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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Author:Andreas U. SchmidtGND
Editor:Charles V. Benton
Document Type:Part of a Book
Year of Completion:2004
Date of first Publication:2004/10/04
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2005/06/21
Tag:Quantum Zeno Effect; Trotter's product formula; anti-Zeno effect; degenerate semigroup; measurement; modular automorphism group; operator algebra
Page Number:32
First Page:1
Last Page:32
Aktualisierte Fassung, zuerst erschienen in: Charles V. Benton (Hrsg.): Mathematical physics research on the leading edge, Hauppauge NY : Nova Science, 2004, S. 113-143, ISBN 1-59033-905-3
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 ,
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC-Classification:46-XX FUNCTIONAL ANALYSIS (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx) / 46Lxx Selfadjoint operator algebras (C*-algebras, von Neumann (W*-) algebras, etc.) [See also 22D25, 47Lxx] / 46L60 Applications of selfadjoint operator algebras to physics [See also 46N50, 46N55, 47L90, 81T05, 82B10, 82C10]
47-XX OPERATOR THEORY / 47Dxx Groups and semigroups of linear operators, their generalizations and applications / 47D03 Groups and semigroups of linear operators (For nonlinear operators, see 47H20; see also 20M20)
81-XX QUANTUM THEORY / 81Pxx Axiomatics, foundations, philosophy / 81P15 Quantum measurement theory
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)
Licence (German):License LogoDeutsches Urheberrecht