Zeno dynamics in quantum statistical mechanics

We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time beh
We study the quantum Zeno effect in quantum statistical mechanics within the operator algebraic framework. We formulate a condition for the appearance of the effect in W*-dynamical systems, in terms of the short-time behaviour of the dynamics. Examples of quantum spin systems show that this condition can be effectively applied to quantum statistical mechanical models. Furthermore, we derive an explicit form of the Zeno generator, and use it to construct Gibbs equilibrium states for the Zeno dynamics. As a concrete example, we consider the X-Y model, for which we show that a frequent measurement at a microscopic level, e.g. a single lattice site, can produce a macroscopic effect in changing the global equilibrium. PACS - Klassifikation: 03.65.Xp, 05.30.-d, 02.30. See the corresponding papers: Schmidt, Andreas U.: "Zeno Dynamics of von Neumann Algebras" and "Mathematics of the Quantum Zeno Effect" and the talk "Zeno Dynamics in Quantum Statistical Mechanics" - http://publikationen.ub.uni-frankfurt.de/volltexte/2005/1167/
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Metadaten
Author:Andreas U. Schmidt
URN:urn:nbn:de:hebis:30-11361
Document Type:Article
Language:English
Date of Publication (online):2005/06/21
Year of first Publication:2004
Publishing Institution:Univ.-Bibliothek Frankfurt am Main
Release Date:2005/06/21
Tag:Quantum Zeno dynamics; W*-dynamical system; X-Y model; quantum spin systems; return to equilibrium
Source:Version 5. 10. 2004: Revision including published corrigendum, orig. publ. in Journal of Physics A: Mathematical and General 36 (January 2003) 1135-1148 , Corrigendum: ibid. 37 (June 2004) 11309-11310 , http://www.math.uni-frankfurt.de/~aschmidt/#eprints
HeBIS PPN:192302779
Institutes:Mathematik
Dewey Decimal Classification:510 Mathematik
MSC-Classification:81R15 Operator algebra methods [See also 46Lxx, 81T05]
82B10 Quantum equilibrium statistical mechanics (general)
82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
Sammlungen:Universitätspublikationen
Licence (German):License Logo Veröffentlichungsvertrag für Publikationen

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