A quantum fluid refers to any system that exhibits quantum mechanical effects at the macroscopic level such as

superfluid 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 ...

s, superconductors,

ultracold atoms Ultracold atoms are atoms that are maintained at temperatures close to 0 kelvin (absolute zero), typically below several tens of microkelvin (µK). At these temperatures the atom's quantum-mechanical properties become important. To reach such low ...

, etc. Typically, quantum fluids arise in situations where both quantum mechanical effects and quantum statistical effects are significant. Most matter is either solid or gaseous (at low densities) near

absolute zero Absolute zero is the lowest limit of the thermodynamic temperature scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...

. However, for the cases of

helium-4 Helium-4 () is a stable isotope of the element helium. It is by far the more abundant of the two naturally occurring isotopes of helium, making up about 99.99986% of the helium on Earth. Its nucleus is identical to an alpha particle, and consis ...

and its isotope

helium-3 Helium-3 (3He see also helion) is a light, stable isotope of helium with two protons and one neutron (the most common isotope, helium-4, having two protons and two neutrons in contrast). Other than protium (ordinary hydrogen), helium-3 is the ...

, there is a pressure range where they can remain liquid down to absolute zero because the amplitude of the quantum fluctuations experienced by the helium atoms is larger than the inter-atomic distances. In the case of solid quantum fluids, it is only a fraction of its electrons or protons that behave like a “fluid”. One prominent example is that of superconductivity where quasi-particles made up of pairs of electrons and a phonon act as bosons which are then capable of collapsing into the ground state to establish a

supercurrent A supercurrent is a superconducting current, that is, electric current which flows without dissipation in a superconductor. Under certain conditions, an electric current can also flow without dissipation in microscopically small non-superconductin ...

with a resistivity near zero.

Derivation

Quantum mechanical effects become significant for physics in the range of the

de Broglie wavelength Matter waves are a central part of the theory of quantum mechanics, being an example of wave–particle duality. All matter exhibits wave-like behavior. For example, a beam of electrons can be diffracted just like a beam of light or a water wave ...

. For condensed matter, this is when the de Broglie wavelength of a particle is greater than the spacing between the particles in the lattice that comprises the matter. The de Broglie wavelength associated with a massive particle is :

\lambda = \frac

where h is the Planck constant. The momentum can be found from the

kinetic theory of gases Kinetic (Ancient Greek: κίνησις “kinesis”, movement or to move) may refer to: * Kinetic theory, describing a gas as particles in random motion * Kinetic energy, the energy of an object that it possesses due to its motion Art and enter ...

, where :

p = mv_p = m\sqrt = \sqrt

Here, the temperature can be found as :

k_BT = \frac

Of course, we can replace the momentum here with the momentum derived from the de Broglie wavelength like so: :

k_BT = \frac

Hence, we can say that quantum fluids will manifest at approximate temperature regions where

\lambda > d

, where d is the lattice spacing (or inter-particle spacing). Mathematically, this is stated like so: :

k_B T = \frac < \frac

It is easy to see how the above definition relates to the particle density, n. We can write :

k_B T < \fracn^

d = \frac

for a three dimensional lattice The above temperature limit

T

has different meaning depending on the quantum statistics followed by each system, but generally refers to the point at which the system manifests quantum fluid properties. For a system of

fermions In particle physics, a fermion is a particle that follows Fermi–Dirac statistics. Generally, it has a half-odd-integer spin: spin , spin , etc. In addition, these particles obey the Pauli exclusion principle. Fermions include all quarks and ...

T

is an estimation of the

Fermi energy The Fermi energy is a concept in quantum mechanics usually referring to the energy difference between the highest and lowest occupied single-particle states in a quantum system of non-interacting fermions at absolute zero temperature. In a Fermi ga ...

of the system, where processes important to phenomena such as superconductivity take place. For

bosons In particle physics, a boson ( ) is a subatomic particle whose spin quantum number has an integer value (0,1,2 ...). Bosons form one of the two fundamental classes of subatomic particle, the other being fermions, which have odd half-integer spi ...

T

gives an estimation of the Bose-Einstein condensation temperature.

References

#{{cite book , last1 = Lerner , author1-link = Rita G. Lerner , first1 = Rita G. , last2 = Trigg , first2 = George L. , title = Encyclopedia of Physics , publisher = VHC Publishers , year = 1990 , isbn = 0-89573-752-3 , url-access = registration , url = https://archive.org/details/encyclopediaofph00lern Condensed matter physics Quantum phases Exotic matter

Derivation

See also

References