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Zbl 1031.81010
Ługiewicz, P.; Olkiewicz, R.
Classical properties of infinite quantum open systems. (English)
[J] Commun. Math. Phys. 239, No.1-2, 241-259 (2003). ISSN 0010-3616; ISSN 1432-0916/e

In recent years so-called environmental decoherence has been accepted as a possible mechanism responsible for the appearance of classical features in quantum measurements.\par The present paper investigates the long time asymptotics of a class of environmentally induced dynamical semigroups on arbitrary von Neumann algebras. Such semigroup selected effective observables which are immune to decoherence and evolve reversibly. It is shown that these observables of the quantum system in the thermodynamic limit, specifically interacting with another quantum system obey classical dynamics. The importance of this result stems from the fact that typical studies of decoherence pertain to quantum systems with a finite number of degrees of freedom. Here, specific circumstances were found, under which infinite quantum systems may show up a classical behaviour.
[Piotr Garbaczewski (Zielona Gora)]

MSC 2000:: *81P15 Quantum measurement theory
81P68 Quantum computation and quantum cryptography
81R15 Operator algebra methods
46L57 Derivations etc. in $C^*$-algebras
46N50 Appl. of functional analysis in quantum physics
47D03 (Semi)groups of linear operators
81S25 Quantum stochastic calculus

Keywords: decoherence; von Neumann algebra; dynamical semigroups; thermodynamic limit; factors

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