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Asymptotic orbits in a free Fermi gas

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Abstract

We consider the time evolution of local observables and physical states in an infinite system of non-interacting Fermi particles. The orbit of an observable in theC*-algebra of the canonical anticommutation relations is proved to be asymptotic to a set of observables consisting of sums of products of elements of grade two and lower with support in a family of separated cells in ℝ3 (alacunary paving of ℝ3) under time evolution. A space-factorization (“clustering”) property for primary, even, locally Fock states is established. A class of such states whose space-correlations decay as (logd)−(1+a) witha positive andd the (space-) separation is, then, proved to be time-asymptotic to their associated quasi-free states.

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Authors and Affiliations

  1. II. Institut für Theoretische Physik der Universität Hamburg, Germany

    R. Haag

  2. Department of Mathematics, University of Pennsylvania, USA

    R. V. Kadison

  3. Centre Universitaire de Marseille-Luminy, France

    D. Kastler

  4. CPT, CNRS, 31 Chemin Joseph Aiguier, F-13, Marseille 9e, France

    D. Kastler

Authors
  1. R. Haag
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  2. R. V. Kadison
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  3. D. Kastler
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Haag, R., Kadison, R.V. & Kastler, D. Asymptotic orbits in a free Fermi gas. Commun.Math. Phys. 33, 1–22 (1973). https://doi.org/10.1007/BF01645603

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  • DOI: https://doi.org/10.1007/BF01645603

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