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Stochastic Behavior in Classical and Quantum Hamiltonian Systems pp 232–240Cite as

Dynamics and ergodicity of the infinite harmonic crystal a review of some salient features

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Part of the book series: Lecture Notes in Physics ((LNP,volume 93))

Abstract

We review some recent developments and rigorous results concerning the dynamics and ergodicity of the a priori infinite harmonic crystal. We present several ways of constructing the dynamics, indicate the relevance of the technique of fourier transforms of measures in studying the classical states, and discuss the result that (nearly) every perfect infinite harmonic crystal in thermal equilibrium is a Bernoulli system, so is at the top of the ergodic hierarchy: Finally we exemplify the classical KMS condition.

Supported by the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).

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Author notes

  1. J. L. van Hemmen

    Present address: Math. Dept., Duke University, 27706, Durham, NC, USA

Authors and Affiliations

  1. Institut des Hautes Etudes Scientifiques, 91440, Bures-sur-Yvette, France

    J. L. van Hemmen

Authors
  1. J. L. van Hemmen
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Giulio Casati Joseph Ford

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© 1979 Springer-Verlag

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van Hemmen, J.L. (1979). Dynamics and ergodicity of the infinite harmonic crystal a review of some salient features. In: Casati, G., Ford, J. (eds) Stochastic Behavior in Classical and Quantum Hamiltonian Systems. Lecture Notes in Physics, vol 93. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0021747

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  • DOI: https://doi.org/10.1007/BFb0021747

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09120-2

  • Online ISBN: 978-3-540-35510-6

  • eBook Packages: Springer Book Archive

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