 9635 Graffi S., Martinez A.
 Ergodic Properties of Infinite Harmonic
Crystals: an Analytic Approach
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Feb 5, 96

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Abstract. We give through pseudodifferential operator calculus
a proof that the quantum dynamics of a class of
infinite harmonic crystals becomes ergodic and
mixing with respect to the quantum Gibbs measure if
the classical infinite dynamics is respectively
ergodic and mixing with respect to the classical
infinite Gibbs measure. The classical ergodicity and
mixing properties are recovered as
$\hbar\to 0$, and the infinitely many particles
limits of the quantum Gibbs averages are proved to be
the averages over a classical infinite Gibbs measure
of the symbols generating the quantum observables
under Weyl quantization.
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