Classical Properties of Infinite Quantum Open Systems

Long time asymptotic properties of a class of environmentally induced dynamical semigroups on arbitrary von Neumann algebras are discussed. Such a semigroup selects observables, called effective observables, which are immune to the process of decoherence and so evolve in a reversible automorphic way. In particular, it is shown that effective observables of the quantum system in the thermodynamic limit, subjected to a specific interaction with another quantum system, obey classical dynamics.This work was supported by the KBN research grant no 5P03B 081 21