superfluid helium-4


  • [37][38] Hard-sphere models[edit] The models are based on the simplified form of the inter-particle potential between helium-4 atoms in the superfluid phase.

  • It is possible to create density waves of the normal component (and hence of the superfluid component since ρn + ρs = constant) which are similar to ordinary sound waves.

  • To explain the early specific heat data on superfluid helium-4, Landau posited the existence of a type of excitation he called a “roton”, but as better data became available
    he considered that the “roton” was the same as a high momentum version of sound.

  • 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.

  • The short-wavelength part describes the interior structure of the fluid element using a non-perturbative approach based on the logarithmic Schrödinger equation; it suggests
    the Gaussian-like behaviour of the element’s interior density and interparticle interaction potential.

  • 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.

  • Gaussian cluster approach[edit] This is a two-scale approach which describes the superfluid component of liquid helium-4.

  • This pressure drives the normal component from the hot end to the cold end according to Here ηn is the viscosity of the normal component,[30] Z some geometrical factor, and
    the volume flow.

  • 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.

  • However, the superfluid component can flow through this superleak without any problem (below a critical velocity of about 20 cm/s).

  • The long-wavelength part is the quantum many-body theory of such elements which deals with their dynamics and interactions.

  • [19] 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.

  • 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.

  • (Helium-4 actually has a lower flow velocity than the sound velocity, but this model is useful to illustrate the concept.)

  • 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.

  • [13][14] Some emerging theories posit that the supersolid signal observed in helium-4 was actually an observation of either a superglass state[15] or intrinsically superfluid
    grain boundaries in the helium-4 crystal.

  • (1) shows that, in the case of the superfluid component, the force contains a term due to the gradient of the chemical potential.

  • 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).

  • 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.

  • So, in many experiments, the fountain pressure has a bigger effect on the motion of the superfluid helium than gravity.

  • 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.

  • [42] The approach provides a unified description of the phonon, maxon and roton excitations, and has noteworthy agreement with experiment: with one essential parameter to
    fit one reproduces at high accuracy the Landau roton spectrum, sound velocity and structure factor of superfluid helium-4.

  • (7) 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.

  • 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.

  • [11][12] 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.

  • 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.

  • 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.

  • 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.

  • 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”.

  • (1) only holds if vs is below a certain critical value, which usually is determined by the diameter of the flow channel.

  • 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.

  • Transport of heat by a counterflow of the normal and superfluid components of He-II Heat transport[edit] Figure 9 depicts a heat-conduction experiment between two temperatures
    TH and TL connected by a tube filled with He-II.

  • Helium II will “creep” along surfaces in order to find its own level – after a short while, the levels in the two containers will equalize.

  • [26][27] In classical mechanics the force is often the gradient of a potential energy.

  • In the case of superfluid 4He in the gravitational field the force is given by[24][25] In this expression μ is the molar chemical potential, g the gravitational acceleration,
    and z the vertical coordinate.

  • Film flow[edit] Many ordinary liquids, like alcohol or petroleum, creep up solid walls, driven by their surface tension.

  • Temperature dependence of the relative superfluid and normal components ρn/ρ and ρs/ρ as functions of T. Figure 1 is the phase diagram of 4He.

  • So far the limit is 1.19 K, but there is a potential to reach 0.7 K.[17] Properties Superfluids, such as helium-4 below the lambda point, exhibit many unusual properties.

  • Comparison with helium-3[edit] 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.

  • This is made obvious by the fact that superfluidity occurs in liquid helium-4 at far higher temperatures than it does in helium-3.

  • Superfluid hydrodynamics[edit] The equation of motion for the superfluid component, in a somewhat simplified form,[23] is given by Newton’s law The mass M4 is the molar mass
    of 4He, and is the velocity of the superfluid component.

  • The name lambda-line comes from the specific heat – temperature plot which has the shape of the Greek letter λ.


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