Quantum hydrodynamics is most generally the study of hydrodynamic systems which demonstrate behavior implicit in quantum

Quantum mechanics

Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

 subsystems (usually quantum tunneling). They arise in semiclassical mechanics in the study of semiconductor devices, in which case being derived from the Wigner-Boltzmann equation

Boltzmann equation

The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in rarefied gas...

. In quantum chemistry

Quantum chemistry

Quantum chemistry is a branch of chemistry whose primary focus is the application of quantum mechanics in physical models and experiments of chemical systems...

 they arise as solutions to chemical kinetic

Chemical kinetics

Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition...

 systems, in which case they are derived from the Schrödinger equation

Schrödinger equation

The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics , it is an equation that describes how the quantum state of a physical system changes in time....

 by way of Madelung equations

Madelung equations

The Madelung equations are Erwin Madelung's alternative formulation of the Schrödinger equation.-Equations:The Madelung equations are quantum Euler equations:\partial_t \rho+\nabla\cdot=0,...

.

An important system of study in quantum hydrodynamics is that of superfluidity. Some other topics of interest in quantum hydrodynamics are quantum turbulence

Quantum turbulence

Quantum turbulence is the name given to the turbulent flow - the chaotic motion of a fluid at high flow rates - of quantum fluids, such as superfluids which have been cooled to a fraction of a degree above absolute zero.-Introduction:...

, quantized vortices, first, second

Second sound

Second sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the more usual mechanism of diffusion. Heat takes the place of pressure in normal sound waves. This leads to a very high thermal conductivity...

 and third sound, and quantum solvent

Quantum solvent

A quantum solvent is essentially a superfluid used to dissolve another chemical species. Any superfluid can theoretically act as a quantum solvent, however in practice the only viable superfluid medium that can currently be used is helium-4, and it has been successfully accomplished in controlled...

s. The quantum hydrodynamic equation is an equation in Bohmian mechanics

Bohm interpretation

The de Broglie–Bohm theory, also called the pilot-wave theory, Bohmian mechanics, and the causal interpretation, is an interpretation of quantum theory. In addition to a wavefunction on the space of all possible configurations, it also includes an actual configuration, even in situations where...

, which, it turns out, has a mathematical relationship to classical fluid dynamics

Fluid dynamics

In physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

 (see Madelung equations

Madelung equations

The Madelung equations are Erwin Madelung's alternative formulation of the Schrödinger equation.-Equations:The Madelung equations are quantum Euler equations:\partial_t \rho+\nabla\cdot=0,...

). This is a rich theoretical field.

Some common experimental applications of these studies are in liquid helium

Helium

Helium is the chemical element with atomic number 2 and an atomic weight of 4.002602, which is represented by the symbol He. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas that heads the noble gas group in the periodic table...

 (He-3 and He-4), and of the interior of neutron star

Neutron star

A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...

s and the quark-gluon plasma

Quark-gluon plasma

A quark–gluon plasma or quark soup is a phase of quantum chromodynamics which exists at extremely high temperature and/or density. This phase consists of asymptotically free quarks and gluons, which are several of the basic building blocks of matter...

. Many famous scientists have worked in quantum hydrodynamics, including Richard Feynman

Richard Feynman

Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...

, Lev Landau, and Pyotr L. Kapitsa.