Why can superfluid helium-4 flow through a narrow capillary without any pressure drop, even though it is a real physical substance with mass?
AIts molecules are so small that they slip through gaps without interacting with the walls
BAt very low temperatures, all thermal motion ceases, eliminating friction
CBelow the Landau critical velocity, energy-momentum conservation forbids any dissipative excitation — there are no available low-energy states for the flow to scatter into
DThe fluid becomes so dense that it self-lubricates, reducing viscosity to zero
Superfluidity is not simply 'very low friction' — it is the complete absence of dissipation arising from macroscopic quantum coherence. The condensate is described by a single coherent wavefunction, and creating a dissipative excitation (such as scattering off a wall or creating a phonon) requires exceeding the Landau critical velocity. Below this threshold, energy-momentum conservation simply does not permit any process that would slow the flow — there are no available low-energy excitations. Option B is wrong: some thermal motion remains below T_λ in the normal component. Option A is classical reasoning that misses the quantum mechanism entirely.
Question 2 Multiple Choice
When a bucket of superfluid helium-4 is rotated, what happens instead of the uniform solid-body rotation seen in classical fluids?
AThe superfluid does not rotate at all — it remains stationary while the bucket spins around it
BThe entire fluid rotates as a solid body, just as a classical viscous fluid would
CAn array of quantized vortices forms, each carrying circulation in integer multiples of h/m
DThe fluid rotates only in the outermost layer while the interior remains still
Vortex quantization follows directly from the single-valuedness of the macroscopic wavefunction. Because the superfluid velocity is v_s = (ℏ/m)∇θ, the circulation around any closed loop must equal nh/m for integer n — it cannot vary continuously. Solid-body rotation (option B) would require continuously varying circulation, which is topologically forbidden. Instead, the superfluid accommodates rotation only through discrete quantized vortex lines, each carrying exactly one quantum of circulation, arranged in a regular array. This is direct experimental evidence of macroscopic quantum coherence.
Question 3 True / False
A superfluid can rotate as a solid body, exactly like a classical fluid in a spinning bucket.
TTrue
FFalse
Answer: False
This is precisely what the quantization of circulation rules out. The superfluid velocity v_s = (ℏ/m)∇θ must satisfy the quantization condition ∮v_s · dl = nh/m around any closed path. Solid-body rotation would require v_s proportional to the radius, giving continuously varying circulation — forbidden by the quantum constraint. Superfluids accommodate rotation only through arrays of quantized vortices, each a topological defect where the superfluid density drops to zero at the core and the phase winds by 2π. This is a defining experimental signature of the superfluid state.
Question 4 True / False
Superfluidity is ultimately a consequence of macroscopic quantum coherence, not merely of being at very low temperature.
TTrue
FFalse
Answer: True
Temperature alone does not cause superfluidity — the phase transition requires Bose-Einstein condensation, in which a macroscopic fraction of bosons occupy the same ground state, forming a single coherent wavefunction Ψ(r,t). It is this coherence — not merely the low temperature — that forbids dissipation (Landau criterion), quantizes vortices, and produces the fountain effect. This is why superfluidity is a distinctly quantum phenomenon: a classical fluid at the same temperature would still scatter, dissipate, and rotate without quantized vortices.
Question 5 Short Answer
Why does the fountain effect occur in superfluid helium-4, and what does it reveal about the two-fluid model?
Think about your answer, then reveal below.
Model answer: In the fountain effect, superfluid He-4 flows spontaneously through a narrow capillary toward a heated region, building up a pressure difference. This occurs because the two-fluid model treats helium below T_λ as a mixture of a superfluid component (zero viscosity, zero entropy) and a normal component (carrying all entropy). Heating one end increases the entropy there. Since the superfluid component carries no entropy, it flows toward the heated region to equalize entropy, creating a macroscopic pressure fountain. The capillary blocks the normal (viscous) component but allows the superfluid through.
The fountain effect is striking because it appears to violate thermodynamic intuition — a fluid flowing from cold to hot. But the two-fluid model makes it sensible: only the superfluid component (the condensate) flows through the fine capillary, driven not by pressure but by entropy gradients. The superfluid carries zero entropy and moves to minimize the system's free energy. This reveals that below T_λ, helium is not a single uniform fluid but a superposition of two components with completely different transport properties — a consequence of macroscopic quantum coherence.