditions in terms of semi-classical asymptotic behavior of eigenfunctions of a quantum Hamiltonian.
Mathematics Subject Classification ID: 37K20
Mathematics Subject Classification ID: 81Q50
Mathematics Subject Classification ID: 37N20
Mathematics Subject Classification ID: 37A05
zbMATH DE Number: 1398930
zbMATH Keywords: ergodic systems
zbMATH Keywords: Riemannian manifolds
zbMATH Keywords: Hamiltonian
zbMATH Keywords: homogeneous systems
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/05140867
OpenAlex ID: W2087301349
DOI: 10.2969/JMSJ/05140867
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description: scientific article; zbMATH DE number 1398930