Asymptotic orbits in a free Fermi gas |
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Authors: | R Haag R V Kadison D Kastler |
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Institution: | (1) II. Institut für Theoretische Physik der Universität Hamburg, Germany;(2) Department of Mathematics, University of Pennsylvania, USA;(3) Centre Universitaire de Marseille-Luminy, France;(4) CPT, CNRS, 31 Chemin Joseph Aiguier, F-13 Marseille 9e, France |
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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 3 (alacunary paving of 3) 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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