Objectivity in the quantum Brownian motion revisited

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. 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>π</mml:mi> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> .