  We discuss the hydrodynamic representation of a wide class of quantum media
exhibiting similar elementary excitations and dispersion properties. The
representation covers quantum systems characterized by any type of (long-range)
self-interaction, associated with an arbitrary potential. It also accounts for
possible nonlinearities, which may arise e.g., due to short-range interactions
(collisions) in the case of bosons, or from the Pauli exclusion principle for
fermions. The approach equally applies to various physical scenarios, such as
self-gravitating quantum media (e.g., dark matter), quantum plasmas,
Bose-Einstein condensates, and non-condensed cold atomic clouds. We discuss the
formal analogies that can be drawn between these different systems and how they
can be used to realize laboratory experiments emulating gravitational
phenomena, especially in the context of alternative theories of gravity. To
substantiate our point, we elaborate more closely on the case of non-minimal
matter-curvature coupling gravity theories.
