A liquid can carry heat without behaving like ordinary water
Helium can flow through a narrow passage with extraordinarily little resistance, yet it can also damp an oscillating object. It has a measurable heat capacity, carries sound and changes its response with temperature. A theory of superfluidity must explain these observations together. Saying that atoms occupy a low-energy quantum state does not yet explain what carries heat at a nonzero temperature, or which processes allow a moving liquid to lose energy.
In 1941 Landau organized the problem around excitations of the liquid. An excitation is an additional, propagating disturbance above its equilibrium state. Instead of following every atom, ask which disturbances the interacting liquid permits, how much energy they cost and what momentum they carry. This approach made predictions possible before a complete microscopic calculation of the dense liquid was available. It also connected experiments that appeared to ask quite different questions.
Sources: [3][1]
A sound wave becomes a countable excitation
Consider a long compression wave in a liquid. Atoms become slightly crowded in one region, push on their neighbors and transmit the disturbance. An individual atom need not travel all the way to the receiver. Quantum theory divides that acoustic motion into countable excitations called phonons. A phonon is therefore not an extra helium atom. It describes a coordinated motion of many atoms.
For sufficiently long wavelengths, phonon energy is approximately proportional to momentum, with sound speed as the proportionality constant. Energy has units of joules, momentum of kilogram meters per second and sound speed of meters per second. In three dimensions the number of available acoustic modes grows with momentum, and their thermal occupation gives a heat capacity proportional to temperature cubed in the phonon-dominated limit. Halving temperature then reduces this contribution by about a factor of eight. The prediction has a specified range of validity and a directly measurable consequence.
Sources: [3][4]
The spectrum has more structure than its sound-wave end
Long-wavelength phonons do not describe all thermal behavior of liquid helium. The subsequently developed phonon–roton spectrum contains a local energy minimum at larger momentum. Excitations near that minimum are called rotons. They are collective disturbances of the liquid. The historical name should not be taken as a picture of an atom rotating in a little circle, or identified with a quantized vortex.
A roton costs a nonzero minimum energy. At very low temperature such excitations are rare; as temperature rises their population grows rapidly and changes heat capacity and transport. The shape of energy versus momentum thus determines how the liquid stores thermal energy. Agreement with heat measurements is useful, but testing that shape requires another kind of experiment that can transfer a known momentum and determine the associated energy.
Sources: [5][4]
A slowing flow must give its energy and momentum somewhere to go
Consider a very heavy obstacle moving through an initially stationary liquid. It can transfer kinetic energy and momentum to an excitation. Here velocity means the obstacle’s velocity in the liquid-rest frame, and momentum means that transferred to the excitation. Neglecting the small recoil correction of the heavy obstacle, its kinetic-energy loss is their scalar product. The total energy cost is the excitation energy minus that loss. The process becomes energetically allowed only when an available excitation makes the cost nonpositive. The resulting threshold depends on relative speed between obstacle and liquid.
This gives Landau’s criterion: minimize excitation energy divided by momentum over the permitted spectrum. The ratio has units of speed. A spectrum containing only ideal acoustic phonons would give the sound speed. A roton minimum can set a lower threshold. For a deliberately illustrative spectrum, suppose its acoustic part gives two hundred meters per second and another part gives sixty. The relevant threshold is sixty. Checking only the sound-wave end would miss an available route for energy loss. These illustrative numbers show how the lowest available ratio selects the first accessible excitation channel.
Sources: [3][4]
Two velocities describe one liquid
At a nonzero temperature, thermal excitations carry entropy and momentum and produce a normal response to walls and probes. The superfluid response has its own velocity. Two-fluid hydrodynamics divides the mass density into normal and superfluid densities, and adds their contributions to the total mass current. Density is measured in kilograms per cubic meter; multiplying by velocity gives mass crossing unit area per unit time.
This is not a permanent sorting of individual atoms into two named groups. It describes how the same liquid responds, with temperature-dependent proportions. Nor is superfluid density simply the number of atoms occupying the lowest single-particle state. Interactions in dense helium make condensate fraction and superfluid response different observables. Tisza’s earlier two-fluid ideas and Landau’s excitation theory made distinct contributions to the resulting description.
Sources: [4][1]
Heat pulses and neutrons test different parts of the explanation
Ordinary sound is mainly an oscillation of pressure and density. The two components can also move approximately in opposite directions, producing little net mass current while transporting entropy. Heat then propagates as a wave called second sound. Under suitable hydrodynamic conditions, a small heater launches a pulse and a distant temperature-sensitive detector records its arrival. Changing their separation tests propagation speed. This is a different collective mode, not a second name for an ordinary pressure wave.
Inelastic neutron scattering asks a more direct spectral question. Measure the incident neutron, then the outgoing neutron’s energy and direction; their differences determine what energy and momentum the liquid received. In 1961 Henshaw and Woods reported peaks at many scattering angles and reconstructed a dispersion curve with an acoustic part and a larger-momentum minimum, including differences from theoretical details. Heat capacity sums over excitations, second sound tests coupled motion and neutron scattering resolves energy against momentum.
Sources: [4][5]
A spectral threshold is not a guaranteed pipe speed
Landau’s argument identifies an energy threshold for producing specified excitations. Real flow can fail through other processes. Walls, sharp corners and pre-existing defects can assist vortex creation or motion, leading to critical velocities below the spectral estimate. Comparing a measured flow curve with theory therefore requires the geometry, temperature and available dissipation channels. A calculated spectral threshold cannot be used as the guaranteed operating speed of every passage.
The 1962 Nobel Prize recognized Landau’s theories of condensed matter, especially liquid helium. His approach identified the liquid’s low-energy motions and made them account for heat capacity, sound and flow together. Strong interactions did not make quantitative understanding impossible: choosing collective variables connected a temperature pulse, a neutron spectrum and a persistent current. Heat could have mobile carriers even when a flowing liquid had no energetically accessible route for creating excitations. That connection was the achievement of the theory.
Sources: [4][1][2]