Decoherence Induced Transition From Quantum to Classical Dynamics

Abstract

Framework for a general discussion of environmentally induced classical properties, like superselection rules, privileged basis and classical behavior, in quantum systems with both finite and infinite number of degrees of freedom is proposed. A number of examples showing that classical properties do not have to be postulated as an independent ingredient are given. In particular, it is shown that infinite open quantum systems in some cases may behave like simple classical dynamical systems.

Decoherence in infinite quantum systems

“…A notion of decoherence in the algebraic framework was first introduced into the literature in [46], after it was introduced and studied in a special case in [105] and [106]. Following [46] we will now introduce the notion of decoherence which underlies the present work.…”

“…Following [46] we will now introduce the notion of decoherence which underlies the present work. We base our considerations on the setup of Section 1.3.2.…”

“…A number of examples showing discrete as well as continuous environment induced superselection rules were given in [46].…”

“…Besides giving a new proof for a special case of a theorem of Lugiewicz and Olkiewicz [94] we will also discuss the Jacobs-de LeeuwGlicksberg splitting for quantum dynamical semigroups as well as a notion of detailed balance which will lead to a sufficient condition for a quantum dynamical semigroup to display decoherence in the sense of Blanchard and Olkiewicz. In Chapter 3 we will introduce the notion of decoherence due to Ph. Blanchard and R. Olkiewicz and, following [46], discuss its consequences. Physically its main virtue lies in a classification of the possible scenarios of decoherence and thus provides an answer to the question about the possibilities of decoherence.…”

“…In order to clarify the status of decoherence and to provide a rigorous definition, Ph. Blanchard and R. Olkiewicz suggested a notion of decoherence formulated in the algebraic framework of quantum physics in [46], drawing on earlier work of R. Olkiewicz [105]. The algebraic framework is an alternative mathematical formulation of quantum physics besides the traditional textbook formulation, which is contained in the algebraic framework as a special case.…”