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- W3044779042 abstract "We define a notion of quantum or non-commutative, ergodicity for a class ofC*-dynamical systems (A, G, α) which we callquantized 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 ∈A equals the “space average” ω(A)I plus an errorK which is negligible in the classical limit. We prove that ergodicity of ω is a sufficient condition for quantum ergodicity of (A, G, α) if the classical limit system is abelian, give a conditional converse, and discuss a number of applications." @default.
- W3044779042 created "2020-07-29" @default.
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- W3044779042 date "1995-01-01" @default.
- W3044779042 modified "2023-10-13" @default.
- W3044779042 title "Quantum ergodicity of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:msup><mml:mi>C</mml:mi> <mml:mo>*</mml:mo> </mml:msup></mml:math>-dynamical systems" @default.
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- W3044779042 doi "https://doi.org/10.5802/tsg.154" @default.
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