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 s ...

, 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, qu ...

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 equilibrium, devised by Ludwig Boltzmann in 1872.Encyclopaedia of Physics (2nd Edition), R. G. Lern ...

combined with

Wigner quasiprobability distribution The Wigner quasiprobability distribution (also called the Wigner function or the Wigner–Ville distribution, after Eugene Wigner and Jean-André Ville) is a quasiprobability distribution. It was introduced by Eugene Wigner in 1932 to study qu ...

. 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 contribution ...

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. 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 i ...

. Some other topics of interest in quantum hydrodynamics are quantum turbulence, quantized vortices, second and

third sound A Rollin film, named after Bernard V. Rollin, is a 30 nm-thick liquid film of helium in the helium II state. It exhibits a "creeping" effect in response to surfaces extending past the film's level (wave propagation). Helium II can escape fro ...

, and

quantum solvent A quantum solvent is essentially a superfluid (aka a quantum liquid) used to dissolve another chemical species. Any superfluid can theoretically act as a quantum solvent, but in practice the only viable superfluid medium that can currently be u ...

s. 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) ...

(see Madelung equations). 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 t ...

( 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 superf ...

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 a ...

, 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 physic ...

References

Robert E. Wyatt Robert Eugene Wyatt is an emeritus Professor of Chemistry at the University of Texas at Austin, Department of Chemistry and Biochemistry. Work Wyatt's work is focussed on theoretical chemistry, including the quantum chemistry, quantum theory of c ...

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

See also

References