Casimir effects for classical and quantum liquids in slab geometry: A brief review

Abstract

We analytically explore Casimir effects for confinement of classical and quantum fluctuations in slab (film) geometry (i) for classical (critical) fluctuations over 4He liquid around the Λ point, and (ii) for quantum (phonon) fluctuations of Bogoliubov excitations over an interacting Bose-Einstein condensate. We also briefly review Casimir effects for confinement of quantum vacuum fluctuations confined to two plates of different geometries.