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In condensed matter physics, quantum hydrodynamics (QHD) is most generally the study of hydrodynamic-like systems which demonstrate quantum mechanical behavior. They arise in semiclassical mechanics in the study of metal and semiconductor devices, in which case being derived from the Boltzmann transport equation combined with Wigner quasiprobability distribution. In quantum chemistry they arise as solutions to chemical kinetic systems, in which case they are derived from the Schrödinger equation by way of 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, 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).

Some common experimental applications of these studies are in liquid helium (He and He), and of the interior of neutron stars and the quark–gluon plasma. Many famous scientists have worked in quantum hydrodynamics, including Richard Feynman, Lev Landau, and Pyotr Kapitsa.

See also

• Quantum turbulence
• Hydrodynamic quantum analogs

References

1. Shabbir A. Khan; Michael Bonitz (2014). "Quantum Hydrodynamics". In Michael Bonitz; Jose Lopez; Kurt Becker; Hauke Thomsen (eds.). Complex Plasmas. Springer Series on Atomic, Optical, and Plasma Physics. Vol. 82. Springer. pp. 103–152. Bibcode:2014cpsc.book.....B. doi:10.1007/978-3-319-05437-7. ISBN 978-3-319-05436-0. ISSN 1615-5653.

• Robert E. Wyatt (2005). Quantum Dynamics with Trajectories: Introduction to Quantum Hydrodynamics. Springer. ISBN 978-0-387-22964-5.

v t e Quantum field theories
Theories	Algebraic QFT Axiomatic QFT Conformal field theory Lattice field theory Noncommutative QFT Gauge theory QFT in curved spacetime String theory Supergravity Thermal QFT Topological QFT Two-dimensional conformal field theory
Models	Regular Born–Infeld Euler–Heisenberg Ginzburg–Landau Non-linear sigma Proca Quantum electrodynamics Quantum chromodynamics Quartic interaction Scalar electrodynamics Scalar chromodynamics Soler Yang–Mills Yang–Mills–Higgs Yukawa Low dimensional 2D Yang–Mills Bullough–Dodd Gross–Neveu Schwinger Sine-Gordon Thirring Thirring–Wess Toda Conformal 2D free massless scalar Liouville Minimal Polyakov Wess–Zumino–Witten Supersymmetric 4D N = 1 N = 1 super Yang–Mills Seiberg–Witten Super QCD Wess–Zumino Superconformal 6D (2,0) ABJM N = 4 super Yang–Mills Supergravity Pure 4D N = 1 4D N = 1 4D N = 8 Higher dimensional Type I Type IIA Type IIB 11D Topological BF Chern–Simons Particle theory Chiral Fermi MSSM Nambu–Jona-Lasinio NMSSM Standard Model Stueckelberg
Related	Casimir effect Cosmic string History Loop quantum gravity Loop quantum cosmology On shell and off shell Quantum chaos Quantum dynamics Quantum foam Quantum fluctuations links Quantum gravity links Quantum hadrodynamics Quantum hydrodynamics Quantum information Quantum information science links Quantum logic Quantum thermodynamics
See also: Template:Quantum mechanics topics

• Quantum mechanics
• Lev Landau