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Classical properties of infinite quantum open systems. (English) Zbl 1031.81010

In recent years so-called environmental decoherence has been accepted as a possible mechanism responsible for the appearance of classical features in quantum measurements.

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.

81P15Quantum measurement theory
81P68Quantum computation
81R15Operator algebra methods (quantum theory)
46L57Derivations, dissipations and positive semigroups in C * -algebras
46N50Applications of functional analysis in quantum physics
47D03(Semi)groups of linear operators
81S25Quantum stochastic calculus