Quantum hydrodynamics (QHD) is most generally the study of hydrodynamic systems which demonstrate behavior implicit in
quantumQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
subsystems (usually quantum tunneling). They arise in
semiclassical mechanicsIn physics, the adjective semiclassical has different precise meanings depending on the context. All these meanings usually refer to some approximation, limit or situation that combines quantum and classical aspects in a given problem...
in the study of semiconductor devices, in which case being derived from the
Wigner-Boltzmann equationThe Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in a fluid...
. In
quantum chemistryQuantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. The description of the electronic behavior of atoms and molecules as pertaining to their reactivity is one of the applications of quantum...
they arise as solutions to
chemical kineticChemical 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
Schrodinger equationIn physics, specifically quantum mechanics, the Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time...
by way of
Bohmian mechanicsThe Bohm or Bohmian interpretation of quantum mechanics, which Bohm called the causal, or later, the ontological interpretation, is an interpretation postulated by David Bohm in 1952 as an alternative to the standard Copenhagen interpretation. The Bohm interpretation grew out of the search for...
.
An important system of study in quantum hydrodynamics is that of superfluidity.
Quantum hydrodynamics (QHD) is most generally the study of hydrodynamic systems which demonstrate behavior implicit in
quantumQuantum mechanics is a set of principles describing the physical reality at the atomic level of matter and the subatomic . These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation...
subsystems (usually quantum tunneling). They arise in
semiclassical mechanicsIn physics, the adjective semiclassical has different precise meanings depending on the context. All these meanings usually refer to some approximation, limit or situation that combines quantum and classical aspects in a given problem...
in the study of semiconductor devices, in which case being derived from the
Wigner-Boltzmann equationThe Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of one particle in a fluid...
. In
quantum chemistryQuantum chemistry is a branch of theoretical chemistry, which applies quantum mechanics and quantum field theory to address issues and problems in chemistry. The description of the electronic behavior of atoms and molecules as pertaining to their reactivity is one of the applications of quantum...
they arise as solutions to
chemical kineticChemical 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
Schrodinger equationIn physics, specifically quantum mechanics, the Schrödinger equation is an equation that describes how the quantum state of a physical system changes in time...
by way of
Bohmian mechanicsThe Bohm or Bohmian interpretation of quantum mechanics, which Bohm called the causal, or later, the ontological interpretation, is an interpretation postulated by David Bohm in 1952 as an alternative to the standard Copenhagen interpretation. The Bohm interpretation grew out of the search for...
.
An important system of study in quantum hydrodynamics is that of superfluidity. Some other topics of interest in quantum hydrodynamics are
quantum turbulenceQuantum 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,
secondSecond sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the more usual mechanism of diffusion. This leads to a very high thermal conductivity...
and
third soundWhen a surface extends past the level of helium II, the helium II moves along the surface, seemingly against the force of gravity. It moves in a 30 nm-thick film regardless of surface material. This film is called a Rollin film...
, and
quantum solventA 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 mechanicsThe Bohm or Bohmian interpretation of quantum mechanics, which Bohm called the causal, or later, the ontological interpretation, is an interpretation postulated by David Bohm in 1952 as an alternative to the standard Copenhagen interpretation. The Bohm interpretation grew out of the search for...
, which, it turns out, has a mathematical relationship to classical
fluid dynamicsIn 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...
. This is a rich theoretical field.
Some common experimental applications of these studies are in liquid
heliumHelium is the chemical element with atomic number 2, and 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 starA neutron star is a type of 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 roughly the same mass as protons...
s and the
quark-gluon plasmaA quark–gluon plasma is a phase of quantum chromodynamics which exists at extremely high temperature and/or density. This phase consists of free quarks and gluons, which are the basic building blocks of matter...
. Many famous scientists have worked in quantum hydrodynamics, including
Richard FeynmanRichard Phillips Feynman was an American physicist known for 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 work in particle physics...
, Lev Landau, and Pyotr L. Kapitsa.