Objectivity in the quantum Brownian motion revisited

TL;DR

This paper revisits the conditions for objectivity in quantum Brownian motion, clarifying previous analyses and showing objectivity depends on timescales related to environmental oscillators.

Contribution

It corrects and clarifies prior spectrum broadcast structure analysis, demonstrating objectivity in finite environments depends on specific timescales and phase relations.

Findings

Objectivity cannot be fully achieved with finite environments, only approximately over certain timescales.

Objectivity is enhanced when the phase approaches π/2 due to oscillator trajectory influence.

Objectivity depends on the frequency relation between the system and environmental oscillators.

Abstract

In this article we revisit objectivity conditions for the quantum Brownian motion (QBM) model under the recoilless (Born-Oppenheimer) limit. The purpose of this study is to correct and clarify the previous objectivity analysis based on the spectrum broadcast structure (SBS). We find that the objectivity for QBM with the finite number of the environments cannot be achieved completely but only depend on a timescale. We show that a system with the finite number of environmental oscillators can the objectivity only with respect to the associated timescales defined by frequency relation between a central oscillator and environmental oscillators. In addition, our analysis of the influence of a oscillator trajectory on objectivity answers the previous unsolved question why the objectivity is enhanced as the phase gets closer to $\pi/2$.