Environment--Induced Decoherence, Classicality and Consistency of Quantum Histories

TL;DR

This paper demonstrates that in Markovian open quantum systems, consistent histories can be constructed but are unstable unless separated by time intervals larger than the decoherence time, leading to a stable quasiclassical domain.

Contribution

It shows how to achieve stable, classical-like histories in open quantum systems by using time intervals larger than the decoherence time, clarifying environment-induced superselection.

Findings

Infinite consistent histories can be constructed in Markovian regimes.

Stability of histories requires separation by time intervals larger than decoherence time.

Pointer projectors effectively characterize the quasiclassical domain.

Abstract

We prove that for an open system, in the Markovian regime, it is always possible to construct an infinite number of non trivial sets of histories that exactly satisfy the probability sum rules. In spite of being perfectly consistent, these sets manifest a very non--classical behavior: they are quite unstable under the addition of an extra instant to the list of times defining the history. To eliminate this feature --whose implications for the interpretation of the formalism we discuss-- and to achieve the stability that characterizes the quasiclassical domain, it is necessary to separate the instants which define the history by time intervals significantly larger than the typical decoherence time. In this case environment induced superselection is very effective and the quasiclassical domain is characterized by histories constructed with ``pointer projectors''.