Ergodic Properties of Infinite Harmonic Crystals: an Analytic Approach

Details Ergodic Properties of Infinite Harmonic Crystals: an Analytic Approach Ergodic Properties of Infinite Harmonic Crystals: an Analytic Approach

1996-02-02

arxiv.org/abs/chao-dyn/9602003v1

J.Math.Phys. 37 (1996) 5111-5135

Physics

Condensed Matter

30 pages, plain LaTex

Scientific paper

10.1063/1.531741

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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