Time evolution and ergodic properties of harmonic systems
We prove the existence of a time evolution and of a stationary equilibrium measure for the infinite harmonic crystal. The ergodic properties of the system are shown to be related in a simple way to the spectrum of the force matrix; when the spectrum is absolutely continuous, as in the translation invariant crystal, the flow is Bernoulli. The quantum crystal is also discussed.
KeywordsCanonical Ensemble Point Spectrum Orthogonal Transformation Infinite System Complex Hilbert Space
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