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. topics: Bogoliubov transformations, dynamical Casimir effect, quantum-to-classical transitions, mesoscopic degrees of freedom