341:
229:, launched in January 1983 to gather infrared data was cooled by 73 kilograms of superfluid helium, maintaining a temperature of 1.6 K (ā271.55 Ā°C). 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 BoseāEinstein condensate. This evaporation pulls energy from the overall system, which can be pumped out in a way completely analogous to normal refrigeration techniques.
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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.
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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".
207:. 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
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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
2667:). 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
263:
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-IV, 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
3407:
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
3396:
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.
272:
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
254:
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
3363:
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
186:
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
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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
391:
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
3445:
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.
290:
that they obey. Specifically, the superfluidity of helium-4 can be regarded as a consequence of BoseāEinstein 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
58:. The substance, which resembles other liquids such as helium I (conventional, non-superfluid liquid helium), 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
457:
Fig. 5. The liquid helium is in the superfluid phase. As long as it remains superfluid, it creeps up the wall of the cup as a thin film. It comes down on the outside, forming a drop which will fall into the liquid below. Another drop will form ā and so on ā until the cup is
3470:-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
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619:
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 He in the gravitational field the force is given by
372:
of He. 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
881:
285:
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
140:
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
384:
Figure 1 also shows the Ī»-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.
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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.
408:) the density of the normal (superfluid) component, and Ļ (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
255:
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.
1849:
1028:
Fig. 8. Demonstration of the fountain effect. A capillary tube is "closed" at one end by a superleak and is placed into a bath of superfluid helium and then heated. The helium flows up through the tube and squirts like a
2833:
1117:
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698:
2205:= 9.8 m/s 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.
3262:
2318:
3890:
Avenel, O.; Varoquaux, E. (1985). "Observation of Singly
Quantized Dissipation Events Obeying the Josephson Frequency Relation in the Critical Flow of Superfluid ^{4}He through an Aperture".
770:
4687:
4579:
Van Alphen, W. M.; Van
Haasteren, G. J.; De Bruyn Ouboter, R.; Taconis, K. W. (1966). "The dependence of the critical velocity of the superfluid on channel diameter and film thickness".
388:
The name lambda-line comes from the specific heat ā temperature plot which has the shape of the Greek letter Ī». See figure 2, which shows a peak at 2.172 K, the so-called Ī»-point of He.
762:
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
2554:
3085:
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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.
2020:
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617:
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182:. When helium-4 is cooled below about 200 mK under high pressures, a fraction (ā1%) of the solid appears to become superfluid. By quench cooling or lengthening the
2962:
4746:
Alonso, J. L.; Ares, F.; Brun, J. L. (October 5, 2018). "Unraveling the Landau's consistence criterion and the meaning of interpenetration in the "Two-Fluid" Model".
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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
1947:
1921:
1357:
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where heat is transported via gasāliquid conversion. The high thermal conductivity of He-II is applied for stabilizing superconducting magnets such as in the
5323:
A. V. Avdeenkov & K. G. Zloshchastiev (2011). "Quantum Bose liquids with logarithmic nonlinearity: Self-sustainability and emergence of spatial extent".
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In an experiment, arranged as in figure 8, a fountain can be created. The fountain effect is used to drive the circulation of He in dilution refrigerators.
344:
Fig. 2. Heat capacity of liquid He at saturated vapor pressure as function of the temperature. The peak at T=2.17 K marks a (second-order) phase transition.
3828:
5270:
K. G. Zloshchastiev (2012). "Volume element structure and roton-maxon-phonon excitations in superfluid helium beyond the Gross-Pitaevskii approximation".
3482:
excitations, and has noteworthy agreement with experiment: with one essential parameter to fit one reproduces at high accuracy the Landau roton spectrum,
169:
445:
Fig. 4. Helium II will "creep" along surfaces in order to find its own level ā after a short while, the levels in the two containers will equalize. The
187:
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
5538:
Liquid Helium II, Superfluid: demonstrations of Lambda point transition/viscosity paradox /two fluid model/fountain effect/creeping film/ second sound.
3490:
of superfluid helium-4. This model utilizes the general theory of quantum Bose liquids with logarithmic nonlinearities which is based on introducing a
3412:. To date, a number of models of this kind have been proposed, including: models with vortex rings, hard-sphere models, and Gaussian cluster theories.
85:
particle, which can form bosons only by pairing with itself at much lower temperatures, in a weaker process that is similar to the electron pairing in
3408:
authors. Their main objective is to derive the form of the inter-particle potential between helium atoms in superfluid state from first principles of
1678:{\displaystyle \mu (p,T)=\mu (0,0)+\int _{0}^{p}V_{m}(p^{\prime },0)\mathrm {d} p^{\prime }-\int _{0}^{T}S_{m}(p,T^{\prime })\mathrm {d} T^{\prime }.}
5597:
5082:
T. D. Lee; K. Huang & C. N. Yang (1957). "Eigenvalues and
Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties".
4312:
1020:
Fig. 7. Demonstration of the fountain pressure. The two vessels are connected by a superleak through which only the superfluid component can pass.
6160:
625:
5611:
2714:
4075:
Sophie, A; Rittner C (2006). "Observation of
Classical Rotational Inertia and Nonclassical Supersolid Signals in Solid 4 He below 250 mK".
3701:
2168:
is called the fountain pressure. It can be calculated from the entropy of He which, in turn, can be calculated from the heat capacity. For
3749:
Hall, H. E.; Vinen, W. F. (1956). "The
Rotation of Liquid Helium II. II. The Theory of Mutual Friction in Uniformly Rotating Helium II".
3203:
2234:
145:
in superfluid helium-4. In 2006, a group at the
University of Maryland visualized quantized vortices by using small tracer particles of
5643:
2601:
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 (
4054:
3420:
Landau thought that vorticity entered superfluid helium-4 by vortex sheets, but such sheets have since been shown to be unstable.
3400:
To explain the early specific heat data on superfluid helium-4, Landau posited the existence of a type of excitation he called a "
6457:
3548:
3189:
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.
3364:
effective, so the thermal conductivity of He-II is very much better than the best materials. The situation is comparable with
5471:
4635:
4495:
377:
where the difference between gas and liquid disappears. The diagram shows the remarkable property that He is liquid even at
3424:
and, later independently, Feynman showed that vorticity enters by quantized vortex lines. They also developed the idea of
6153:
5542:
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3404:", but as better data became available he considered that the "roton" was the same as a high momentum version of sound.
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4651:
Staas, F. A.; Severijns, A. P.; Van Der
Waerden, H. C.bM. (1975). "A dilution refrigerator with superfluid injection".
69:
of helium atoms. This condensation occurs in liquid helium-4 at a far higher temperature (2.17 K) than it does in
5452:
5444:
5419:
4566:
4528:
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2475:{\displaystyle \rho _{0}{\frac {\mathrm {d} {\vec {v}}_{s}}{\mathrm {d} t}}=-{\vec {\nabla }}(p+\rho _{0}gz-p_{f}).}
130:
129:
on August 2, 1911, the same day that he observed superconductivity in mercury. It has since been described through
5117:
L. Liu; L. S. Liu & K. W. Wong (1964). "Hard-Sphere
Approach to the Excitation Spectrum in Liquid Helium II".
449:
also covers the interior of the larger container; if it were not sealed, the helium II would creep out and escape.
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This is a two-scale approach which describes the superfluid component of liquid helium-4. It consists of two
467:
The equation of motion for the superfluid component, in a somewhat simplified form, is given by Newton's law
418:
It is possible to create density waves of the normal component (and hence of the superfluid component since Ļ
316:
102:
6102:
5975:
5720:
5390:
3568:
287:
66:
5152:
A. P. Ivashin & Y. M. Poluektov (2011). "Short-wave excitations in non-local Gross-Pitaevskii model".
941:
shows that, in the case of the superfluid component, the force contains a term due to the gradient of the
6392:
5548:
Rousseau, V. G. (2014). "Superfluid density in continuous and discrete spaces: Avoiding misconceptions".
876:{\displaystyle M_{4}{\frac {\mathrm {d} {\vec {v}}_{s}}{\mathrm {d} t}}=-{\vec {\nabla }}(\mu +M_{4}gz).}
218:, which allow the measurement of some theoretically predicted gravitational effects (for an example, see
5594:
4478:
Buckingham, M.J.; Fairbank, W.M. (1961). "Chapter III The Nature of the Ī»-Transition in Liquid Helium".
2501:
6407:
6207:
5456:
5378:, III. The Many-Worlds Interpretation of Quantum Mechanics: the theory of the universal wave function.
236:
to lower temperatures. So far the limit is 1.19 K, but there is a potential to reach 0.7 K.
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is below a certain critical value, which usually is determined by the diameter of the flow channel.
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6254:
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2201:
the fountain pressure is equal to 0.692 bar. With a density of liquid helium of 125 kg/m and
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183:
122:
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6169:
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Keesom, W.H.; Keesom, A.P. (1935). "New measurements on the specific heat of liquid helium".
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Fig. 9. Transport of heat by a counterflow of the normal and superfluid components of He-II
1988:
1197:
153:
4734:
Critical velocities and mutual friction in He-He mixtures at low temperatures below 100 mK
3195:. This pressure drives the normal component from the hot end to the cold end according to
2967:
8:
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F. London (1938). "The Ī»-Phenomenon of Liquid Helium and the Bose-Einstein Degeneracy".
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apply to the left and right side of the superleak respectively. In this particular case
1958:
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945:. This is the origin of the remarkable properties of He-II such as the fountain effect.
315:.) A unified description of superconductivity and superfluidity is possible in terms of
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In classical mechanics the force is often the gradient of a potential energy. Eq.
908:
559:
312:
156:
from pairs of ultra-cold fermionic atoms. Under certain conditions, fermion pairs form
4955:
4627:
4487:
4464:
3089:
This means that the pressure in the right vessel is equal to the fountain pressure at
955:
705:
199:
Recently in the field of chemistry, superfluid helium-4 has been successfully used in
6339:
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2118:{\displaystyle \int _{0}^{T}S_{m}(p,T^{\prime })\mathrm {d} T^{\prime }=V_{m0}p_{f}.}
1926:
1900:
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274:
157:
86:
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4408:
Swenson, C. (1950). "The Liquid-Solid Transformation in Helium near Absolute Zero".
4353:"Limited Quantum Helium Transportation through Nano-channels by Quantum Fluctuation"
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4236:
4122:
948:
547:{\displaystyle {\vec {F}}=M_{4}{\frac {\mathrm {d} {\vec {v}}_{s}}{\mathrm {d} t}}.}
415:
to one at zero kelvins. Below 1 K the helium is almost completely superfluid.
6244:
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4973:. World Scientific Series in 20th century Physics. Vol. 27. World Scientific.
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E.L. Andronikashvili Zh. Ćksp. Teor. Fiz, Vol.16 p.780 (1946), Vol.18 p. 424 (1948)
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Pollet, L; Boninsegni M (2007). "Superfuididty of Grain Boundaries in Solid 4 He".
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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5207:"Roton-Maxon Spectrum and Stability of Trapped Dipolar Bose-Einstein Condensates"
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3433:
352:
Fig. 3. Temperature dependence of the relative superfluid and normal components Ļ
219:
204:
164:. At the other limit, the fermions (most notably superconducting electrons) form
136:
In the 1950s, Hall and Vinen performed experiments establishing the existence of
47:
5606:
4136:
Sophie, A; Rittner C (2007). "Disorder and the Supersolid State of Solid 4 He".
3911:
1844:{\displaystyle \int _{0}^{p}V_{m}(p^{\prime },0)\mathrm {d} p^{\prime }=V_{m0}p}
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78:
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Rayfield, G.; Reif, F. (1964). "Quantized Vortex Rings in Superfluid Helium".
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426:= constant) which are similar to ordinary sound waves. This effect is called
378:
369:
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200:
110:
106:
1016:
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191:
state or intrinsically superfluid grain boundaries in the helium-4 crystal.
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427:
165:
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4934:
Bijl, A; de Boer, J; Michels, A (1941). "Properties of liquid helium II".
4719:
3933:
Bewley, Gregory P.; Lathrop, Daniel P.; Sreenivasan, Katepalli R. (2006).
332:
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2828:{\displaystyle p_{l}+\rho _{0}gz_{l}-p_{fl}=p_{r}+\rho _{0}gz_{r}-p_{fr}}
446:
296:
245:
233:
118:
65:
The formation of the superfluid is a manifestation of the formation of a
6138:
4688:"He flow in dilute He-He mixtures at temperatures between 10 and 150 mK"
4021:
2574:
has only mathematical meaning, but in special experimental arrangements
232:
Superfluid-helium technology is used to extend the temperature range of
5970:
5945:
5872:
5842:
5776:
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3389:
3135:
Figure 9 depicts a heat-conduction experiment between two temperatures
1112:{\displaystyle \mathrm {d} \mu =V_{m}\mathrm {d} p-S_{m}\mathrm {d} T.}
292:
188:
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31:
4376:
4329:
3726:
336:
Fig. 1. Phase diagram of He. In this diagram is also given the Ī»-line.
4876:
4851:
4828:
4541:
3678:
3634:
3609:
3429:
3365:
1024:
215:
55:
5705:
3962:
3458:. The short-wavelength part describes the interior structure of the
6107:
5935:
5532:
5527:
4760:
3467:
300:
70:
35:
5562:
5337:
5322:
5284:
5166:
4622:. Progress in Low Temperature Physics. Vol. 13. p. 167.
1423:, so with constant pressure (see figure 6). In the first integral
441:
6067:
5955:
5890:
5807:
5802:
3657:
Allen, J. F.; Misener, A. D. (1938). "Flow of Liquid Helium II".
82:
59:
39:
5537:
4685:
4482:. Progress in Low Temperature Physics. Vol. 3. p. 80.
5676:
4736:, thesis, Appendix A, Eindhoven University of Technology, 1991.
4686:
Castelijns, C.; Kuerten, J.; De Waele, A.; Gijsman, H. (1985).
4616:"Chapter 3: Thermodynamics and Hydrodynamics of HeāHe Mixtures"
3471:
308:
43:
5685:
5671:
4650:
4000:(2004). "Probable Observation of a Supersolid Helium Phase".
3479:
3401:
303:, and the attractive interaction between them is mediated by
74:
51:
5151:
4189:
Boninsegni, M; Prokofev (2006). "Superglass Phase of 4 He".
214:
Superfluids are also used in high-precision devices such as
5204:
5081:
4548:, Vol. 5, Academy of Sciences of the USSR, p. 71.
3373:
2556:
the density of liquid He at zero pressure and temperature.
693:{\displaystyle {\vec {F}}=-{\vec {\nabla }}(\mu +M_{4}gz).}
226:
5681:
5116:
5443:, Vol. I, "SUPERFLOW AND VORTEX LINES", pp. 1ā742,
4933:
3992:
3935:"Superfluid helium: Visualization of quantized vortices"
3932:
3587:"The Nobel Prize in Physics 1996 - Advanced Information"
5205:
Santos, L.; Shlyapnikov, G. V.; Lewenstein, M. (2003).
5000:"Atomic Theory of the Two-Fluid Model of Liquid Helium"
178:
may also have been discovered in 2004 by physicists at
3333:
3313:
3286:
3168:
3141:
3095:
3006:
2970:
2930:
2897:
2877:
2857:
2673:
2640:
2607:
2580:
2504:
2174:
2147:
1961:
1929:
1903:
1873:
1727:
1707:
1460:
1429:
1397:
1365:
1339:
1307:
1275:
1255:
1235:
1200:
1168:
1141:
998:
978:
958:
911:
748:
728:
708:
589:
562:
5432:
Department of Energy Office of Science: Superfluidity
5042:"Energy Spectrum of the Excitations in Liquid Helium"
5039:
3206:
3041:
2717:
2359:
2237:
2023:
1991:
1759:
1502:
1055:
773:
628:
475:
5617:
Video including superfluid helium's strange behavior
5397:. American Journal of Mathematics (1957) pp. 152ā156
3494:-type contribution to energy related to the quantum
5269:
3257:{\displaystyle \Delta p=-\eta _{n}Z{\dot {V}}_{n}.}
2313:{\displaystyle \mu (p,T)=\mu _{0}+V_{m0}(p-p_{f}).}
4971:Selected papers of Richard Feynman with commentary
4620:Thermodynamics and hydrodynamics of HeāHe mixtures
4614:De Waele, A. Th. A. M.; Kuerten, J. G. M. (1992).
4477:
4249:
4188:
3355:
3319:
3299:
3256:
3181:
3154:
3108:
3079:
3025:
2992:
2956:
2916:
2883:
2863:
2827:
2692:
2659:
2626:
2593:
2548:
2474:
2312:
2193:
2160:
2117:
2004:
1977:
1941:
1915:
1889:
1843:
1740:
1713:
1677:
1477:
1446:
1415:
1383:
1351:
1325:
1293:
1261:
1241:
1221:
1181:
1154:
1111:
1004:
984:
964:
924:
875:
754:
734:
714:
692:
611:
575:
546:
3700:van Delft, Dirk; Kes, Peter (September 1, 2010).
1044:in more familiar form we use the general formula
73:(2.5 mK) because each atom of helium-4 is a
6444:
5464:Superconductivity, superfluids, and condensates.
4899:L. Tisza (1947). "The Theory of Liquid Helium".
4613:
4480:The nature of the Ī»-transition in liquid helium
4135:
4074:
3889:
3462:using a non-perturbative approach based on the
5533:http://web.mit.edu/newsoffice/2005/matter.html
5508:London, F. Superfluids (Wiley, New York, 1950)
4745:
4559:An introduction to the theory of superfluidity
3610:"Viscosity of Liquid Helium Below the Ī»-Point"
381:. He is only solid at pressures above 25 bar.
6154:
5637:
4997:
4968:
4442:
3791:
3699:
3656:
3449:
3384:
5651:
462:
280:
6425:
6161:
6147:
5644:
5630:
4542:"The theory of superfluidity of helium II"
3307:is the viscosity of the normal component,
1269:plane. First we integrate from the origin
1229:can be found by a line integration in the
6168:
5561:
5384:
5336:
5283:
5222:
5165:
4875:
4806:
4759:
4384:
4263:
4202:
4149:
4088:
3961:
3851:
3748:
3725:
3633:
3456:nested models linked via parametric space
952:Fig. 6. Integration path for calculating
152:In the early 2000s, physicists created a
5547:
4898:
4849:
3573:Encyclopedia of Condensed Matter Physics
3121:
1023:
1015:
947:
452:
440:
430:. Due to the temperature dependence of Ļ
347:
339:
331:
5476:
4407:
4310:
3826:
3607:
97:Known as a major facet in the study of
16:Superfluid form of the helium-4 isotope
6445:
5612:The Hindu article on superfluid states
5511:Philippe Lebrun & Laurent Tavian:
4324:. Vol. 710. pp. 034911ā1/8.
3549:Timeline of low-temperature technology
1701:We are interested only in cases where
299:takes place between atoms rather than
6142:
5625:
5040:R. P. Feynman & M. Cohen (1956).
3829:"Vortex photography in liquid helium"
3440:
3379:
1897:is the molar volume of the liquid at
322:
5428:(IOP Publishing Ltd., Bristol, 1990)
5426:Superfluidity and Superconductivity,
4350:
3702:"The discovery of superconductivity"
3415:
3197:
2708:
2350:
2228:
2014:
2012:which has the dimension of pressure
1750:
1493:
1046:
1033:
764:
742:the gravitational acceleration, and
225:The Infrared Astronomical Satellite
5514:The technology of superfluid helium
5414:Taylor & Francis, London 2003,
3575:. Elsevier. 2005. pp. 128ā133.
2549:{\textstyle \rho _{0}=M_{4}/V_{m0}}
13:
5445:World Scientific (Singapore, 1989)
5403:
4852:"Transport Phenomena in Helium II"
3496:EverettāHirschman entropy function
3207:
2419:
2400:
2374:
2081:
2072:
2063:
1817:
1808:
1793:
1667:
1658:
1649:
1602:
1593:
1578:
1462:
1431:
1099:
1078:
1057:
833:
814:
788:
650:
531:
505:
14:
6479:
5521:
5466:Oxford Univ. Press, Oxford 2005,
4561:(New York: W. A. Benjamin),
3130:
722:is the molar chemical potential,
327:
125:possibly observed the superfluid
6424:
5704:
5441:Gauge Fields in Condensed Matter
3464:logarithmic Schrƶdinger equation
1955:is also written as a product of
77:particle, by virtue of its zero
5528:Helium-4 Interactive Properties
5369:
5316:
5263:
5198:
5145:
5110:
5075:
5033:
4991:
4962:
4927:
4892:
4843:
4800:
4748:The European Physical Journal B
4739:
4726:
4679:
4644:
4607:
4572:
4551:
4534:
4513:
4504:
4471:
4436:
4401:
4344:
4304:
4243:
4182:
4129:
4068:
4044:
3986:
3926:
3080:{\displaystyle 0=p_{r}-p_{fr}.}
194:
50:in which matter behaves like a
5355:10.1088/0953-4075/44/19/195303
5325:J. Phys. B: At. Mol. Opt. Phys
4050:Moses Chan's Research Group. "
3883:
3820:
3785:
3742:
3693:
3650:
3601:
3579:
3561:
2466:
2428:
2422:
2385:
2304:
2285:
2253:
2241:
2068:
2049:
1804:
1785:
1654:
1635:
1589:
1570:
1539:
1527:
1518:
1506:
1410:
1398:
1378:
1366:
1320:
1308:
1288:
1276:
1216:
1204:
867:
842:
836:
799:
684:
659:
653:
635:
597:
516:
482:
1:
6093:Macroscopic quantum phenomena
5241:10.1103/PhysRevLett.90.250403
4986:Section IV (pages 313 to 414)
4956:10.1016/S0031-8914(41)90422-6
4628:10.1016/S0079-6417(08)60052-9
4519:S. J. Putterman (1974),
4488:10.1016/S0079-6417(08)60134-1
4465:10.1016/S0031-8914(35)90128-8
4282:10.1103/PhysRevLett.98.135301
4221:10.1103/PhysRevLett.96.135301
4168:10.1103/PhysRevLett.98.175302
4107:10.1103/PhysRevLett.97.165301
3555:
3327:some geometrical factor, and
583:is the molar mass of He, and
295:of superconductivity. In it,
239:
103:macroscopic quantum phenomena
6103:Order and disorder (physics)
4673:10.1016/0375-9601(75)90087-0
4601:10.1016/0031-9163(66)90958-9
3862:10.1016/0378-4363(82)90510-1
3827:Packard, Richard E. (1982).
1748:is practically constant. So
1478:{\textstyle \mathrm {d} p=0}
1447:{\textstyle \mathrm {d} T=0}
438:are also temperature waves.
258:
7:
5607:Superfluid phases of helium
5543:Physics Today February 2001
5424:D.R. Tilley and J. Tilley,
4557:Khalatnikov, I. M. (1965),
4523:(Amsterdam: North-Holland)
3912:10.1103/PhysRevLett.55.2704
3501:
3356:{\textstyle {\dot {V}}_{n}}
3270:
3191:
2841:
2702:
2570:
2561:
2488:
2344:
2338:
2326:
2222:
2216:
2210:
2194:{\textstyle T=T_{\lambda }}
2131:
1951:
1857:
1691:
1487:
1191:
1125:
1040:
937:
901:
889:
612:{\textstyle {\vec {v}}_{s}}
434:(figure 3) these waves in Ļ
267:
10:
6484:
6408:Thermoacoustic heat engine
5580:10.1103/PhysRevB.90.134503
5502:10.1103/RevModPhys.71.S318
5302:10.1140/epjb/e2012-30344-3
4969:Braun, L. M., ed. (2000).
4778:10.1140/epjb/e2018-90105-x
4318:AIP Conference Proceedings
4313:"Superfluid Vortex Cooler"
1189:the molar volume. With Eq.
243:
162:BoseāEinstein condensation
133:and microscopic theories.
92:
81:. Helium-3, however, is a
6458:BoseāEinstein condensates
6420:
6393:Immersive virtual reality
6353:
6183:
6176:
6055:
6009:
5881:
5795:
5769:
5713:
5702:
5664:
5482:Reviews of Modern Physics
5480:(1999). "Superfluidity".
5184:10.2478/s11534-010-0124-7
5139:10.1103/PhysRev.135.A1166
4988:deals with liquid helium.
3814:10.1103/PhysRev.136.A1194
3450:Gaussian cluster approach
3385:Landau two-fluid approach
1359:. Next we integrate from
1162:is the molar entropy and
307:fluctuations rather than
109:effect was discovered by
6376:Digital scent technology
6128:Thermo-dielectric effect
6027:Enthalpy of vaporization
5721:BoseāEinstein condensate
5595:superfluid hydrodynamics
5104:10.1103/PhysRev.106.1135
5069:10.1103/PhysRev.102.1189
4712:10.1103/PhysRevB.32.2870
4521:Superfluid Hydrodynamics
2957:{\textstyle z_{l}=z_{r}}
463:Superfluid hydrodynamics
288:BoseāEinstein statistics
281:Comparison with helium-3
67:BoseāEinstein condensate
6022:Enthalpy of sublimation
5211:Physical Review Letters
4351:Ohba, Tomonori (2016).
4311:Tanaeva, I. A. (2004).
3892:Physical Review Letters
1949:. The other term in Eq.
1038:In order to rewrite Eq.
317:gauge symmetry breaking
246:Helium Ā§ Helium II
6398:Magnetic refrigeration
6037:Latent internal energy
5787:Color-glass condensate
5600:March 3, 2016, at the
5380:Everett's Dissertation
5027:10.1103/PhysRev.94.262
4998:R. P. Feynman (1954).
4921:10.1103/PhysRev.72.838
4540:Landau, L. D. (1941),
4430:10.1103/PhysRev.79.626
4063:Penn State University,
3838:. 109ā110: 1474ā1484.
3771:10.1098/rspa.1956.0215
3357:
3321:
3301:
3300:{\textstyle \eta _{n}}
3258:
3183:
3156:
3127:
3110:
3081:
3027:
2994:
2958:
2918:
2885:
2865:
2829:
2694:
2661:
2628:
2595:
2550:
2476:
2314:
2195:
2162:
2119:
2006:
1979:
1943:
1917:
1891:
1845:
1742:
1715:
1679:
1479:
1448:
1417:
1385:
1353:
1327:
1295:
1263:
1243:
1223:
1222:{\textstyle \mu (p,T)}
1183:
1156:
1113:
1030:
1021:
1013:
1006:
986:
966:
926:
877:
756:
736:
716:
694:
613:
577:
548:
459:
450:
365:
345:
337:
6371:Cloak of invisibility
6170:Emerging technologies
5847:Magnetically ordered
3514:Large Hadron Collider
3370:Large Hadron Collider
3358:
3322:
3302:
3259:
3184:
3157:
3125:
3111:
3082:
3028:
2995:
2993:{\textstyle p_{fl}=0}
2959:
2919:
2886:
2866:
2830:
2695:
2662:
2634:) and zero pressure (
2629:
2596:
2551:
2477:
2315:
2196:
2163:
2120:
2007:
2005:{\displaystyle p_{f}}
1980:
1944:
1918:
1892:
1846:
1743:
1716:
1680:
1480:
1449:
1418:
1386:
1354:
1328:
1296:
1264:
1244:
1224:
1184:
1157:
1114:
1027:
1019:
1007:
987:
967:
951:
927:
878:
757:
737:
717:
695:
614:
578:
549:
456:
444:
351:
343:
335:
277:in a superconductor.
180:Penn State University
99:quantum hydrodynamics
5726:Fermionic condensate
5410:Antony M. GuƩnault:
3608:Kapitza, P. (1938).
3524:Polariton superfluid
3331:
3311:
3284:
3204:
3166:
3139:
3093:
3039:
3026:{\textstyle T_{l}=0}
3004:
2968:
2928:
2917:{\textstyle p_{l}=0}
2895:
2875:
2855:
2715:
2693:{\textstyle v_{s}=0}
2671:
2660:{\textstyle p_{l}=0}
2638:
2627:{\textstyle T_{l}=0}
2605:
2578:
2502:
2357:
2235:
2172:
2145:
2021:
1989:
1959:
1927:
1901:
1871:
1757:
1725:
1705:
1500:
1458:
1427:
1395:
1363:
1337:
1305:
1273:
1253:
1233:
1198:
1166:
1139:
1053:
996:
976:
956:
909:
771:
746:
726:
706:
626:
587:
560:
473:
154:Fermionic condensate
46:. A superfluid is a
6403:Phased-array optics
6361:Acoustic levitation
5941:Chemical ionization
5833:Programmable matter
5823:Quantum spin liquid
5691:Supercritical fluid
5572:2014PhRvB..90m4503R
5494:1999RvMPS..71..318L
5391:I.I. Hirschman, Jr.
5347:2011JPhB...44s5303A
5294:2012EPJB...85..273Z
5233:2003PhRvL..90y0403S
5176:2011CEJPh...9..857I
5131:1964PhRv..135.1166L
5125:(5A): A1166āA1172.
5096:1957PhRv..106.1135L
5061:1956PhRv..102.1189F
5019:1954PhRv...94..262F
4948:1941Phy.....8..655B
4913:1947PhRv...72..838T
4868:1938Natur.141..913T
4821:1938Natur.141..643L
4770:2018EPJB...91..226A
4704:1985PhRvB..32.2870C
4665:1975PhLA...53..327S
4593:1966PhL....20..474V
4457:1935Phy.....2..557K
4422:1950PhRv...79..626S
4369:2016NatSR...628992O
4274:2007PhRvL..98m5301P
4213:2006PhRvL..96m5301W
4160:2007PhRvL..98q5302R
4099:2006PhRvL..97p5301R
4022:10.1038/nature02220
4014:2004Natur.427..225K
3954:2006Natur.441..588B
3904:1985PhRvL..55.2704A
3871:on November 7, 2017
3844:1982PhyBC.109.1474P
3806:1964PhRv..136.1194R
3763:1956RSPSA.238..215H
3718:2010PhT....63i..38V
3671:1938Natur.142..643A
3626:1938Natur.141...74K
3509:Douglas D. Osheroff
2336:Substitution of Eq.
2038:
1978:{\textstyle V_{m0}}
1890:{\textstyle V_{m0}}
1774:
1624:
1559:
702:In this expression
360:/Ļ as functions of
20:Superfluid helium-4
6088:Leidenfrost effect
6017:Enthalpy of fusion
5782:Quarkāgluon plasma
5412:Basic superfluids.
5154:Cent. Eur. J. Phys
4732:Zeegers, J. C. H.
4546:Journal of Physics
4357:Scientific Reports
4057:2013-04-08 at the
3589:. Nobel Foundation
3466:; it suggests the
3441:Hard-sphere models
3432:in the 1940s, and
3380:Microscopic theory
3353:
3317:
3297:
3254:
3182:{\textstyle T_{L}}
3179:
3155:{\textstyle T_{H}}
3152:
3128:
3109:{\textstyle T_{r}}
3106:
3077:
3023:
2990:
2954:
2914:
2881:
2861:
2851:where the indexes
2825:
2690:
2657:
2624:
2594:{\textstyle p_{f}}
2591:
2546:
2472:
2310:
2191:
2161:{\textstyle p_{f}}
2158:
2115:
2024:
2002:
1975:
1939:
1913:
1887:
1841:
1760:
1741:{\textstyle V_{m}}
1738:
1711:
1675:
1610:
1545:
1475:
1454:and in the second
1444:
1416:{\textstyle (p,T)}
1413:
1384:{\textstyle (p,0)}
1381:
1349:
1326:{\textstyle (p,0)}
1323:
1294:{\textstyle (0,0)}
1291:
1259:
1239:
1219:
1182:{\textstyle V_{m}}
1179:
1155:{\textstyle S_{m}}
1152:
1109:
1031:
1022:
1014:
1002:
982:
962:
943:chemical potential
925:{\textstyle v_{s}}
922:
873:
752:
732:
712:
690:
609:
576:{\textstyle M_{4}}
573:
544:
460:
451:
366:
346:
338:
323:Macroscopic theory
313:fermion condensate
158:diatomic molecules
6440:
6439:
6416:
6415:
6223:complexity theory
6208:cellular automata
6136:
6135:
6118:Superheated vapor
6113:Superconductivity
6083:Equation of state
5931:Flash evaporation
5883:Phase transitions
5868:String-net liquid
5761:Photonic molecule
5731:Degenerate matter
5550:Physical Review B
5472:978-0-19-850756-7
5462:James F. Annett:
5395:A note on entropy
4850:L. Tisza (1938).
4815:(3571): 643ā644.
4692:Physical Review B
4653:Physics Letters A
4637:978-0-444-89109-9
4497:978-0-444-53309-8
4377:10.1038/srep28992
4330:10.1063/1.1774894
4008:(6971): 225ā227.
3898:(24): 2704ā2707.
3727:10.1063/1.3490499
3539:Superdiamagnetism
3534:Quantum gyroscope
3529:Quantum acoustics
3416:Vortex ring model
3410:quantum mechanics
3344:
3278:
3277:
3242:
3033:). Consequently,
2849:
2848:
2496:
2495:
2425:
2408:
2388:
2334:
2333:
2226:obtains the form
2139:
2138:
1865:
1864:
1721:is small so that
1699:
1698:
1133:
1132:
1034:Fountain pressure
965:{\textstyle \mu }
897:
896:
839:
822:
802:
715:{\textstyle \mu }
656:
638:
600:
539:
519:
485:
275:Abrikosov lattice
170:BEC-BCS crossover
87:superconductivity
6475:
6428:
6427:
6305:machine learning
6280:key distribution
6265:image processing
6255:error correction
6181:
6180:
6163:
6156:
6149:
6140:
6139:
6073:Compressed fluid
5708:
5653:States of matter
5646:
5639:
5632:
5623:
5622:
5591:
5565:
5505:
5488:(2): S318āS323.
5455:(also available
5398:
5388:
5382:
5373:
5367:
5366:
5340:
5320:
5314:
5313:
5287:
5267:
5261:
5260:
5226:
5224:cond-mat/0301474
5202:
5196:
5195:
5169:
5149:
5143:
5142:
5114:
5108:
5107:
5090:(6): 1135ā1145.
5079:
5073:
5072:
5055:(5): 1189ā1204.
5046:
5037:
5031:
5030:
5004:
4995:
4989:
4984:
4966:
4960:
4959:
4931:
4925:
4924:
4896:
4890:
4889:
4879:
4877:10.1038/141913a0
4847:
4841:
4840:
4829:10.1038/141643a0
4804:
4798:
4797:
4763:
4743:
4737:
4730:
4724:
4723:
4698:(5): 2870ā2886.
4683:
4677:
4676:
4648:
4642:
4641:
4611:
4605:
4604:
4576:
4570:
4555:
4549:
4538:
4532:
4517:
4511:
4508:
4502:
4501:
4475:
4469:
4468:
4440:
4434:
4433:
4405:
4399:
4398:
4388:
4348:
4342:
4341:
4323:
4308:
4302:
4301:
4267:
4265:cond-mat/0702159
4247:
4241:
4240:
4206:
4204:cond-mat/0603003
4186:
4180:
4179:
4153:
4151:cond-mat/0702665
4133:
4127:
4126:
4092:
4090:cond-mat/0604528
4072:
4066:
4048:
4042:
4041:
3990:
3984:
3983:
3965:
3939:
3930:
3924:
3923:
3887:
3881:
3880:
3878:
3876:
3870:
3864:. Archived from
3855:
3833:
3824:
3818:
3817:
3789:
3783:
3782:
3746:
3740:
3739:
3729:
3697:
3691:
3690:
3679:10.1038/142643a0
3654:
3648:
3647:
3637:
3635:10.1038/141074a0
3605:
3599:
3598:
3596:
3594:
3583:
3577:
3576:
3565:
3488:structure factor
3362:
3360:
3359:
3354:
3352:
3351:
3346:
3345:
3337:
3326:
3324:
3323:
3318:
3306:
3304:
3303:
3298:
3296:
3295:
3272:
3263:
3261:
3260:
3255:
3250:
3249:
3244:
3243:
3235:
3228:
3227:
3198:
3188:
3186:
3185:
3180:
3178:
3177:
3161:
3159:
3158:
3153:
3151:
3150:
3115:
3113:
3112:
3107:
3105:
3104:
3086:
3084:
3083:
3078:
3073:
3072:
3057:
3056:
3032:
3030:
3029:
3024:
3016:
3015:
2999:
2997:
2996:
2991:
2983:
2982:
2963:
2961:
2960:
2955:
2953:
2952:
2940:
2939:
2923:
2921:
2920:
2915:
2907:
2906:
2890:
2888:
2887:
2882:
2870:
2868:
2867:
2862:
2843:
2834:
2832:
2831:
2826:
2824:
2823:
2808:
2807:
2795:
2794:
2782:
2781:
2769:
2768:
2753:
2752:
2740:
2739:
2727:
2726:
2709:
2699:
2697:
2696:
2691:
2683:
2682:
2666:
2664:
2663:
2658:
2650:
2649:
2633:
2631:
2630:
2625:
2617:
2616:
2600:
2598:
2597:
2592:
2590:
2589:
2555:
2553:
2552:
2547:
2545:
2544:
2532:
2527:
2526:
2514:
2513:
2490:
2481:
2479:
2478:
2473:
2465:
2464:
2446:
2445:
2427:
2426:
2418:
2409:
2407:
2403:
2397:
2396:
2395:
2390:
2389:
2381:
2377:
2371:
2369:
2368:
2351:
2328:
2319:
2317:
2316:
2311:
2303:
2302:
2284:
2283:
2268:
2267:
2229:
2204:
2200:
2198:
2197:
2192:
2190:
2189:
2167:
2165:
2164:
2159:
2157:
2156:
2133:
2124:
2122:
2121:
2116:
2111:
2110:
2101:
2100:
2085:
2084:
2075:
2067:
2066:
2048:
2047:
2037:
2032:
2015:
2011:
2009:
2008:
2003:
2001:
2000:
1984:
1982:
1981:
1976:
1974:
1973:
1948:
1946:
1945:
1942:{\textstyle p=0}
1940:
1922:
1920:
1919:
1916:{\textstyle T=0}
1914:
1896:
1894:
1893:
1888:
1886:
1885:
1859:
1850:
1848:
1847:
1842:
1837:
1836:
1821:
1820:
1811:
1797:
1796:
1784:
1783:
1773:
1768:
1751:
1747:
1745:
1744:
1739:
1737:
1736:
1720:
1718:
1717:
1712:
1693:
1684:
1682:
1681:
1676:
1671:
1670:
1661:
1653:
1652:
1634:
1633:
1623:
1618:
1606:
1605:
1596:
1582:
1581:
1569:
1568:
1558:
1553:
1494:
1484:
1482:
1481:
1476:
1465:
1453:
1451:
1450:
1445:
1434:
1422:
1420:
1419:
1414:
1390:
1388:
1387:
1382:
1358:
1356:
1355:
1352:{\textstyle T=0}
1350:
1332:
1330:
1329:
1324:
1300:
1298:
1297:
1292:
1268:
1266:
1265:
1260:
1248:
1246:
1245:
1240:
1228:
1226:
1225:
1220:
1188:
1186:
1185:
1180:
1178:
1177:
1161:
1159:
1158:
1153:
1151:
1150:
1127:
1118:
1116:
1115:
1110:
1102:
1097:
1096:
1081:
1076:
1075:
1060:
1047:
1011:
1009:
1008:
1003:
991:
989:
988:
983:
971:
969:
968:
963:
931:
929:
928:
923:
921:
920:
891:
882:
880:
879:
874:
860:
859:
841:
840:
832:
823:
821:
817:
811:
810:
809:
804:
803:
795:
791:
785:
783:
782:
765:
761:
759:
758:
753:
741:
739:
738:
733:
721:
719:
718:
713:
699:
697:
696:
691:
677:
676:
658:
657:
649:
640:
639:
631:
618:
616:
615:
610:
608:
607:
602:
601:
593:
582:
580:
579:
574:
572:
571:
553:
551:
550:
545:
540:
538:
534:
528:
527:
526:
521:
520:
512:
508:
502:
500:
499:
487:
486:
478:
368:Figure 1 is the
203:techniques as a
143:Josephson effect
138:quantized vortex
131:phenomenological
127:phase transition
6483:
6482:
6478:
6477:
6476:
6474:
6473:
6472:
6443:
6442:
6441:
6436:
6412:
6349:
6260:finite automata
6172:
6167:
6137:
6132:
6063:Baryonic matter
6051:
6005:
5976:Saturated fluid
5916:Crystallization
5877:
5851:Antiferromagnet
5791:
5765:
5709:
5700:
5660:
5650:
5602:Wayback Machine
5524:
5519:
5406:
5404:Further reading
5401:
5389:
5385:
5374:
5370:
5321:
5317:
5272:Eur. Phys. J. B
5268:
5264:
5203:
5199:
5150:
5146:
5115:
5111:
5080:
5076:
5044:
5038:
5034:
5002:
4996:
4992:
4981:
4967:
4963:
4932:
4928:
4897:
4893:
4848:
4844:
4805:
4801:
4744:
4740:
4731:
4727:
4684:
4680:
4649:
4645:
4638:
4612:
4608:
4581:Physics Letters
4577:
4573:
4556:
4552:
4539:
4535:
4518:
4514:
4509:
4505:
4498:
4476:
4472:
4441:
4437:
4410:Physical Review
4406:
4402:
4349:
4345:
4321:
4309:
4305:
4252:Phys. Rev. Lett
4248:
4244:
4191:Phys. Rev. Lett
4187:
4183:
4138:Phys. Rev. Lett
4134:
4130:
4077:Phys. Rev. Lett
4073:
4069:
4059:Wayback Machine
4049:
4045:
3991:
3987:
3963:10.1038/441588a
3937:
3931:
3927:
3888:
3884:
3874:
3872:
3868:
3853:10.1.1.210.8701
3831:
3825:
3821:
3794:Physical Review
3790:
3786:
3747:
3743:
3698:
3694:
3655:
3651:
3606:
3602:
3592:
3590:
3585:
3584:
3580:
3569:"Superfluidity"
3567:
3566:
3562:
3558:
3553:
3544:Superfluid film
3504:
3452:
3443:
3434:Richard Feynman
3418:
3387:
3382:
3347:
3336:
3335:
3334:
3332:
3329:
3328:
3312:
3309:
3308:
3291:
3287:
3285:
3282:
3281:
3245:
3234:
3233:
3232:
3223:
3219:
3205:
3202:
3201:
3173:
3169:
3167:
3164:
3163:
3146:
3142:
3140:
3137:
3136:
3133:
3100:
3096:
3094:
3091:
3090:
3065:
3061:
3052:
3048:
3040:
3037:
3036:
3011:
3007:
3005:
3002:
3001:
2975:
2971:
2969:
2966:
2965:
2948:
2944:
2935:
2931:
2929:
2926:
2925:
2902:
2898:
2896:
2893:
2892:
2876:
2873:
2872:
2856:
2853:
2852:
2816:
2812:
2803:
2799:
2790:
2786:
2777:
2773:
2761:
2757:
2748:
2744:
2735:
2731:
2722:
2718:
2716:
2713:
2712:
2678:
2674:
2672:
2669:
2668:
2645:
2641:
2639:
2636:
2635:
2612:
2608:
2606:
2603:
2602:
2585:
2581:
2579:
2576:
2575:
2537:
2533:
2528:
2522:
2518:
2509:
2505:
2503:
2500:
2499:
2460:
2456:
2441:
2437:
2417:
2416:
2399:
2398:
2391:
2380:
2379:
2378:
2373:
2372:
2370:
2364:
2360:
2358:
2355:
2354:
2298:
2294:
2276:
2272:
2263:
2259:
2236:
2233:
2232:
2202:
2185:
2181:
2173:
2170:
2169:
2152:
2148:
2146:
2143:
2142:
2106:
2102:
2093:
2089:
2080:
2076:
2071:
2062:
2058:
2043:
2039:
2033:
2028:
2022:
2019:
2018:
1996:
1992:
1990:
1987:
1986:
1985:and a quantity
1966:
1962:
1960:
1957:
1956:
1928:
1925:
1924:
1902:
1899:
1898:
1878:
1874:
1872:
1869:
1868:
1829:
1825:
1816:
1812:
1807:
1792:
1788:
1779:
1775:
1769:
1764:
1758:
1755:
1754:
1732:
1728:
1726:
1723:
1722:
1706:
1703:
1702:
1666:
1662:
1657:
1648:
1644:
1629:
1625:
1619:
1614:
1601:
1597:
1592:
1577:
1573:
1564:
1560:
1554:
1549:
1501:
1498:
1497:
1461:
1459:
1456:
1455:
1430:
1428:
1425:
1424:
1396:
1393:
1392:
1364:
1361:
1360:
1338:
1335:
1334:
1306:
1303:
1302:
1274:
1271:
1270:
1254:
1251:
1250:
1234:
1231:
1230:
1199:
1196:
1195:
1173:
1169:
1167:
1164:
1163:
1146:
1142:
1140:
1137:
1136:
1098:
1092:
1088:
1077:
1071:
1067:
1056:
1054:
1051:
1050:
1036:
997:
994:
993:
977:
974:
973:
957:
954:
953:
916:
912:
910:
907:
906:
855:
851:
831:
830:
813:
812:
805:
794:
793:
792:
787:
786:
784:
778:
774:
772:
769:
768:
747:
744:
743:
727:
724:
723:
707:
704:
703:
672:
668:
648:
647:
630:
629:
627:
624:
623:
603:
592:
591:
590:
588:
585:
584:
567:
563:
561:
558:
557:
530:
529:
522:
511:
510:
509:
504:
503:
501:
495:
491:
477:
476:
474:
471:
470:
465:
437:
433:
425:
421:
414:
407:
403:
399:
395:
359:
355:
330:
325:
283:
270:
261:
252:
242:
220:Gravity Probe B
205:quantum solvent
197:
95:
48:state of matter
42:of the element
17:
12:
11:
5:
6481:
6471:
6470:
6465:
6463:Fluid dynamics
6460:
6455:
6438:
6437:
6435:
6434:
6421:
6418:
6417:
6414:
6413:
6411:
6410:
6405:
6400:
6395:
6390:
6389:
6388:
6378:
6373:
6368:
6363:
6357:
6355:
6351:
6350:
6348:
6347:
6342:
6337:
6332:
6327:
6322:
6320:neural network
6317:
6312:
6307:
6302:
6297:
6292:
6287:
6282:
6277:
6272:
6267:
6262:
6257:
6252:
6247:
6242:
6241:
6240:
6230:
6225:
6220:
6215:
6210:
6205:
6200:
6195:
6189:
6187:
6178:
6174:
6173:
6166:
6165:
6158:
6151:
6143:
6134:
6133:
6131:
6130:
6125:
6120:
6115:
6110:
6105:
6100:
6095:
6090:
6085:
6080:
6075:
6070:
6065:
6059:
6057:
6053:
6052:
6050:
6049:
6044:
6042:Trouton's rule
6039:
6034:
6029:
6024:
6019:
6013:
6011:
6007:
6006:
6004:
6003:
5998:
5993:
5988:
5983:
5978:
5973:
5968:
5963:
5958:
5953:
5948:
5943:
5938:
5933:
5928:
5923:
5918:
5913:
5911:Critical point
5908:
5903:
5898:
5893:
5887:
5885:
5879:
5878:
5876:
5875:
5870:
5865:
5864:
5863:
5858:
5853:
5845:
5840:
5835:
5830:
5825:
5820:
5815:
5813:Liquid crystal
5810:
5805:
5799:
5797:
5793:
5792:
5790:
5789:
5784:
5779:
5773:
5771:
5767:
5766:
5764:
5763:
5758:
5753:
5748:
5746:Strange matter
5743:
5741:Rydberg matter
5738:
5733:
5728:
5723:
5717:
5715:
5711:
5710:
5703:
5701:
5699:
5698:
5693:
5688:
5679:
5674:
5668:
5666:
5662:
5661:
5649:
5648:
5641:
5634:
5626:
5620:
5619:
5614:
5609:
5604:
5592:
5556:(13): 134503.
5545:
5540:
5535:
5530:
5523:
5522:External links
5520:
5518:
5517:
5509:
5506:
5474:
5460:
5437:Hagen Kleinert
5434:
5429:
5422:
5407:
5405:
5402:
5400:
5399:
5383:
5368:
5331:(19): 195303.
5315:
5262:
5217:(25): 250403.
5197:
5160:(3): 857ā864.
5144:
5109:
5074:
5032:
4990:
4980:978-9810241315
4979:
4961:
4942:(7): 655ā675.
4926:
4907:(9): 838ā854.
4891:
4842:
4799:
4738:
4725:
4678:
4643:
4636:
4606:
4571:
4550:
4533:
4512:
4503:
4496:
4470:
4435:
4400:
4343:
4303:
4258:(13): 135301.
4242:
4197:(13): 135301.
4181:
4144:(17): 175302.
4128:
4083:(16): 165301.
4067:
4043:
3985:
3925:
3882:
3819:
3784:
3741:
3692:
3649:
3600:
3578:
3559:
3557:
3554:
3552:
3551:
3546:
3541:
3536:
3531:
3526:
3521:
3516:
3511:
3505:
3503:
3500:
3484:sound velocity
3451:
3448:
3442:
3439:
3426:quantum vortex
3417:
3414:
3390:L. D. Landau's
3386:
3383:
3381:
3378:
3350:
3343:
3340:
3320:{\textstyle Z}
3316:
3294:
3290:
3276:
3275:
3266:
3264:
3253:
3248:
3241:
3238:
3231:
3226:
3222:
3218:
3215:
3212:
3209:
3176:
3172:
3149:
3145:
3132:
3131:Heat transport
3129:
3103:
3099:
3076:
3071:
3068:
3064:
3060:
3055:
3051:
3047:
3044:
3022:
3019:
3014:
3010:
2989:
2986:
2981:
2978:
2974:
2951:
2947:
2943:
2938:
2934:
2913:
2910:
2905:
2901:
2884:{\textstyle r}
2880:
2864:{\textstyle l}
2860:
2847:
2846:
2837:
2835:
2822:
2819:
2815:
2811:
2806:
2802:
2798:
2793:
2789:
2785:
2780:
2776:
2772:
2767:
2764:
2760:
2756:
2751:
2747:
2743:
2738:
2734:
2730:
2725:
2721:
2689:
2686:
2681:
2677:
2656:
2653:
2648:
2644:
2623:
2620:
2615:
2611:
2588:
2584:
2543:
2540:
2536:
2531:
2525:
2521:
2517:
2512:
2508:
2494:
2493:
2484:
2482:
2471:
2468:
2463:
2459:
2455:
2452:
2449:
2444:
2440:
2436:
2433:
2430:
2424:
2421:
2415:
2412:
2406:
2402:
2394:
2387:
2384:
2376:
2367:
2363:
2332:
2331:
2322:
2320:
2309:
2306:
2301:
2297:
2293:
2290:
2287:
2282:
2279:
2275:
2271:
2266:
2262:
2258:
2255:
2252:
2249:
2246:
2243:
2240:
2188:
2184:
2180:
2177:
2155:
2151:
2137:
2136:
2127:
2125:
2114:
2109:
2105:
2099:
2096:
2092:
2088:
2083:
2079:
2074:
2070:
2065:
2061:
2057:
2054:
2051:
2046:
2042:
2036:
2031:
2027:
1999:
1995:
1972:
1969:
1965:
1938:
1935:
1932:
1912:
1909:
1906:
1884:
1881:
1877:
1863:
1862:
1853:
1851:
1840:
1835:
1832:
1828:
1824:
1819:
1815:
1810:
1806:
1803:
1800:
1795:
1791:
1787:
1782:
1778:
1772:
1767:
1763:
1735:
1731:
1714:{\textstyle p}
1710:
1697:
1696:
1687:
1685:
1674:
1669:
1665:
1660:
1656:
1651:
1647:
1643:
1640:
1637:
1632:
1628:
1622:
1617:
1613:
1609:
1604:
1600:
1595:
1591:
1588:
1585:
1580:
1576:
1572:
1567:
1563:
1557:
1552:
1548:
1544:
1541:
1538:
1535:
1532:
1529:
1526:
1523:
1520:
1517:
1514:
1511:
1508:
1505:
1474:
1471:
1468:
1464:
1443:
1440:
1437:
1433:
1412:
1409:
1406:
1403:
1400:
1380:
1377:
1374:
1371:
1368:
1348:
1345:
1342:
1322:
1319:
1316:
1313:
1310:
1290:
1287:
1284:
1281:
1278:
1262:{\textstyle T}
1258:
1242:{\textstyle p}
1238:
1218:
1215:
1212:
1209:
1206:
1203:
1176:
1172:
1149:
1145:
1131:
1130:
1121:
1119:
1108:
1105:
1101:
1095:
1091:
1087:
1084:
1080:
1074:
1070:
1066:
1063:
1059:
1035:
1032:
1005:{\textstyle T}
1001:
985:{\textstyle p}
981:
961:
919:
915:
905:only holds if
895:
894:
885:
883:
872:
869:
866:
863:
858:
854:
850:
847:
844:
838:
835:
829:
826:
820:
816:
808:
801:
798:
790:
781:
777:
755:{\textstyle z}
751:
735:{\textstyle g}
731:
711:
689:
686:
683:
680:
675:
671:
667:
664:
661:
655:
652:
646:
643:
637:
634:
606:
599:
596:
570:
566:
543:
537:
533:
525:
518:
515:
507:
498:
494:
490:
484:
481:
464:
461:
435:
431:
423:
419:
412:
405:
401:
397:
393:
375:critical point
357:
353:
329:
328:Thermodynamics
326:
324:
321:
297:Cooper pairing
282:
279:
269:
266:
260:
257:
241:
238:
196:
193:
147:solid hydrogen
94:
91:
15:
9:
6:
4:
3:
2:
6480:
6469:
6468:Superfluidity
6466:
6464:
6461:
6459:
6456:
6454:
6453:Liquid helium
6451:
6450:
6448:
6433:
6432:
6423:
6422:
6419:
6409:
6406:
6404:
6401:
6399:
6396:
6394:
6391:
6387:
6386:Plasma window
6384:
6383:
6382:
6379:
6377:
6374:
6372:
6369:
6367:
6364:
6362:
6359:
6358:
6356:
6352:
6346:
6345:teleportation
6343:
6341:
6338:
6336:
6333:
6331:
6328:
6326:
6323:
6321:
6318:
6316:
6313:
6311:
6308:
6306:
6303:
6301:
6298:
6296:
6293:
6291:
6288:
6286:
6283:
6281:
6278:
6276:
6273:
6271:
6268:
6266:
6263:
6261:
6258:
6256:
6253:
6251:
6248:
6246:
6243:
6239:
6236:
6235:
6234:
6231:
6229:
6226:
6224:
6221:
6219:
6216:
6214:
6211:
6209:
6206:
6204:
6201:
6199:
6196:
6194:
6191:
6190:
6188:
6186:
6182:
6179:
6175:
6171:
6164:
6159:
6157:
6152:
6150:
6145:
6144:
6141:
6129:
6126:
6124:
6121:
6119:
6116:
6114:
6111:
6109:
6106:
6104:
6101:
6099:
6098:Mpemba effect
6096:
6094:
6091:
6089:
6086:
6084:
6081:
6079:
6078:Cooling curve
6076:
6074:
6071:
6069:
6066:
6064:
6061:
6060:
6058:
6054:
6048:
6045:
6043:
6040:
6038:
6035:
6033:
6030:
6028:
6025:
6023:
6020:
6018:
6015:
6014:
6012:
6008:
6002:
6001:Vitrification
5999:
5997:
5994:
5992:
5989:
5987:
5984:
5982:
5979:
5977:
5974:
5972:
5969:
5967:
5966:Recombination
5964:
5962:
5961:Melting point
5959:
5957:
5954:
5952:
5949:
5947:
5944:
5942:
5939:
5937:
5934:
5932:
5929:
5927:
5924:
5922:
5919:
5917:
5914:
5912:
5909:
5907:
5906:Critical line
5904:
5902:
5899:
5897:
5896:Boiling point
5894:
5892:
5889:
5888:
5886:
5884:
5880:
5874:
5871:
5869:
5866:
5862:
5859:
5857:
5854:
5852:
5849:
5848:
5846:
5844:
5841:
5839:
5836:
5834:
5831:
5829:
5828:Exotic matter
5826:
5824:
5821:
5819:
5816:
5814:
5811:
5809:
5806:
5804:
5801:
5800:
5798:
5794:
5788:
5785:
5783:
5780:
5778:
5775:
5774:
5772:
5768:
5762:
5759:
5757:
5754:
5752:
5749:
5747:
5744:
5742:
5739:
5737:
5734:
5732:
5729:
5727:
5724:
5722:
5719:
5718:
5716:
5712:
5707:
5697:
5694:
5692:
5689:
5687:
5683:
5680:
5678:
5675:
5673:
5670:
5669:
5667:
5663:
5658:
5654:
5647:
5642:
5640:
5635:
5633:
5628:
5627:
5624:
5618:
5615:
5613:
5610:
5608:
5605:
5603:
5599:
5596:
5593:
5589:
5585:
5581:
5577:
5573:
5569:
5564:
5559:
5555:
5551:
5546:
5544:
5541:
5539:
5536:
5534:
5531:
5529:
5526:
5525:
5516:
5515:
5510:
5507:
5503:
5499:
5495:
5491:
5487:
5483:
5479:
5475:
5473:
5469:
5465:
5461:
5458:
5454:
5453:9971-5-0210-0
5450:
5446:
5442:
5438:
5435:
5433:
5430:
5427:
5423:
5421:
5420:0-7484-0891-6
5417:
5413:
5409:
5408:
5396:
5392:
5387:
5381:
5377:
5372:
5364:
5360:
5356:
5352:
5348:
5344:
5339:
5334:
5330:
5326:
5319:
5311:
5307:
5303:
5299:
5295:
5291:
5286:
5281:
5277:
5273:
5266:
5258:
5254:
5250:
5246:
5242:
5238:
5234:
5230:
5225:
5220:
5216:
5212:
5208:
5201:
5193:
5189:
5185:
5181:
5177:
5173:
5168:
5163:
5159:
5155:
5148:
5140:
5136:
5132:
5128:
5124:
5120:
5113:
5105:
5101:
5097:
5093:
5089:
5085:
5078:
5070:
5066:
5062:
5058:
5054:
5050:
5043:
5036:
5028:
5024:
5020:
5016:
5012:
5008:
5001:
4994:
4987:
4982:
4976:
4972:
4965:
4957:
4953:
4949:
4945:
4941:
4937:
4930:
4922:
4918:
4914:
4910:
4906:
4902:
4895:
4887:
4883:
4878:
4873:
4869:
4865:
4862:(3577): 913.
4861:
4857:
4853:
4846:
4838:
4834:
4830:
4826:
4822:
4818:
4814:
4810:
4803:
4795:
4791:
4787:
4783:
4779:
4775:
4771:
4767:
4762:
4757:
4753:
4749:
4742:
4735:
4729:
4721:
4717:
4713:
4709:
4705:
4701:
4697:
4693:
4689:
4682:
4674:
4670:
4666:
4662:
4658:
4654:
4647:
4639:
4633:
4629:
4625:
4621:
4617:
4610:
4602:
4598:
4594:
4590:
4586:
4582:
4575:
4568:
4567:0-7382-0300-9
4564:
4560:
4554:
4547:
4543:
4537:
4530:
4529:0-444-10681-2
4526:
4522:
4516:
4507:
4499:
4493:
4489:
4485:
4481:
4474:
4466:
4462:
4458:
4454:
4450:
4446:
4439:
4431:
4427:
4423:
4419:
4415:
4411:
4404:
4396:
4392:
4387:
4382:
4378:
4374:
4370:
4366:
4362:
4358:
4354:
4347:
4339:
4335:
4331:
4327:
4320:
4319:
4314:
4307:
4299:
4295:
4291:
4287:
4283:
4279:
4275:
4271:
4266:
4261:
4257:
4253:
4246:
4238:
4234:
4230:
4226:
4222:
4218:
4214:
4210:
4205:
4200:
4196:
4192:
4185:
4177:
4173:
4169:
4165:
4161:
4157:
4152:
4147:
4143:
4139:
4132:
4124:
4120:
4116:
4112:
4108:
4104:
4100:
4096:
4091:
4086:
4082:
4078:
4071:
4064:
4060:
4056:
4053:
4047:
4039:
4035:
4031:
4027:
4023:
4019:
4015:
4011:
4007:
4003:
3999:
3998:M. H. W. Chan
3995:
3989:
3981:
3977:
3973:
3969:
3964:
3959:
3955:
3951:
3948:(7093): 588.
3947:
3943:
3936:
3929:
3921:
3917:
3913:
3909:
3905:
3901:
3897:
3893:
3886:
3867:
3863:
3859:
3854:
3849:
3845:
3841:
3837:
3830:
3823:
3815:
3811:
3807:
3803:
3800:(5A): A1194.
3799:
3795:
3788:
3780:
3776:
3772:
3768:
3764:
3760:
3757:(1213): 215.
3756:
3752:
3745:
3737:
3733:
3728:
3723:
3719:
3715:
3711:
3707:
3706:Physics Today
3703:
3696:
3688:
3684:
3680:
3676:
3672:
3668:
3665:(3597): 643.
3664:
3660:
3653:
3645:
3641:
3636:
3631:
3627:
3623:
3619:
3615:
3611:
3604:
3588:
3582:
3574:
3570:
3564:
3560:
3550:
3547:
3545:
3542:
3540:
3537:
3535:
3532:
3530:
3527:
3525:
3522:
3520:
3519:London moment
3517:
3515:
3512:
3510:
3507:
3506:
3499:
3497:
3493:
3489:
3485:
3481:
3477:
3473:
3469:
3465:
3461:
3460:fluid element
3457:
3447:
3438:
3435:
3431:
3427:
3423:
3413:
3411:
3405:
3403:
3398:
3394:
3391:
3377:
3375:
3371:
3367:
3348:
3341:
3338:
3314:
3292:
3288:
3274:
3267:
3265:
3251:
3246:
3239:
3236:
3229:
3224:
3220:
3216:
3213:
3210:
3200:
3199:
3196:
3194:
3193:
3174:
3170:
3147:
3143:
3124:
3120:
3117:
3101:
3097:
3087:
3074:
3069:
3066:
3062:
3058:
3053:
3049:
3045:
3042:
3034:
3020:
3017:
3012:
3008:
2987:
2984:
2979:
2976:
2972:
2949:
2945:
2941:
2936:
2932:
2911:
2908:
2903:
2899:
2878:
2858:
2845:
2838:
2836:
2820:
2817:
2813:
2809:
2804:
2800:
2796:
2791:
2787:
2783:
2778:
2774:
2770:
2765:
2762:
2758:
2754:
2749:
2745:
2741:
2736:
2732:
2728:
2723:
2719:
2711:
2710:
2707:
2705:
2704:
2687:
2684:
2679:
2675:
2654:
2651:
2646:
2642:
2621:
2618:
2613:
2609:
2586:
2582:
2573:
2572:
2566:
2564:
2563:
2557:
2541:
2538:
2534:
2529:
2523:
2519:
2515:
2510:
2506:
2492:
2485:
2483:
2469:
2461:
2457:
2453:
2450:
2447:
2442:
2438:
2434:
2431:
2413:
2410:
2404:
2392:
2382:
2365:
2361:
2353:
2352:
2349:
2347:
2346:
2341:
2340:
2330:
2323:
2321:
2307:
2299:
2295:
2291:
2288:
2280:
2277:
2273:
2269:
2264:
2260:
2256:
2250:
2247:
2244:
2238:
2231:
2230:
2227:
2225:
2224:
2219:
2218:
2213:
2212:
2206:
2186:
2182:
2178:
2175:
2153:
2149:
2141:The pressure
2135:
2128:
2126:
2112:
2107:
2103:
2097:
2094:
2090:
2086:
2077:
2059:
2055:
2052:
2044:
2040:
2034:
2029:
2025:
2017:
2016:
2013:
1997:
1993:
1970:
1967:
1963:
1954:
1953:
1936:
1933:
1930:
1910:
1907:
1904:
1882:
1879:
1875:
1861:
1854:
1852:
1838:
1833:
1830:
1826:
1822:
1813:
1801:
1798:
1789:
1780:
1776:
1770:
1765:
1761:
1753:
1752:
1749:
1733:
1729:
1708:
1695:
1688:
1686:
1672:
1663:
1645:
1641:
1638:
1630:
1626:
1620:
1615:
1611:
1607:
1598:
1586:
1583:
1574:
1565:
1561:
1555:
1550:
1546:
1542:
1536:
1533:
1530:
1524:
1521:
1515:
1512:
1509:
1503:
1496:
1495:
1492:
1490:
1489:
1472:
1469:
1466:
1441:
1438:
1435:
1407:
1404:
1401:
1375:
1372:
1369:
1346:
1343:
1340:
1317:
1314:
1311:
1285:
1282:
1279:
1256:
1236:
1213:
1210:
1207:
1201:
1194:
1193:
1174:
1170:
1147:
1143:
1129:
1122:
1120:
1106:
1103:
1093:
1089:
1085:
1082:
1072:
1068:
1064:
1061:
1049:
1048:
1045:
1043:
1042:
1026:
1018:
999:
979:
972:at arbitrary
959:
950:
946:
944:
940:
939:
933:
917:
913:
904:
903:
893:
886:
884:
870:
864:
861:
856:
852:
848:
845:
827:
824:
818:
806:
796:
779:
775:
767:
766:
763:
749:
729:
709:
700:
687:
681:
678:
673:
669:
665:
662:
644:
641:
632:
621:
604:
594:
568:
564:
554:
541:
535:
523:
513:
496:
492:
488:
479:
468:
455:
448:
443:
439:
429:
416:
411:
389:
386:
382:
380:
379:absolute zero
376:
371:
370:phase diagram
363:
350:
342:
334:
320:
318:
314:
310:
306:
302:
298:
294:
289:
278:
276:
265:
256:
251:
250:superfluidity
247:
237:
235:
230:
228:
223:
221:
217:
212:
210:
206:
202:
201:spectroscopic
192:
190:
185:
181:
177:
173:
171:
167:
163:
159:
155:
150:
148:
144:
139:
134:
132:
128:
124:
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115:John F. Allen
112:
111:Pyotr Kapitsa
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107:superfluidity
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6366:Anti-gravity
6310:metamaterial
6238:post-quantum
6233:cryptography
6123:Superheating
5996:Vaporization
5991:Triple point
5986:Supercooling
5951:Lambda point
5901:Condensation
5818:Time crystal
5796:Other states
5736:Quantum Hall
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3422:Lars Onsager
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166:Cooper pairs
160:and undergo
151:
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6330:programming
6290:logic clock
6275:information
6250:electronics
6032:Latent heat
5981:Sublimation
5926:Evaporation
5861:Ferromagnet
5856:Ferrimagnet
5838:Dark matter
5770:High energy
5478:Leggett, A.
4754:(10): 226.
3875:November 7,
3492:dissipative
447:Rollin film
234:cryocoolers
176:Supersolids
119:Don Misener
6447:Categories
6295:logic gate
6193:algorithms
6047:Volatility
6010:Quantities
5971:Regelation
5946:Ionization
5921:Deposition
5873:Superglass
5843:Antimatter
5777:QCD matter
5756:Supersolid
5751:Superfluid
5714:Low energy
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4052:Supersolid
3556:References
3366:heat pipes
2568:So far Eq.
1491:we obtain
1485:. With Eq.
400:/Ļ, with Ļ
293:BCS theory
244:See also:
240:Properties
216:gyroscopes
209:rovibronic
189:superglass
54:with zero
32:superfluid
6340:simulator
6228:computing
6198:amplifier
5588:118518974
5563:1403.5472
5363:119248001
5338:1108.0847
5310:118545094
5285:1204.4652
5192:118633189
5167:1004.0442
5119:Phys. Rev
5084:Phys. Rev
5049:Phys. Rev
5007:Phys. Rev
4901:Phys. Rev
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301:electrons
259:Film flow
184:annealing
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6245:dynamics
6108:Spinodal
6056:Concepts
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3502:See also
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2706:implies
1333:, so at
396:/Ļ and Ļ
356:/Ļ and Ļ
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6068:Binodal
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5803:Colloid
5568:Bibcode
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