Quantum fluid

A quantum liquid is a liquid in which quantum effects occur and which can no longer be described using classical statistical mechanics .

Quantum fluids can have superfluidity and can be divided into the following according to the underlying quantum statistics :

• Fermi liquids (e.g. liquid ³ He or conduction electrons in metals in three dimensions); Luttinger's fluid , which has unusual properties, takes its place in the one-dimensional .
• Bose fluids (e.g. liquid ⁴ He).

The existence of liquid helium at any low temperature is a macroscopic quantum effect .

In 1998, Robert B. Laughlin ( USA ), Horst Ludwig Störmer ( Germany ) and Daniel Chee Tsui ( USA ) received the Nobel Prize in Physics “for their discovery of a new type of quantum fluid with fractionally charged excitations ” (essentially the fractional one Quantum Hall effect ).

Differences to classical physics

In the classical area, the kinetic energy per particle of the atomic mass is of the order of magnitude of the thermal energy ${\displaystyle m}$ ${\displaystyle k\cdot T:}$

${\displaystyle E_{\mathrm {kin} }={\frac {1}{2}}\cdot {\frac {p^{2}}{m}}\approx k\cdot T}$

With

• pulse ${\displaystyle p=m\cdot v}$
  • speed ${\displaystyle v}$
• Boltzmann's constant ${\displaystyle k}$
• absolute temperature . ${\displaystyle T}$

This results in the impulse:

${\displaystyle \Rightarrow p\simeq {\sqrt {m\cdot k\cdot T}}}$

and for the wavelength according to de Broglie :

${\displaystyle \Rightarrow \lambda =h/p\simeq {\frac {h}{\sqrt {m\cdot k\cdot T}}}}$

with Planck's quantum of action . ${\displaystyle h}$

Therefore, quantum effects are to be expected for low temperatures , which are stronger the smaller the atomic masses are. ${\displaystyle T}$ ${\displaystyle m}$

According to classical mechanics, all substances would have to crystallize or solidify in the vicinity of , since there is no longer any kinetic energy and atoms should always be arranged in a regular lattice structure due to the requirement for minimal potential energy . However, the zero-point energy in quantum liquids is so great that no transition of the system into the solid phase is allowed. ${\displaystyle T=0}$

literature

• Anthony J. Leggett: Quantum liquids: Bose condensation and Cooper pairing in condensed-matter systems. Oxford Univ. Press, Oxford 2007, ISBN 978-0-19-852643-8 .
• James F. Annett: Superconductivity, superfluids, and condensates. Oxford Univ. Press, Oxford 2009, ISBN 978-0-19-850755-0 .
• Alberto Bramati: Physics of quantum fluids: new trends and hot topics in atomic and polariton condensates. Springer, Berlin 2013, ISBN 978-3-642-37568-2 .