Quantum hydrodynamics (QHD) is most generally the study of hydrodynamic systems which demonstrate behavior implicit in quantum subsystems (usually quantum tunneling). They arise in semiclassical mechanics in the study of semiconductor devices, in which case being derived from the WignerBoltzmann equation. In quantum chemistry they arise as solutions to chemical kinetic systems, in which case they are derived from the Schrodinger equation by way of Bohmian mechanics or Madelung equations.
An important system of study in quantum hydrodynamics is that of superfluidity. Some other topics of interest in quantum hydrodynamics are quantum turbulence, quantized vortices, first, second and third sound, and quantum solvents. The quantum hydrodynamic equation is an equation in Bohmian mechanics, which, it turns out, has a mathematical relationship to classical fluid dynamics (see Madelung equations). This is a rich theoretical field.
Some common experimental applications of these studies are in liquid helium (He3 and He4), and of the interior of neutron stars and the quarkgluon plasma. Many famous scientists have worked in quantum hydrodynamics, including Richard Feynman, Lev Landau, and Pyotr L. Kapitsa.
