TY - JOUR

T1 - Quantum ergodicity at a finite energy level

AU - Tate, Tatsuya

N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.

PY - 1999

Y1 - 1999

N2 - 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].

AB - 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].

KW - Quantum ergodicity

KW - Reduction

KW - Semi-classical limit

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U2 - 10.2969/jmsj/05140867

DO - 10.2969/jmsj/05140867

M3 - Article

AN - SCOPUS:0033211859

VL - 51

SP - 867

EP - 885

JO - Journal of the Mathematical Society of Japan

JF - Journal of the Mathematical Society of Japan

SN - 0025-5645

IS - 4

ER -