Phase-Space Decoherence: a comparison between Consistent Histories and Environment Induced Superselection

TL;DR

This paper compares decoherence in quantum open systems using the Environment Induced Superselection and Consistent Histories frameworks, introducing measures of coherence and analyzing effects of temperature, time, and grain size.

Contribution

It introduces a general coherence measure for reduced density matrices and compares decoherence behavior in EIS and CH frameworks under various conditions.

Findings

EIS decoherence occurs in multiple bases and increases with bath temperature.

Consistency of histories improves with higher temperature, time, and larger final grain size.

Coherence measures show similar trends, confirming the agreement between frameworks.

Abstract

We examine the decoherence properties of a quantum open system as modeled by a quantum optical system in the Markov regime. We look for decoherence in both the Environment Induced Superselection (EIS) and Consistent Histories (CH) frameworks. We propose a general measure of the coherence of the reduced density matrix and find that EIS decoherence occurs in a number of bases for this model. The degree of ``diagonality'' achieved increases with bath temperature. We evaluate the Decoherence Functional of Consistent Histories for coarse grained phase space two-time projected histories. Using the measures proposed by Dowker and Halliwell we find that the consistency of the histories improves with increasing bath temperature, time and final grain size and decreases with initial grain size. The peaking increases with increasing grain size and decreases with increasing bath temperature. Adopting the above proposed measure of ``coherence'' to the Decoherence Functional gives similar results. The results agree in general with expectations while the anomalous dependence of the consistency on the initial grain size is discussed.