Classicality of the Bogoliubov Transformations and the Dynamical Casimir Effect Through the Reduced State of the Field

We use the reduced state of the field formalism (Entropy 21, 705 (2019)) to derive conditions under which a Bogoliubov transformation can be considered semi-classical. We apply this result to the dynamical Casimir effect in a moving medium (Phys. Rev. A 78, 042109 (2008)), discussing its classical and quantum features.