TY - JOUR
T1 - Quantum ergodicity of C* dynamical systems
AU - Zelditch, Steven
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1996
Y1 - 1996
N2 - We define a notion of quantum, or non-commutative, ergodicity for a class of C*-dynamical systems (script A sign, G, α) which we call quantized GNS systems. Such a system possesses a natural classical limit state ω, which induces a classical limit system by the GNS construction. The criterion for quantum ergodicity is that the time average 〈A〉 of an observable A ∈ script A sign equals the "space average" ω(A)I plus an error K which is negligible in the classical limit. We prove that ergodicity of ω is a sufficient condition for quantum ergodicity of (script A sign, G, α.) if the classical limit system is abelian, give a conditional converse, and discuss a number of applications.
AB - We define a notion of quantum, or non-commutative, ergodicity for a class of C*-dynamical systems (script A sign, G, α) which we call quantized GNS systems. Such a system possesses a natural classical limit state ω, which induces a classical limit system by the GNS construction. The criterion for quantum ergodicity is that the time average 〈A〉 of an observable A ∈ script A sign equals the "space average" ω(A)I plus an error K which is negligible in the classical limit. We prove that ergodicity of ω is a sufficient condition for quantum ergodicity of (script A sign, G, α.) if the classical limit system is abelian, give a conditional converse, and discuss a number of applications.
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U2 - 10.1007/BF02101904
DO - 10.1007/BF02101904
M3 - Article
AN - SCOPUS:0030550843
SN - 0010-3616
VL - 177
SP - 507
EP - 528
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -