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 -