# Lambda point The lambda point is the temperature at which liquid [[Helium-4|helium-4]] stops being a liquid like any other and becomes two things at once. Above it, helium I: a cold, ordinary, viscous [[Fluid_dynamics|fluid]]. Below it, helium II, in which a [[Superfluidity|superfluid]] fraction carrying zero [[Viscosity|viscosity]] and zero [[Entropy|entropy]] shares the same volume with a normal fraction carrying all of both. The name of the [[Phase_transition|transition]] is not a claim about mechanism — it is the shape of a graph. ## Microsims — three.js <iframe src="https://wikitube-3d-microsims.netlify.app/Lambda_point.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Lambda point — three.js microsim"></iframe> **`Lambda_point` (three.js).** The scene is Andronikashvili's 1946 apparatus rebuilt in three dimensions: a stack of closely spaced discs hung on a torsion fibre in a [[Cryogenics|cryogenic]] bath of [[Liquid_helium|liquid helium]], the gaps deliberately narrower than the [[Viscosity|viscous]] penetration depth so that the normal component between the plates is locked to them and the superfluid component is not. Drag *Temperature* down through the marked tick at 2.1768 K and watch one population convert into the other — that conversion, and its dependence on temperature alone, is the whole concept. Orange normal-component tracers swing with the discs and add their inertia to the [[Simple_harmonic_motion|torsional]] [[Oscillation|oscillation]]; cyan superfluid tracers glide through and add none, so the period falls as you cool. The live HUD quantity is a *measured* rho_n/rho, read off the running oscillator's period rather than copied from the model curve and printed beside the tabulated value; the panel at right is the real specific-heat curve, and it is the lambda. ## The name is a curve shape, not a mechanism Plot the specific heat of liquid [[Helium-4|helium-4]] against temperature and you get a flat foot, a violently steep rise, and a cliff back down: the Greek letter lambda. Willem Keesom and collaborators found that peak in 1932 and named the [[Phase_transition|transition]] after the picture. That is the entire etymology. Nothing in the [[Physics|physics]] is lambda-shaped — no lambda [[Crystal_structure|structure]], no lambda parameter, no relation to the other quantities that letter labels in [[Thermodynamics|thermodynamics]] or [[Quantum_mechanics|quantum mechanics]]. The [[Superfluidity|superfluid]] transition took its name from a graph, and the graph took its shape from a critical exponent nobody measured properly for another sixty years. The companion naming is older still: Keesom and Wolfke had already split the [[Liquid_helium|liquid]] into helium I above and helium II below, before anyone knew what distinguished them. ## The number, and the conditions it cannot be quoted without **T_lambda = 2.1768 K at 5041.8 Pa** — that pressure being the saturated [[Boiling_point|vapour pressure]] of [[Helium-4|helium-4]] at that temperature, on the ITS-90 scale. The BIPM's realisation guide states it in exactly that paired form: "The 4He equations coincide at the lambda point (2.1768 K, 5041.8 Pa)". The [[Accuracy_and_precision|commonly seen]] "2.17 K" and "2.172 K" are truncations of it, and 2.172 K additionally carries the ghost of the pre-1990 [[Thermodynamics|temperature]] scales. Neither is a different [[Estimation_theory|measurement]]. A bare temperature is nevertheless an incomplete statement, because the lambda point is one end of a **lambda line**. Raise the pressure and the [[Phase_transition|transition]] falls, down to the **lower lambda point at 1.762 K and 29.725 atm (3011.9 kPa)**, where helium I, helium II and the body-centred [[Cubic_crystal_system|cubic]] solid meet at a triple point. The line drops 0.415 K across 30.07 bar — an average near 14 mK per bar. So "[[Helium|helium]] goes superfluid at 2.17 K" holds only in a [[Cryogenics|cryostat]] open to its own vapour; in a pressurised cell it is wrong by up to four-tenths of a kelvin, which on this scale is enormous. (Solid helium needs that pressure at all only because [[Zero-point_energy|zero-point energy]] keeps the liquid liquid.) Every [[Helium_cryogenics|cryogenic]] number in this cluster carries its pressure for the same reason. ## What changes: helium I, helium II, and a decomposition Above the line the [[Liquid_helium|liquid]] is unremarkable except for being cold. It has a [[Density|density]], a [[Viscosity|viscosity]], an [[Entropy|entropy]], and it boils. Below the line, [[Fluid_dynamics|hydrodynamics]] needs two [[Velocity|velocity]] fields instead of one. The **two-fluid model** — László Tisza's, in 1938, on the back of Fritz London's suggestion that helium II is a Bose-condensed liquid, then rebuilt from an excitation spectrum by Lev Landau in 1941 — writes the [[Density|density]] as **rho = rho_s + rho_n** and the momentum density as **j = rho_s·v_s + rho_n·v_n**. The superfluid component carries no [[Entropy|entropy]] and no [[Viscosity|viscosity]]; the normal component carries all of each. The fraction rho_s/rho is a function of temperature and of nothing else, rising from exactly 0 at T_lambda — already 0.093 at 2.16 K, twenty millikelvin down — to 0.993 by 1.00 K, so below about 1 K the [[Fluid_dynamics|fluid]] is superfluid for nearly every purpose. **The misreading worth heading off: these are not two populations of atoms.** Helium-4 atoms are identical [[Boson|bosons]] and strictly indistinguishable; [[Quantum_mechanics|quantum mechanics]] forbids labelling any one of them "the superfluid one". The components interpenetrate in every cubic micron, with no boundary, no interface, nothing you could filter or settle. The model decomposes the *momentum density*, not the particle inventory: a [[Mathematical_model|phenomenology]] fitted to the observed [[Fluid_dynamics|hydrodynamics]]. Tisza reached it through the condensate, Landau through phonons and rotons, and that two such different routes give identical [[Thermodynamics|thermodynamics]] is the sign the equations describe the [[Thermodynamic_equilibrium|state]] and not the bookkeeping. ## Six things you can watch happen **[[Viscosity|Viscosity]] collapses — but only if you measure it the right way.** In January 1938 two letters ran back to back in one issue of *Nature*: Kapitza pushing [[Helium|helium]] through a slit between polished discs, Allen and Misener through capillaries whose bore they varied by a factor of fifty. Allen and Misener had already bounded the [[Viscosity|viscosity]] at 10⁻⁵ CGS units with an oscillating cylinder; below the lambda point they found flow speed nearly independent of driving pressure *and* of bore, and concluded that "any known formula cannot, from our data, give a value of the 'viscosity' which would have much meaning." Kapitza supplied the word *superfluid*, by deliberate analogy with [[Superconductivity|superconductivity]]. The subtlety usually lost: an oscillating disc in helium II still registers finite [[Damping|damping]], because it couples to the normal component, while capillary [[Fluid_dynamics|flow]] registers essentially zero because the superfluid component leaks through. Both are right, and the apparent contradiction is the two-fluid model's first and best evidence — what Andronikashvili's torsional [[Oscillation|oscillator]] turned into a measurement of rho_n/rho. **[[Heat_transfer|Heat]] stops being conducted and starts being carried.** Helium II's apparent thermal conductivity beats every solid, but it is not [[Diffusion|conduction]]: apply heat and the normal component streams away from the source at up to about 20 cm/s while the superfluid streams back, so [[Energy|energy]] moves by counterflow convection at constant total [[Density|density]]. There is therefore no material constant to quote. In the quiescent Landau regime the flux obeys a Fourier law; in the turbulent Gorter–Mellink regime that real [[Thermal_engineering|hardware]] runs in, heat flux goes as the *cube root* of the [[Thermodynamics|temperature]] gradient, and the effective conductivity depends on flux, channel radius and vortex line density. It is why a [[Superconducting_magnet|superconducting magnet]] bath — the [[Magnetic_resonance_imaging|MRI]] case, and the [[Dilution_refrigerator|dilution refrigerator]] still line — is designed around helium II [[Fluid_dynamics|transport]] rather than a tabulated conductivity. **The boiling stops.** Cross T_lambda watching a dewar and the [[Liquid_helium|liquid]] goes abruptly, visibly still. Balibar: "When crossing Tλ, the liquid stops boiling. This is because the thermal conductivity of liquid helium has suddenly increased, so that the temperature is very homogeneous." No bulk superheating means no bubble nucleation; evaporation retreats to the free surface. It is a [[Heat_transfer|transport]] effect — the [[Boiling_point|vapour-pressure]] curve does nothing dramatic there. **The liquid climbs out of the vessel.** A [[Rollin_film|Rollin film]] tens of nanometres thick creeps up any wetted wall, over the rim and away, because a film that thin is immobilised by [[Viscosity|viscous]] drag in every ordinary liquid and is a free channel in this one. Across a [[Porous_medium|porous]] plug or a narrow neck it becomes the dominant heat [[Leak|leak]]. **Heat propagates as a [[Wave|wave]].** [[Second_sound|Second sound]] is an [[Oscillation|oscillation]] of the *ratio* rho_s/rho at constant total [[Density|density]] — the two components counterflowing exactly out of phase, net mass flux zero — and therefore an oscillation of [[Entropy|entropy]] and of temperature. It has a definite [[Velocity|speed]], it reflects, and it builds standing [[Acoustic_wave|waves]] in a tunable cavity. Above the lambda point it does not exist: rho_s = 0, there is no second field to oscillate, and heat reverts to [[Diffusion|diffusing]]. **Circulation is quantised.** [[Fluid_dynamics|Flow]] of the superfluid component round any closed loop comes in integer multiples of h/m₄ = 9.97 × 10⁻⁸ m² s⁻¹, predicted by Onsager and Feynman, detected by Vinen in 1961 with a vibrating wire, and visible as [[Torus|toroidal]] vortex rings. It is a macroscopic [[Quantum_mechanics|quantum]] constraint — the single-valuedness of a [[Schrödinger_equation|wavefunction]] phase — that you can read off a laboratory instrument. ## Why it belongs to the lambda class, and why it had to leave the planet The [[Phase_transition|transition]] is **continuous**: no latent heat, no jump in [[Density|density]], no [[Thermodynamic_equilibrium|coexistence]] of distinguishable phases at the line. In Ehrenfest's scheme that makes it second order, and the label deserves its caveat — Ehrenfest assumed the second derivative of the free [[Energy|energy]] jumps by a *finite* amount, whereas the specific heat here climbs to a sharp finite cusp with unbounded slope, for which his classification has no slot. The modern statement is that this is a critical point in the **three-dimensional XY universality class**: a two-component order parameter in three spatial dimensions, shared with the transition of a neutral [[Superconductivity|superconductor]]. Its critical exponents should be identical across the whole class, which is what makes measuring them worth extraordinary effort. On the ground the [[Accuracy_and_precision|measurement]] is impossible. [[Helium|Helium]]'s own weight puts a [[Fluid_dynamics|hydrostatic]] head across the sample and T_lambda is pressure-dependent, so the [[Phase_transition|transition]] arrives at different heights at different moments: **it is smeared over about 1.3 μK per centimetre of sample depth**. A 1 cm cell rounds the singularity over a reduced-temperature window of order 6 × 10⁻⁷ — exactly where the interesting behaviour lives. You cannot switch off a [[Gravitational_field|gravitational field]]; you can only fall. So the **Lambda Point Experiment flew on Space Shuttle mission STS-52 in late October 1992**, on the USMP-1 [[Aerospace_engineering|payload]]. In orbit the [[Superfluidity|transition]] should stay sharp to a reduced temperature near 10⁻¹². Lipa and colleagues resolved the specific heat with sub-nanokelvin [[Sensor|thermometry]] to **within 2 nK of the transition, with no detectable rounding**; their revised 2003 analysis gives **alpha = −0.0127 ± 0.0003**, with amplitude ratio A⁺/A⁻ = 1.053 ± 0.002. The negative sign matters: alpha < 0 makes the peak a finite cusp, not a true divergence. It still looks like a lambda. This is routinely called the most precisely measured critical exponent in [[Physics|physics]], and it is the flagship [[Experimental_system|experiment]] that had to leave the planet to exist at all. **And it is, right now, in trouble.** Hyperscaling gives nu = (2 − alpha)/3, so the flight value implies nu = 0.6709(1). Independent [[Monte_Carlo_method|Monte Carlo]] [[Mathematical_model|simulation]] gives nu = 0.67169(7); the conformal bootstrap gives nu = 0.67175(10). The two theory routes agree with each other to a part in ten thousand and disagree with the flight [[Estimation_theory|measurement]] by roughly **8 [[Probability|standard deviations]]** — a gap Chester and co-workers call "decades-old" and say their work sharpens rather than closes. Nor is the flight result isolated: Singsaas and Ahlers' superfluid-[[Density|density]] exponent, zeta = 0.6717 ± 0.0004, sits on the theory side and by scaling implies alpha ≈ −0.015, not −0.0127. Do not average these into a consensus. Either the flight analysis carries an unidentified [[Accuracy_and_precision|systematic]], or 3D XY criticality is not what everyone believes, and nobody has shown which. ## Bose–Einstein condensation: a real relation, not an identity London's 1938 insight was that a gas of [[Boson|bosons]] condenses, and [[Helium-4|helium-4]] is a boson because its nucleus holds two [[Proton|protons]] and two [[Neutron|neutrons]] and its [[Spin_(physics)|spin]] is zero — the property that separates it categorically from [[Helium-3|helium-3]], a [[Fermion|fermion]] that stays normal until roughly a thousand times colder. Evaluate the ideal-gas condensation temperature at the actual number [[Density|density]] of the liquid, n = 2.18 × 10²² cm⁻³, and you get **about 3.1 K** against a measured 2.1768 K. Close. Not equal. The gap is what the interatomic [[Force|forces]] do, and the fact that it is only about 30 per cent is why London's argument persuaded people. The popular account then overreaches, implying that below T_lambda the [[Liquid_helium|liquid]] *is* the condensate — that every atom drops into the ground state, and that the superfluid fraction and the condensate fraction are one number. They are not, and the difference is enormous. rho_s/rho reaches 0.993 by 1.00 K; the **condensate fraction at T = 0 is of order 7 to 10 per cent**, and the literature genuinely disputes where in that band it sits. Glyde and colleagues' [[Neutron_diffraction|neutron]] [[Accuracy_and_precision|measurement]] gives (7.25 ± 0.75) per cent at saturated vapour pressure; Prisk and colleagues find about 7.5 per cent at 1.09 K; path-integral ground-state [[Monte_Carlo_method|Monte Carlo]] gives 8.1 ± 0.2 per cent; Balibar's review reports the then-accepted value as 10 ± 1.5 per cent, with 1980s work above 10 before [[Sensor|instrumental]] resolution improved. Ninety per cent or more of the liquid is *never* in the condensate, even at absolute zero, because the [[Force|interactions]] deplete it. The honest formulation: [[Superfluidity|superfluidity]] and Bose–Einstein condensation are distinct properties that happen to arrive together here. The condensate supplies the macroscopic phase coherence that quantises the circulation; the [[Superfluid_helium-4|superfluid density]] is a hydrodynamic response function counting almost the whole [[Liquid_helium|liquid]]. Conflating the two is the commonest error made about the lambda point, and it is made almost universally. ## Sources Annotated; one clause each on what the source establishes. Bibliography lines are link-light by house rule (§4). **The transition temperature and its conditions** - Bureau International des Poids et Mesures, Consultative Committee for Thermometry, *Guide to the Realization of the ITS-90: Vapour-Pressure Scales for ³He and ⁴He* (2018). [bipm.org](https://www.bipm.org/documents/20126/41773843/Guide_ITS-90_3_VPS_p_2018.pdf/dcd65f47-8699-d2f2-cace-44885f4f49fb) — verbatim: "The 4He equations coincide at the lambda point (2.1768 K, 5041.8 Pa)"; also the He I / He II naming convention. The authority for the paired temperature-and-pressure form used throughout this article. - Donnelly, R. J., and Barenghi, C. F. (1998). "The Observed Properties of Liquid Helium at the Saturated Vapor Pressure." *Journal of Physical and Chemical Reference Data* **27**(6), 1217–1274. doi:[10.1063/1.556028](https://doi.org/10.1063/1.556028) · [NIST reprint](https://srd.nist.gov/jpcrdreprint/1.556028.pdf) — T_lambda = 2.1768 K on ITS-90; the adopted asymptotic superfluid-density parameters zeta = 0.6717, k₀ = 2.403, k₁ = −1.46 (p. 1225); Table 2.4 giving rho_s/rho = 0.093 at 2.16 K and 0.993 at 1.00 K. The standard tabulation for every thermophysical number in this cluster. - Wikipedia, "Lambda point" — the two triple points bounding the lambda line, verbatim: the vapour–He-I–He-II triple point "at 2.1768 K (−270.9732 °C) and 5.0418 kPa (0.049759 atm)" and the bcc–He-I–He-II triple point "at 1.762 K (−271.388 °C), 29.725 atm (3,011.9 kPa)". Tertiary; used because it agrees with BIPM at the SVP end and supplies the melting-curve end in the same units. The 14 mK/bar average slope is this article's own arithmetic on those two endpoints, not a quoted value. **Discovery and the two-fluid model** - Kapitza, P. (1938). "Viscosity of Liquid Helium below the λ-Point." *Nature* **141**(3558), 74. doi:[10.1038/141074a0](https://doi.org/10.1038/141074a0) — submitted 3 December 1937; the slit experiment, the upper bound on viscosity, and the coining of "superfluid" by analogy with superconductivity. - Allen, J. F., and Misener, A. D. (1938). "Flow of Liquid Helium II." *Nature* **141**(3558), 75. doi:[10.1038/141075a0](https://doi.org/10.1038/141075a0) — submitted 22 December 1937, published in the same issue on the facing page; the prior "upper limit of 10⁻⁵ C.G.S. units for the viscosity of helium II by measuring the damping of an oscillating cylinder", and the capillary result independent of pressure head and bore. The back-to-back publication is why credit for the discovery of superfluidity is joint, a point the popular account routinely gets wrong in Kapitza's favour. - *Il Nuovo Saggiatore* (Società Italiana di Fisica), "Who discovered superfluidity?" [ilnuovosaggiatore.sif.it](https://www.ilnuovosaggiatore.sif.it/article/142) — the submission dates, the independence of the two methods, and the modern attribution to both groups. - Balibar, S. "Looking Back at Superfluid Helium." *Séminaire Poincaré*. [seminaire-poincare.pages.math.cnrs.fr](https://seminaire-poincare.pages.math.cnrs.fr/balibar.pdf) — Keesom's specific-heat peak and the naming of the lambda point; verbatim on boiling, "When crossing Tλ, the liquid stops boiling. This is because the thermal conductivity of liquid helium has suddenly increased, so that the temperature is very homogeneous"; London's ideal-gas estimate, "Inserting a number density n = 2.18 × 10²²cm⁻³ … leads to TBEC = 3.1 K while Tλ = 2.2 K"; and the condensate fraction quoted as "10 ± 1.5 %". - Balibar, S. (2017). "Laszlo Tisza and the two-fluid model of superfluidity." *Comptes Rendus Physique*. [sciencedirect.com](https://www.sciencedirect.com/science/article/pii/S163107051730097X) — the Tisza-to-Landau lineage of the two-fluid picture. **Paywalled; not opened for this article, cited for the record only.** - Tisza, L. (1938). "Transport Phenomena in Helium II." *Nature* **141**, 913 — the two-fluid picture, built on London's condensate suggestion. Landau, L. D. (1941). "Theory of the Superfluidity of Helium II." *Physical Review* **60**, 356 [also *J. Phys. USSR* **5**, 71] — the same hydrodynamics rebuilt on phonons and rotons with no condensate bookkeeping. Andronikashvili, E. L. (1946). *J. Phys. USSR* **10**, 201 — the disc-stack torsional oscillator that measures rho_n/rho directly, and the experiment rendered in the microsim above. **[UNVERIFIED]**: these three citations were not independently opened during this pass; the pagination is as given in the standard literature and in the microsim's source header. **Critical behaviour, and the flight** - Lipa, J. A., Nissen, J. A., Stricker, D. A., Swanson, D. R., and Chui, T. C. P. (2003). "Specific heat of liquid helium in zero gravity very near the lambda point." *Physical Review B* **68**, 174518. doi:[10.1103/PhysRevB.68.174518](https://doi.org/10.1103/PhysRevB.68.174518) · [arXiv:cond-mat/0310163](https://arxiv.org/abs/cond-mat/0310163) — verbatim: "The optimum value of the critical exponent describing the specific heat singularity was found to be α = −0.0127 ± 0.0003"; A⁺/A⁻ = 1.053 ± 0.002; the experiment "was flown in late October 1992 on STS-52"; data "to within 2 nK of the transition"; and the reason it had to fly, that on the ground "the lambda transition will be severely rounded over a temperature interval of about 1.3 μK per centimetre of hydrostatic head in a sample". Also the universality statement: "the primary example of the universality class with a two-dimensional order parameter in three spatial dimensions (n=2, D=3)". - Singsaas, A., and Ahlers, G. (1984). "Universality of static properties near the superfluid transition in ⁴He." *Physical Review B* **30**(9), 5103. doi:[10.1103/PhysRevB.30.5103](https://doi.org/10.1103/PhysRevB.30.5103) — the superfluid-density exponent "ζ = 0.6717 ± 0.0004 at vapor pressure", which "yields a specific-heat exponent α = −0.015 via scaling". This is the second experimental leg of the dispute and it lands on the theory side, not on the flight value. - Chester, S. M., Landry, W., Liu, J., Poland, D., Simmons-Duffin, D., Su, N., and Vichi, A. (2020). "Carving out OPE space and precise O(2) model critical exponents." *Journal of High Energy Physics* **2020**(6), 142. doi:[10.1007/JHEP06(2020)142](https://doi.org/10.1007/JHEP06(2020)142) · [arXiv:1912.03324](https://arxiv.org/abs/1912.03324) — conformal-bootstrap nu = 0.67175(10) against Monte Carlo 0.67169(7) and experiment 0.6709(1); verbatim from the abstract, their results "sharpen the existing decades-old 8σ discrepancy between theory and experiment", and from the body, "experimental results and Monte Carlo results for the critical exponents of the O(2) model have been in 8σ tension for two decades". - *Journal Club for Condensed Matter Physics* (January 2020), "Conformal bootstrap and the λ-point specific heat experimental anomaly." [condmatjclub.org](https://www.condmatjclub.org/uploads/2020/01/JCCM_January_2020_02.pdf) — a readable statement of the same three numbers side by side and of what would have to be wrong for each to be reconciled. **Transport, and the condensate fraction** - Sciacca, M., Jou, D., and Mongiovì, M. S. (2013). "Effective thermal conductivity of helium II: from Landau to Gorter–Mellink regimes." [arXiv:1310.6094](https://arxiv.org/abs/1310.6094) — the heat flux "becomes proportional to the cubic root of the temperature gradient" in the turbulent regime, and the effective conductivity depends on temperature, channel radius, vortex line density and heat current. The load-bearing point that helium II has no single quotable thermal conductivity. - Wikipedia, "Superfluid helium-4" — verbatim: "heat is transported, not by heat conduction, but by convection", with the normal-component flow "up to 20 cm/s", and the rho_s/rho rise from zero at T_lambda to one at zero kelvin. Tertiary; used for the qualitative transport statement alongside the primary source above. - Prisk, T. R., Bryan, M. S., Sokol, P. E., Granroth, G. E., Moroni, S., and Boninsegni, M. (2017). "The Momentum Distribution of Liquid ⁴He." [arXiv:1703.03018](https://arxiv.org/abs/1703.03018) — the condensate fraction "is zero in the normal fluid, becomes finite in the critical region below T_λ, and reaches a value of 7.5% at 1.09 K"; also that it builds up rapidly just below the transition rather than gradually. - Rota, R., and Boronat, J. (2012). "Condensate Fraction in Liquid ⁴He at Zero Temperature." *Journal of Low Temperature Physics* **166**. doi:[10.1007/s10909-011-0410-9](https://doi.org/10.1007/s10909-011-0410-9) · [arXiv:1109.6133](https://arxiv.org/abs/1109.6133) — path-integral ground-state Monte Carlo n₀ = 0.081 ± 0.002 at the equilibrium density, falling to 0.8 % at 87 bar; also the source for the experimental n₀ = (7.25 ± 0.75) % at SVP attributed to Glyde and colleagues, and the note that the 1980s measurements "slightly above 10%" were "affected by a poor instrumental resolution". **Page number not verified; volume, year and DOI were.** The Glyde primary paper was not opened directly. - Vinen, W. F. (1961). "The detection of single quanta of circulation in liquid helium II." *Proceedings of the Royal Society A* **260**, 218. doi:[10.1098/rspa.1961.0029](https://doi.org/10.1098/rspa.1961.0029); preceded by Vinen, W. F. (1958), "Detection of Single Quanta of Circulation in Rotating Helium II", *Nature* **181**, 1524. doi:[10.1038/1811524a0](https://doi.org/10.1038/1811524a0) — the vibrating-wire detection of quantised circulation predicted by Onsager and Feynman. The value h/m₄ = 9.97 × 10⁻⁸ m² s⁻¹ printed above is this article's own arithmetic from the 2019 SI Planck constant and the helium-4 atomic mass, not a quoted figure. **Volume and page as standardly cited; the DOIs resolve but the papers are behind a paywall and were not opened.** <!-- COMPENDIUMLINK:BEGIN g19 — generated from _registry/plans/THURY_COMPENDIUM_SECTIONS.md; do not hand-edit inside --> *Linked from the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]], section 26, Cryogenics.* <!-- COMPENDIUMLINK:END --> <!-- THURYSIM:BEGIN g21 — Thury Compendium microsim (framework build, specs/variants/Lambda_point.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Lambda point* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Lambda_point.html" data-title="Lambda point"></div> *Built from `MICROSIM_GUIDE/specs/variants/Lambda_point.json`; part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]] set.* <!-- THURYSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Lambda_point) : [Wikitube](https://en.wikitube.io/wiki/Lambda_point) ## Previous hub tags Hubs: `Life_Physics`. 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