condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the su ...

, quantum hydrodynamics is most generally the study of hydrodynamic-like systems which demonstrate

quantum mechanical Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qua ...

behavior. They arise in semiclassical mechanics in the study of metal and semiconductor devices, in which case being derived from the

Boltzmann transport equation The Boltzmann equation or Boltzmann transport equation (BTE) describes the statistical behaviour of a thermodynamic system not in a state of Thermodynamic equilibrium, equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics ( ...

combined with Wigner quasiprobability distribution. In

quantum chemistry Quantum chemistry, also called molecular quantum mechanics, is a branch of physical chemistry focused on the application of quantum mechanics to chemical systems, particularly towards the quantum-mechanical calculation of electronic contributions ...

they arise as solutions to chemical kinetic systems, in which case they are derived from the

Schrödinger equation The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of th ...

by way of

Madelung equations The Madelung equations, or the equations of quantum hydrodynamics, are Erwin Madelung's equivalent alternative formulation of the Schrödinger equation, written in terms of hydrodynamical variables, similar to the Navier–Stokes equations of flui ...

. An important system of study in quantum hydrodynamics is that of

superfluidity Superfluidity is the characteristic property of a fluid with zero viscosity which therefore flows without any loss of kinetic energy. When stirred, a superfluid forms vortices that continue to rotate indefinitely. Superfluidity occurs in two ...

. Some other topics of interest in quantum hydrodynamics are quantum turbulence,

quantized vortices In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. In most cases, quantum vortices are a type of topological defect exhibited in superfluids and superconductors. The existence of quantum vortices was fi ...

second The second (symbol: s) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ea ...

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 In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...

(see

). Some common experimental applications of these studies are in

liquid helium Liquid helium is a physical state of helium at very low temperatures at standard atmospheric pressures. Liquid helium may show superfluidity. At standard pressure, the chemical element helium exists in a liquid form only at the extremely low temp ...

( ³He and ⁴He), and of the interior of

neutron star A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. w ...

s and the

quark–gluon plasma Quark–gluon plasma (QGP) or quark soup is an interacting localized assembly of quarks and gluons at thermal (local kinetic) and (close to) chemical (abundance) equilibrium. The word ''plasma'' signals that free color charges are allowed. In a ...

. Many famous scientists have worked in quantum hydrodynamics, including

Richard Feynman Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superfl ...

Lev Landau Lev Davidovich Landau (russian: Лев Дави́дович Ланда́у; 22 January 1908 – 1 April 1968) was a Soviet-Azerbaijani physicist of Jewish descent who made fundamental contributions to many areas of theoretical physics. His ac ...

, and

Pyotr Kapitsa Pyotr Leonidovich Kapitsa or Peter Kapitza ( Russian: Пётр Леонидович Капица, Romanian: Petre Capița ( – 8 April 1984) was a leading Soviet physicist and Nobel laureate, best known for his work in low-temperature physics ...

References

* Robert E. Wyatt: ''Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics'' (Springer, 2005) {{Quantum field theories Quantum mechanics Lev Landau

See also

References