Mathematics of the quantum Zeno effect

We present an overview of the mathematics underlying the quantum Zeno effect. Classical, functional analytic results are put into perspective and compared with more recent ones. This yields some new insights into mathematical preconditions entailing the Zeno paradox, in particular a simplified proof of Misra's and Sudarshan's theorem. We empahsise the complex-analytic structures associated to the issue of existence of the Zeno dynamics. On grounds of the assembled material, we reason about possible future mathematical developments pertaining to the Zeno paradox and its counterpart, the anti-Zeno paradox, both of which seem to be close to complete characterisations. PACS-Klassifikation: 03.65.Xp, 03.65Db, 05.30.-d, 02.30.T . See the corresponding presentation: Schmidt, Andreas U.: "Zeno Dynamics of von Neumann Algebras" and "Zeno Dynamics in Quantum Statistical Mechanics"

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Metadaten
Author:Andreas U. Schmidt
URN:urn:nbn:de:hebis:30-11371
Document Type:Article
Language:English
Date of Publication (online):21.06.2005
Year of first Publication:2004
Publishing Institution:Univ.-Bibliothek Frankfurt am Main
Tag:Quantum Zeno Effect; Trotter's product formula; anti-Zeno effect; degenerate semigroup; measurement; modular automorphism group; operator algebra
Source:Version 5. October 2004, orig. publ. in Mathematical Physics Research on the Leading Edge, Charles V. Benton ed., Nova Science Publishers, Hauppauge NY, pp. 113-143, ISBN 1-59033-905-3, 2004 , http://www.math.uni-frankfurt.de/~aschmidt/#eprints
HeBIS PPN:191548308
Institutes:Mathematik
Dewey Decimal Classification:510 Mathematik
MSC-Classification:46L60 Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]
47D03 Groups and semigroups of linear operators (For nonlinear operators, see 47H20; see also 20M20)
81P15 Quantum measurement theory
81R15 Operator algebra methods [See also 46Lxx, 81T05]
82B10 Quantum equilibrium statistical mechanics (general)
Sammlungen:Universitätspublikationen
Licence (German):License Logo Veröffentlichungsvertrag für Publikationen ohne Print on Demand

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