Action scales for quantum decoherence and their relation to structures in phase space

Abstract

A characteristic action $ΔS$ is defined whose magnitude determines some properties of the expectation value of a general quantum displacement operator. These properties are related to the capability of a given environmental `monitoring' system to induce decoherence in quantum systems coupled to it. We show that the scale for effective decoherence is given by $ΔS\approx\hbar$. We relate this characteristic action with a complementary quantity, $ΔZ$, and analyse their connection with the main features of the pattern of structures developed by the environmental state in different phase space representations. The relevance of the $ΔS$-action scale is illustrated using both a model quantum system solved numerically and a set of model quantum systems for which analytical expressions for the time-averaged expectation value of the displacement operator are obtained explicitly.

12 pages, 3 figures