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 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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Author:Andreas U. SchmidtGND
Document Type:Article
Year of Completion:2004
Date of first Publication:2004/10/05
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2005/06/21
Tag:Quantum Zeno dynamics; W*-dynamical system; X-Y model; quantum spin systems; return to equilibrium
Page Number:15
First Page:1
Last Page:15
Aktualisierte Fassung, zuerst erschienen in: Journal of physics. A, Mathematical and general, 36.2003, S. 1135-1148, enthält Corrigendum erschienen in: Journal of physics. A, Mathematical and general, 37.2004, S. 11309-11310
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
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:81-XX QUANTUM THEORY / 81Rxx Groups and algebras in quantum theory / 81R15 Operator algebra methods [See also 46Lxx, 81T05]
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Bxx Equilibrium statistical mechanics / 82B10 Quantum equilibrium statistical mechanics (general)
82-XX STATISTICAL MECHANICS, STRUCTURE OF MATTER / 82Cxx Time-dependent statistical mechanics (dynamic and nonequilibrium) / 82C10 Quantum dynamics and nonequilibrium statistical mechanics (general)
Licence (German):License LogoDeutsches Urheberrecht