Quantum ergodicity of C* dynamical systems

Steven Zelditch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)507-528
Number of pages22
JournalCommunications in Mathematical Physics
Volume177
Issue number2
DOIs
StatePublished - 1996

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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