A quantum fluid refers to any system that exhibits quantum mechanical effects at the macroscopic level such as superfluids, superconductors, ultracold atoms, 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. However, for the cases of helium-4 and its isotope helium-3, there is a pressure range where they can remain liquid down to absolute zero because the wavelength 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 with a resistivity near zero.
Derivation Quantum mechanical effects become significant for physics in the range of the de Broglie wavelength. 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
λ = h p {\displaystyle \lambda ={\frac {h}{p}}}
where h is the Planck constant. The momentum can be found from the kinetic theory of gases, where
p = m v p = m 2 k B T m = 2 m k B T {\displaystyle p=mv_{p}=m{\sqrt {2{\frac {k_{B}T}{m}}}}={\sqrt {2mk_{B}T}}}
Here, the temperature can be found as
k B T = p 2 2 m {\displaystyle k_{B}T={\frac {p^{2}}{2m}}}
Of course, we can replace the momentum here with the momentum derived from the de Broglie wavelength like so:
k B T = h 2 2 m λ 2 {\displaystyle k_{B}T={\frac {h^{2}}{2m\lambda ^{2}}}}
Hence, we can say that quantum fluids will manifest at approximate temperature regions where λ > d {\displaystyle \lambda >d} , where d is the lattice spacing (or inter-particle spacing). Mathematically, this is stated like so:
k B T = h 2 2 m λ 2 < h 2 2 m d 2 {\displaystyle k_{B}T={\frac {h^{2}}{2m\lambda ^{2}}}<{\frac {h^{2}}{2md^{2}}}}
It is easy to see how the above definition relates to the particle density, n. We can write
k B T < h 2 2 m n 2 3 {\displaystyle k_{B}T<{\frac {h^{2}}{2m}}n^{\frac {2}{3}}}
as n = 1 d 3 {\displaystyle n={\frac {1}{d^{3}}}} for a three dimensional lattice The above temperature limit T {\displaystyle 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, T {\displaystyle T} is an estimation of the Fermi energy of the system, where processes important to phenomena such as superconductivity take place. For bosons, T {\displaystyle T} gives an estimation of the Bose-Einstein condensation temperature.
New technology for quantum fluids In recent years, there has been a significant surge in the adoption of advanced technological tools and methodologies in the investigation of quantum fluids, particularly in their preparation and characterization. These cutting-edge approaches have revolutionized the way researchers study these complex systems, offering unprecedented levels of detail and precision. Among these innovations is the employment of sophisticated simulation techniques, such as Multiphase Computational Fluid Dynamics (CFD) modeling. This powerful computational approach enables scientists to perform comprehensive analyses of superfluid behaviors and other quantum fluid phenomena, capturing intricate fluid dynamics at the quantum level that were previously inaccessible through traditional experimental methods. Furthermore, the integration of artificial intelligence (AI) and machine learning algorithms into research workflows has opened new horizons for understanding quantum fluids. These AI-driven techniques facilitate more accurate predictions of fluid properties, enhance data analysis capabilities, and optimize experimental design and procedures. By automating complex data processing and uncovering subtle patterns within large datasets, AI tools significantly accelerate discovery and deepen our insights into the underlying physics of quantum fluids. Together, these technological advancements are not only advancing our fundamental understanding of the unique properties of quantum fluids but are also catalyzing the development of innovative applications across various fields. From quantum computing and cryogenics to materials science and energy storage, the synergy of sophisticated simulation methods and AI-driven analysis promises to unlock new potentials and drive future research breakthroughs in the study of quantum fluids.
See also Bose–Einstein condensate Superconductivity Superfluidity Classical fluid Liquid helium Fermi liquid Luttinger liquid Quantum spin liquid Macroscopic quantum phenomena Topological order
References Lerner, Rita G.; Trigg, George L. (1990). Encyclopedia of Physics. VHC Publishers. ISBN 0-89573-752-3.