Superfluid helium-4 is the
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 ...
form 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 ...
, an
isotope
Isotopes are two or more types of atoms that have the same atomic number (number of protons in their nuclei) and position in the periodic table (and hence belong to the same chemical element), and that differ in nucleon numbers (mass numb ...
of the element
helium
Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert, monatomic gas and the first in the noble gas group in the periodic table. ...
. A superfluid is a
state of matter
In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, ...
in which matter behaves like a
fluid with zero
viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water.
Viscosity quantifies the inte ...
. The substance, which looks like a normal liquid, flows without friction past any surface, which allows it to continue to circulate over obstructions and through pores in containers which hold it, subject only to its own
inertia
Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...
.
The formation of the superfluid is known to be related to the formation of a
Bose–Einstein condensate
In condensed matter physics, a Bose–Einstein condensate (BEC) is a state of matter that is typically formed when a gas of bosons at very low densities is cooled to temperatures very close to absolute zero (−273.15 °C or −459.6 ...
. This is made obvious by the fact that superfluidity occurs in liquid helium-4 at far higher temperatures than it does in
helium-3. Each atom of helium-4 is a
boson
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 ...
particle, by virtue of its zero spin. Helium-3, however, is a
fermion particle, which can form bosons only by pairing with itself at much lower temperatures, in a process similar to the electron pairing in
superconductivity.
History
Known as a major facet in the study of
quantum hydrodynamics
In condensed matter physics, quantum hydrodynamics 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 wh ...
and
macroscopic quantum phenomena
Macroscopic quantum phenomena are processes showing quantum behavior at the macroscopic scale, rather than at the atomic scale where quantum effects are prevalent. The best-known examples of macroscopic quantum phenomena are superfluidity and su ...
, the
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 ...
effect was discovered by
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 physics ...
and
John F. Allen, and
Don Misener Don Misener (A.D. Misener) (1911-1996) was a physicist. Along with Pyotr Leonidovich Kapitsa and John F. Allen, Misener discovered the superfluid phase of matter in 1937.
Misener was a graduate student at the University of Toronto in 1935. He j ...
in 1937. It has since been described through
phenomenological and microscopic theories.
In the 1950s, Hall and Vinen performed experiments establishing the existence of
quantized vortex lines in superfluid helium. In the 1960s, Rayfield and Reif established the existence of quantized vortex rings. Packard has observed the intersection of vortex lines with the free surface of the fluid,
and Avenel and Varoquaux have studied the
Josephson effect
In physics, the Josephson effect is a phenomenon that occurs when two superconductors are placed in proximity, with some barrier or restriction between them. It is an example of a macroscopic quantum phenomenon, where the effects of quantum mec ...
in superfluid helium-4. In 2006, a group at the University of Maryland visualized quantized vortices by using small tracer particles of
solid hydrogen
Solid hydrogen is the solid state of the element hydrogen, achieved by decreasing the temperature below hydrogen's melting point of . It was collected for the first time by James Dewar in 1899 and published with the title "Sur la solidification de ...
.
In the early 2000s, physicists created a
Fermionic condensate
A fermionic condensate or Fermi–Dirac condensate is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic atoms under similar cond ...
from pairs of ultra-cold fermionic atoms. Under certain conditions, fermion pairs form
diatomic molecule
Diatomic molecules () are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen () or oxygen (), then it is said to be homonuclear. O ...
s and undergo
Bose–Einstein condensation Bose–Einstein may refer to:
* Bose–Einstein condensate
** Bose–Einstein condensation (network theory)
* Bose–Einstein correlations
* Bose–Einstein statistics
In quantum statistics, Bose–Einstein statistics (B–E statistics) describe ...
. At the other limit, the fermions (most notably superconducting electrons) form
Cooper pairs
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
which also exhibit superfluidity. This work with ultra-cold atomic gases has allowed scientists to study the region in between these two extremes, known as the
BEC-BCS crossover.
Supersolids may also have been discovered in 2004 by physicists at
Penn State University. When helium-4 is cooled below about 200 mK under high pressures, a fraction (≈1%) of the solid appears to become superfluid. By quench cooling or lengthening the
annealing time, thus increasing or decreasing the defect density respectively, it was shown, via torsional oscillator experiment, that the supersolid fraction could be made to range from 20% to completely non-existent. This suggested that the supersolid nature of helium-4 is not intrinsic to helium-4 but a property of helium-4 and disorder. Some emerging theories posit that the supersolid signal observed in helium-4 was actually an observation of either a
superglass
A superglass is a phase of matter which is characterized (at the same time) by superfluidity and a frozen amorphous structure.
J.C. Séamus Davis theorised that frozen helium-4
Helium-4 () is a stable isotope of the element helium. It is by ...
state or intrinsically superfluid grain boundaries in the helium-4 crystal.
Applications
Recently in the field of chemistry, superfluid helium-4 has been successfully used in
spectroscopic
Spectroscopy is the field of study that measures and interprets the electromagnetic spectra that result from the interaction between electromagnetic radiation and matter as a function of the wavelength or frequency of the radiation. Matter wa ...
techniques as a
quantum solvent. Referred to as superfluid helium droplet spectroscopy (SHeDS), it is of great interest in studies of gas molecules, as a single molecule solvated in a superfluid medium allows a molecule to have effective rotational freedom, allowing it to behave similarly to how it would in the "gas" phase. Droplets of superfluid helium also have a characteristic temperature of about 0.4 K which cools the solvated molecule(s) to its ground or nearly ground
rovibronic state.
Superfluids are also used in high-precision devices such as
gyroscopes, which allow the measurement of some theoretically predicted gravitational effects (for an example, see
Gravity Probe B
Gravity Probe B (GP-B) was a satellite-based experiment to test two unverified predictions of general relativity: the geodetic effect and frame-dragging. This was to be accomplished by measuring, very precisely, tiny changes in the direction of ...
).
The Infrared Astronomical Satellite
IRAS
The Infrared Astronomical Satellite (Dutch: ''Infrarood Astronomische Satelliet'') (IRAS) was the first space telescope to perform a survey of the entire night sky at infrared wavelengths. Launched on 25 January 1983, its mission lasted ten mo ...
, launched in January 1983 to gather infrared data was cooled by 73 kilograms of superfluid helium, maintaining a temperature of . When used in conjunction with helium-3, temperatures as low as 40 mK are routinely achieved in extreme low temperature experiments. The helium-3, in liquid state at 3.2 K, can be evaporated into the superfluid helium-4, where it acts as a gas due to the latter's properties as a Bose–Einstein condensate. This evaporation pulls energy from the overall system, which can be pumped out in a way completely analogous to normal refrigeration techniques.
Superfluid-helium technology is used to extend the temperature range of
cryocoolers
A refrigerator designed to reach cryogenic temperatures (below ) is often called a cryocooler. The term is most often used for smaller systems, typically table-top size, with input powers less than about 20 kW. Some can have input powers as lo ...
to lower temperatures. So far the limit is 1.19 K, but there is a potential to reach 0.7 K.
Properties
Superfluids, such as helium-4 below the lambda point, exhibit many unusual properties. A superfluid acts as if it were a mixture of a normal component, with all the properties of a normal fluid, and a superfluid component. The superfluid component has zero viscosity and zero entropy. Application of heat to a spot in superfluid helium results in a flow of the normal component which takes care of the heat transport at relatively high velocity (up to 20 cm/s) which leads to a very high effective thermal conductivity.
Film flow
Many ordinary liquids, like alcohol or petroleum, creep up solid walls, driven by their surface tension. Liquid helium also has this property, but, in the case of He-II, the flow of the liquid in the layer is not restricted by its viscosity but by a critical velocity which is about 20 cm/s. This is a fairly high velocity so superfluid helium can flow relatively easily up the wall of containers, over the top, and down to the same level as the surface of the liquid inside the container, in a siphon effect. It was, however, observed, that the flow through nanoporous membrane becomes restricted if the pore diameter is less than 0.7 nm (i.e. roughly three times the classical diameter of helium atom), suggesting the unusual hydrodynamic properties of He arise at larger scale than in the classical liquid helium.
Rotation
Another fundamental property becomes visible if a superfluid is placed in a rotating container. Instead of rotating uniformly with the container, the rotating state consists of quantized vortices. That is, when the container is rotated at speeds below the first critical angular velocity, the liquid remains perfectly stationary. Once the first critical angular velocity is reached, the superfluid will form a vortex. The vortex strength is quantized, that is, a superfluid can only spin at certain "allowed" values. Rotation in a normal fluid, like water, is not quantized. If the rotation speed is increased more and more quantized vortices will be formed which arrange in nice patterns similar to the
Abrikosov lattice in a superconductor.
Comparison with helium-3
Although the phenomenologies of the superfluid states of helium-4 and helium-3 are very similar, the microscopic details of the transitions are very different. Helium-4 atoms are bosons, and their superfluidity can be understood in terms of the
Bose–Einstein statistics
In quantum statistics, Bose–Einstein statistics (B–E statistics) describes one of two possible ways in which a collection of non-interacting, indistinguishable particles may occupy a set of available discrete energy states at thermodynamic ...
that they obey. Specifically, the superfluidity of helium-4 can be regarded as a consequence of Bose–Einstein condensation in an interacting system. On the other hand, helium-3 atoms are fermions, and the superfluid transition in this system is described by a generalization of the
BCS theory
BCS theory or Bardeen–Cooper–Schrieffer theory (named after John Bardeen, Leon Cooper, and John Robert Schrieffer) is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes sup ...
of superconductivity. In it,
Cooper pair
In condensed matter physics, a Cooper pair or BCS pair (Bardeen–Cooper–Schrieffer pair) is a pair of electrons (or other fermions) bound together at low temperatures in a certain manner first described in 1956 by American physicist Leon Coope ...
ing takes place between atoms rather than
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no ...
s, and the attractive interaction between them is mediated by
spin fluctuations rather than
phonons. (See
fermion condensate
A fermionic condensate or Fermi–Dirac condensate is a superfluid phase formed by fermionic particles at low temperatures. It is closely related to the Bose–Einstein condensate, a superfluid phase formed by bosonic atoms under similar condi ...
.) A unified description of superconductivity and superfluidity is possible in terms of
gauge symmetry breaking.
Macroscopic theory
Thermodynamics
![Normal and superfluid density 01](https://upload.wikimedia.org/wikipedia/commons/6/6c/Normal_and_superfluid_density_01.jpg)
Figure 1 is the
phase diagram of
4He. It is a pressure-temperature (p-T) diagram indicating the solid and liquid regions separated by the melting curve (between the liquid and solid state) and the liquid and gas region, separated by the vapor-pressure line. This latter ends in the
critical point where the difference between gas and liquid disappears. The diagram shows the remarkable property that
4He is liquid even at
absolute zero.
4He is only solid at pressures above 25 bar.
Figure 1 also shows the λ-line. This is the line that separates two fluid regions in the phase diagram indicated by He-I and He-II. In the He-I region the helium behaves like a normal fluid; in the He-II region the helium is superfluid.
The name lambda-line comes from the specific heat – temperature plot which has the shape of the Greek letter λ. See figure 2, which shows a peak at 2.172 K, the so-called λ-point of
4He.
Below the lambda line the liquid can be described by the so-called two-fluid model. It behaves as if it consists of two components: a normal component, which behaves like a normal fluid, and a superfluid component with zero viscosity and zero entropy. The ratios of the respective densities ρ
n/ρ and ρ
s/ρ, with ρ
n (ρ
s) the density of the normal (superfluid) component, and ρ (the total density), depends on temperature and is represented in figure 3. By lowering the temperature, the fraction of the superfluid density increases from zero at ''T''
λ to one at zero kelvins. Below 1 K the helium is almost completely superfluid.
It is possible to create density waves of the normal component (and hence of the superfluid component since ρ
n + ρ
s = constant) which are similar to ordinary sound waves. This effect is called
second sound
Second sound is a quantum mechanical phenomenon in which heat transfer occurs by wave-like motion, rather than by the more usual mechanism of diffusion. Its presence leads to a very high thermal conductivity. It is known as "second sound" because t ...
. Due to the temperature dependence of ρ
n (figure 3) these waves in ρ
n are also temperature waves.
Superfluid hydrodynamics
The equation of motion for the superfluid component, in a somewhat simplified form, is given by Newton's law
:
The mass ''M''
4 is the molar mass of
4He, and
is the velocity of the superfluid component. The time derivative is the so-called hydrodynamic derivative, i.e. the rate of increase of the velocity when moving with the fluid. In the case of superfluid
4He in the gravitational field the force is given by
:
In this expression μ is the molar chemical potential, ''g'' the gravitational acceleration, and ''z'' the vertical coordinate. Thus we get the equation which states that the thermodynamics of a certain constant will be amplified by the force of the natural gravitational acceleration
Eq. only holds if ''v''
s is below a certain critical value, which usually is determined by the diameter of the flow channel.
In classical mechanics the force is often the gradient of a potential energy. Eq. shows that, in the case of the superfluid component, the force contains a term due to the gradient of the
chemical potential
In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
. This is the origin of the remarkable properties of He-II such as the fountain effect.
Fountain pressure
In order to rewrite Eq. in more familiar form we use the general formula
Here ''S''
m is the molar entropy and ''V''
m the molar volume. With Eq. μ(''p'',''T'') can be found by a line integration in the p-T plane. First we integrate from the origin (0,0) to (''p'',0), so at ''T'' =0. Next we integrate from (''p'',0) to (''p'',''T''), so with constant pressure (see figure 6). In the first integral d''T''=0 and in the second d''p''=0. With Eq. we obtain
We are interested only in cases where ''p'' is small so that ''V''
m is practically constant. So
where ''V''
m0 is the molar volume of the liquid at ''T'' =0 and ''p'' =0. The other term in Eq. is also written as a product of ''V''
m0 and a quantity ''p''
f which has the dimension of pressure
The pressure ''p''
f is called the fountain pressure. It can be calculated from the entropy of
4He which, in turn, can be calculated from the heat capacity. For ''T'' =''T''
λ the fountain pressure is equal to 0.692 bar. With a density of liquid helium of 125 kg/m
3 and ''g'' = 9.8 m/s
2 this corresponds with a liquid-helium column of 56 meter height. So, in many experiments, the fountain pressure has a bigger effect on the motion of the superfluid helium than gravity.
With Eqs. and , Eq. obtains the form
Substitution of Eq. in gives
with ρ
0 = ''M''
4/''V''
m0 the density of liquid
4He at zero pressure and temperature.
Eq. shows that the superfluid component is accelerated by gradients in the pressure and in the gravitational field, as usual, but also by a gradient in the fountain pressure.
So far Eq. has only mathematical meaning, but in special experimental arrangements ''p''
f can show up as a real pressure. Figure 7 shows two vessels both containing He-II. The left vessel is supposed to be at zero kelvins (''T''
l=0) and zero pressure (''p''
l = 0). The vessels are connected by a so-called superleak. This is a tube, filled with a very fine powder, so the flow of the normal component is blocked. However, the superfluid component can flow through this superleak without any problem (below a critical velocity of about 20 cm/s). In the steady state ''v''
s=0 so Eq. implies
where the index l (r) applies to the left (right) side of the superleak. In this particular case ''p''
l = 0, ''z''
l = ''z''
r, and ''p''
fl = 0 (since ''T''
l = 0). Consequently,
:
This means that the pressure in the right vessel is equal to the fountain pressure at ''T''
r.
In an experiment, arranged as in figure 8, a fountain can be created. The fountain effect is used to drive the circulation of
3He in dilution refrigerators.
Heat transport
Figure 9 depicts a heat-conduction experiment between two temperatures ''T''
H and ''T''
L connected by a tube filled with He-II. When heat is applied to the hot end a pressure builds up at the hot end according to Eq.. This pressure drives the normal component from the hot end to the cold end according to
Here η
n is the viscosity of the normal component, ''Z'' some geometrical factor, and
the volume flow. The normal flow is balanced by a flow of the superfluid component from the cold to the hot end. At the end sections a normal to superfluid conversion takes place and vice versa. So heat is transported, not by heat conduction, but by convection. This kind of heat transport is very effective, so the thermal conductivity of He-II is very much better than the best materials. The situation is comparable with
heat pipe
A heat pipe is a heat-transfer device that employs phase transition to transfer heat between two solid interfaces.
At the hot interface of a heat pipe, a volatile liquid in contact with a thermally conductive solid surface turns into a vapor b ...
s where heat is transported via gas–liquid conversion. The high thermal conductivity of He-II is applied for stabilizing superconducting magnets such as in the
Large Hadron Collider at
CERN.
Microscopic theory
Landau two-fluid approach
L. D. Landau's phenomenological and semi-microscopic theory of superfluidity of helium-4 earned him the Nobel Prize in physics, in 1962. Assuming that sound waves are the most important excitations in helium-4 at low temperatures, he showed that helium-4 flowing past a wall would not spontaneously create excitations if the flow velocity was less than the sound velocity. In this model, the sound velocity is the "critical velocity" above which superfluidity is destroyed. (Helium-4 actually has a lower flow velocity than the sound velocity, but this model is useful to illustrate the concept.) Landau also showed that the sound wave and other excitations could equilibrate with one another and flow separately from the rest of the helium-4, which is known as the "condensate".
From the momentum and flow velocity of the excitations he could then define a "normal fluid" density, which is zero at zero temperature and increases with temperature. At the so-called Lambda temperature, where the normal fluid density equals the total density, the helium-4 is no longer superfluid.
To explain the early specific heat data on superfluid helium-4, Landau posited the existence of a type of excitation he called a "
roton
In theoretical physics, a roton is an elementary excitation, or quasiparticle, seen in superfluid helium-4 and Bose–Einstein condensates with long-range dipolar interactions or spin-orbit coupling. The dispersion relation of elementary excita ...
", but as better data became available he considered that the "roton" was the same as a high momentum version of sound.
The Landau theory does not elaborate on the microscopic structure of the superfluid component of liquid helium. The first attempts to create a microscopic theory of the superfluid component itself were done by London and subsequently, Tisza.
Other microscopical models have been proposed by different authors. Their main objective is to derive the form of the inter-particle potential between helium atoms in superfluid state from first principles of
quantum mechanics
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 chemistr ...
.
To date, a number of models of this kind have been proposed, including: models with vortex rings, hard-sphere models, and Gaussian cluster theories.
Vortex ring model
Landau thought that vorticity entered superfluid helium-4 by vortex sheets, but such sheets have since been shown to be unstable.
Lars Onsager
Lars Onsager (November 27, 1903 – October 5, 1976) was a Norwegian-born American physical chemist and theoretical physicist. He held the Gibbs Professorship of Theoretical Chemistry at Yale University. He was awarded the Nobel Prize in C ...
and, later independently, Feynman showed that vorticity enters by quantized vortex lines. They also developed the idea of
quantum vortex
In physics, a quantum vortex represents a quantized flux circulation of some physical quantity. In most cases, quantum vortices are a type of topological defect exhibited in superfluids and superconductors. The existence of quantum vortices was ...
rings.
Arie Bijl
Arie Bijl (Maassluis, 23 December 1908 – Hamburg- Neuengamme, 2 January 1945) was a Dutch theoretical physicist and resistance man.
Arie Bijl was the youngest child of Simon Bijl (1869–1951), owner of a milk factory, and Willemijntje van der ...
in the 1940s,
and
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 superfl ...
around 1955, developed microscopic theories for the roton, which was shortly observed with inelastic neutron experiments by Palevsky. Later on, Feynman admitted that his model gives only qualitative agreement with experiment.
Hard-sphere models
The models are based on the simplified form of the inter-particle potential between helium-4 atoms in the superfluid phase. Namely, the potential is assumed to be of the hard-sphere type.
In these models the famous Landau (roton) spectrum of excitations is qualitatively reproduced.
Gaussian cluster approach
This is a two-scale approach which describes the superfluid component of liquid helium-4. It
consists of two
nested models linked via parametric space. The short-wavelength part describes the interior structure of the
fluid element In fluid dynamics, within the framework of continuum mechanics, a fluid parcel is a very small amount of fluid, identifiable throughout its dynamic history while moving with the fluid flow. As it moves, the mass of a fluid parcel remains constan ...
using a non-perturbative approach based on the
Logarithmic Schrödinger equation In theoretical physics, the logarithmic Schrödinger equation (sometimes abbreviated as LNSE or LogSE) is one of the nonlinear modifications of Schrödinger's equation. It is a classical wave equation with applications to extensions of quantum mech ...
; it suggests the
Gaussian
Carl Friedrich Gauss (1777–1855) is the eponym of all of the topics listed below.
There are over 100 topics all named after this German mathematician and scientist, all in the fields of mathematics, physics, and astronomy. The English eponymo ...
-like behaviour of the element's interior density and interparticle interaction potential. The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions. The approach provides a unified description of the
phonon,
maxon and
roton
In theoretical physics, a roton is an elementary excitation, or quasiparticle, seen in superfluid helium-4 and Bose–Einstein condensates with long-range dipolar interactions or spin-orbit coupling. The dispersion relation of elementary excita ...
excitations, and has noteworthy agreement with experiment: with one essential parameter to fit one reproduces at high accuracy the Landau roton spectrum,
sound velocity
The speed of sound is the distance travelled per unit of time by a sound wave as it propagates through an elastic medium. At , the speed of sound in air is about , or one kilometre in or one mile in . It depends strongly on temperature as wel ...
and
structure factor
In condensed matter physics and crystallography, the static structure factor (or structure factor for short) is a mathematical description of how a material scatters incident radiation. The structure factor is a critical tool in the interpretation ...
of superfluid helium-4.
This model utilizes the general theory of quantum Bose liquids with logarithmic nonlinearities which is based on introducing a
dissipative
In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy ( internal, bulk flow kinetic, or system potential) transforms from an initial form to ...
-type contribution to energy related to the quantum
Everett–Hirschman entropy function.
Hugh Everett
Hugh Everett III (; November 11, 1930 – July 19, 1982) was an American physicist who first proposed the many-worlds interpretation (MWI) of quantum physics, which he termed his "relative state" formulation. In contrast to the then-dominant Cope ...
, III. The Many-Worlds Interpretation of Quantum Mechanics: the theory of the universal wave function
Everett's Dissertation
/ref>[ I.I. Hirschman, Jr., ''A note on entropy''. American Journal of Mathematics (1957) pp. 152–156]
See also
* Douglas D. Osheroff
Douglas Dean Osheroff (born August 1, 1945) is an American physicist known for his work in experimental condensed matter physics, in particular for his co-discovery of superfluidity in Helium-3. For his contributions he shared the 1996 Nobel Pr ...
* Large Hadron Collider
* London moment
The London moment (after Fritz London) is a quantum-mechanical phenomenon whereby a spinning superconductor generates a magnetic field whose axis lines up exactly with the spin axis.
The term may also refer to the magnetic moment of any rotati ...
* Polariton superfluid Polariton superfluid is predicted to be a state of the exciton-polaritons system that combines the characteristics of lasers with those of excellent electrical conductors. Researchers look for this state in a solid state optical microcavity coupled ...
* Quantum acoustics
* Quantum gyroscope
A quantum gyroscope is a very sensitive device to measure angular rotation based on quantum mechanical principles. The first of these was built by Richard Packard and his colleagues at the University of California, Berkeley. The extreme sensit ...
* Superdiamagnetism
Superdiamagnetism (or perfect diamagnetism) is a phenomenon occurring in certain materials at low temperatures, characterised by the complete absence of magnetic permeability (i.e. a volume magnetic susceptibility \chi_ = −1) and the exclusion ...
* Superfluid film
* Timeline of low-temperature technology
The following is a timeline of low-temperature technology and cryogenic technology (refrigeration down to –273.15 °C, –459.67 °F or 0 K). It also lists important milestones in thermometry, thermodynamics, statistical physics and c ...
References
Further reading
* Antony M. Guénault: ''Basic superfluids.'' Taylor & Francis, London 2003,
* D.R. Tilley and J. Tilley, ''Superfluidity and Superconductivity,'' (IOP Publishing Ltd., Bristol, 1990)
Department of Energy Office of Science: Superfluidity
* Hagen Kleinert
Hagen Kleinert (born 15 June 1941) is professor of theoretical physics at the Free University of Berlin, Germany (since 1968)Honorary Doctorat the
West University of Timișoaraandat thin Bishkek. He is alsHonorary Memberof th For his contributio ...
, ''Gauge Fields in Condensed Matter'', Vol. I, "SUPERFLOW AND VORTEX LINES", pp. 1–742
World Scientific (Singapore, 1989)
Paperback (also availabl
* James F. Annett: ''Superconductivity, superfluids, and condensates.'' Oxford Univ. Press, Oxford 2005,
*
* London, F. Superfluids (Wiley, New York, 1950)
* Philippe Lebrun & Laurent Tavian:
The technology of superfluid helium
'
External links
Helium-4 Interactive Properties
http://web.mit.edu/newsoffice/2005/matter
Liquid Helium II,Superfluid:demonstrations of Lambda point transition/viscosity paradox /two fluid model/fountain effect/creeping film/ second sound.
*
Video including superfluid helium's strange behavior
{{emerging technologies, quantum=yes, other=yes
Liquid helium
Bose–Einstein condensates
Fluid dynamics
Emerging technologies
Superfluidity