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Time Evolution of Infinite Anharmonic Systems

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Book cover Statistical Mechanics

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Abstract

We prove the existence of a time evolution for infinite anharmonic crystals for a large class of initial configurations. When there are strong forces tying particles to their equilibrium positions then the class of permissible initial conditions can be specified explicitly; otherwise it can only be shown to have full measure with respect to the appropriate Gibbs state. Uniqueness of the time evolution is also proven under suitable assumptions on the solutions of the equations of motion.

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References

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Author information

Author notes

  1. Joel L. Lebowitz

    Present address: Belfer Graduate School of Science, Yeshiva University, New York, New York, USA

Authors and Affiliations

  1. University of California at Berkeley, Berkeley, California, USA

    Oscar E. Lanford III

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

    Joel L. Lebowitz

  3. Princeton University, Princeton, New Jersey, USA

    Elliott H. Lieb

Authors
  1. Oscar E. Lanford III
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  2. Joel L. Lebowitz
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  3. Elliott H. Lieb
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, One Shields Ave., 95616-8633, Davis, CA, USA

    Bruno Nachtergaele

  2. Department of Mathematics, University of Copenhagen, Universitetsparken 5, 2100, Copenhagen, Denmark

    Jan Philip Solovej

  3. Institut für Theoretische Physik, Universität Wien, Boltzmanngasse 5, 1090, Wien, Austria

    Jakob Yngvason

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© 1977 Springer-Verlag Berlin Heidelberg

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Lanford, O.E., Lebowitz, J.L., Lieb, E.H. (1977). Time Evolution of Infinite Anharmonic Systems. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Statistical Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10018-9_23

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  • DOI: https://doi.org/10.1007/978-3-662-10018-9_23

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-06092-2

  • Online ISBN: 978-3-662-10018-9

  • eBook Packages: Springer Book Archive

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