# Superfluidity Superfluidity is the state in which a [[Liquid_helium|liquid]] flows with exactly zero [[Viscosity|viscosity]] and can circulate only in fixed quanta; it is a general property of Bose-condensed and of paired quantum fluids, but the case that carries the [[Physics|physics]] is [[Helium-3|helium-3]], because a ³He atom is a [[Fermion|fermion]] and therefore cannot condense until it has first paired — which is why its transition sits roughly a thousand times colder than [[Helium-4|helium-4]]'s, and why its condensate has [[Structure|structure]], [[Multistability|more than one stable phase]], and an [[Energy|energy]] gap that depends on direction, none of which ⁴He's has. ## Microsims — three.js <iframe src="https://wikitube-3d-microsims.netlify.app/Superfluidity.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Superfluidity — three.js microsim"></iframe> **`Superfluidity` (three.js).** The big sphere is drawn in momentum space, not real space — every point on it is a direction k̂ on the Fermi surface and the radius you see *is* the energy gap |Δ(k̂)| in that direction, so the faint wire cage marks the bare Fermi radius and any bulge beyond the cage is literally the gap; readers get this wrong constantly, so it is worth saying twice that this is an energy plotted over directions and not the shape of a drop of liquid. Use the phase selector to step from s-wave BCS, where the surface is a perfect sphere, to the ³He A phase, where it is pinched to zero at two antipodal point nodes, to the ³He B phase, which has the same radius everywhere and is distinguished only by its d-vector texture — so tilt the **l** axis and switch the texture arrows on and off, because that toggle is the only thing on screen that tells B from an ordinary superconductor. Push the T/Tc slider up through 1 and the gap closes along a genuinely solved weak-coupling BCS gap equation — bisection on a cutoff-free integral form, not the usual tanh interpolation — reproducing Mühlschlegel's published values to four decimals. The live HUD quantity is min|Δ| / max|Δ|, scanned from the actual gap array rather than asserted: it reads exactly 0.00 in the A phase and 1.00 in the other two, and that number is the numeric signature of the point nodes. ## Overview — flow without viscosity A superfluid flows without [[Viscosity|shear stress]]. Driven through a channel narrow enough to clamp any ordinary [[Liquid_helium|liquid]] it passes freely; set rotating in a vessel it keeps circulating without [[Damping|damping]] and without [[Oscillation|decay]]. This is not "very low friction": the [[Energy|energy]] of the flow *cannot* be dissipated, because below a critical [[Velocity|velocity]] there is no excitation of the right [[Angular_frequency|frequency]] and momentum available to absorb it. Ordinary [[Fluid_dynamics|fluid dynamics]] therefore fails outright, and the working description is the two-fluid picture: the [[Physical_system|system]] behaves as an interpenetrating mixture of a normal component carrying all the [[Entropy|entropy]] and all the viscosity, and a superfluid component carrying neither. The two have separate velocity fields, which is why [[Heat_transfer|heat]] in helium II propagates as a [[Wave|wave]] — second sound — rather than by diffusive [[Thermodynamic_equilibrium|equilibration]], and why the fountain effect exists at all. The second half of the definition is quantization. The superfluid component is described by one macroscopic [[Quantum_mechanics|quantum-mechanical]] phase — a single [[Complex_analysis|complex]] field spanning the whole vessel — and requiring that phase to be single-valued around any closed loop forces the circulation into integer multiples of a fixed quantum. Rotation is therefore never smooth. It is carried by a discrete lattice of vortex lines, each a topological defect in the phase field, and this [[Emergence|emergent]] discreteness in a macroscopic [[Dynamics_(mechanics)|mechanical]] quantity is the sharpest fingerprint of the state — the reason superfluidity is a [[Phase_transition|phase]] and not a limit of low [[Second_law_of_thermodynamics|dissipation]]. Superfluidity in ⁴He was found in 1938 by two groups at once — Pyotr Kapitza in Moscow, and John F. Allen with Don Misener in Cambridge — reporting back to back in the same issue of *Nature* on 8 January 1938. The transition is the lambda point: **T_λ = 2.1768 K at p = 5041.8 Pa**, on the saturated-vapour-pressure curve, on ITS-90, where the two BIPM vapour-pressure equations for ⁴He coincide. The familiar "2.17 K" and "2.172 K" are truncations of it, not independent measurements: the [[Accuracy_and_precision|precision]] belongs to the [[Cryogenics|cryogenic]] scale, not to any one experiment. Even here the pressure is load-bearing — the λ-line is a *line*, climbing to the λ-point on the melting curve near 1.76 K and about 30 bar, so the [[Boiling_point|coexistence]] condition travels with the number. [[Superfluid_helium-4|Superfluid helium-4]] carries the ⁴He story; [[Helium|helium]] and the [[Noble_gas|noble gases]] carry the chemistry. ## Why helium-4 is easy and helium-3 is hard Everything here descends from one counting rule. A composite particle behaves as a [[Boson|boson]] if it contains an even total number of constituent fermions and as a [[Fermion|fermion]] if it contains an odd number. A ⁴He atom is two [[Proton|protons]], two [[Neutron|neutrons]] and two [[Electron|electrons]] — six — so it is a boson, with zero nuclear [[Spin_(physics)|spin]]. A ³He atom is two protons, **one** neutron and two electrons — five — so it is a fermion, I = ½. That single odd nucleon is also what makes ³He useful in [[Nuclear_magnetic_resonance|NMR]], in [[Hyperpolarization_(physics)|hyperpolarization]] and in [[Neutron_detection|neutron detection]]; here it is what makes it hard to condense. This is spin-statistics, not an empirical fit. The consequence is asymmetric and severe. ⁴He atoms may all occupy one single-particle state, so the [[Chemical_element|element]] condenses directly on cooling and its order parameter is a single complex number. ³He atoms may not — exclusion forbids it — so they must first bind into pairs, each pair a composite boson, and only that paired object can condense. Pairing is a weak many-body effect built on the residual attraction near the Fermi surface, so it sets its own, far smaller [[Thermodynamics|thermodynamic]] scale: the relevant [[Binding_energy|binding energy]] is millikelvin, not kelvin, and [[Zero-point_energy|zero-point motion]] keeps the [[Liquid_helium|liquid]] from freezing long before it gets there. The [[Accuracy_and_precision|numbers]] say exactly this. Against T_λ = 2.1768 K, the ³He transition is 2.491 mK at melting pressure and 0.929 mK at zero pressure on the Greywall scale — ratios of **874×** and **2,340×**. "About a factor of a thousand" is the right order of magnitude, but the honest form is that ⁴He condenses between roughly 900 and 2,300 times warmer than ³He pairs, depending which ³He pressure you compare against. This is the single most important comparison in the subject: it is why a [[Dilution_refrigerator|dilution refrigerator]] must exist before the [[Experimental_system|experiment]] can, why ³He [[Cryogenics|cryogenics]] is a different engineering problem from [[Helium_cryogenics|⁴He cryogenics]], and why the same fridges now sit under [[Quantum_computing|quantum computing]] and millikelvin [[Sensor|sensing]]. ## Superfluid helium-3: unconventional pairing In a conventional [[Superconductivity|superconductor]], and in [[Superfluid_helium-4|superfluid ⁴He]], the condensate is one complex scalar: the gap Δ is identical in every direction, there is no axis to point at, no [[Pattern_formation|texture]] to form, no [[Multistability|second stable phase]] to find. Superfluid ³He pairs instead with orbital angular momentum **L = 1** (p-wave) and spin **S = 1** (spin triplet). The hard repulsive core of the interatomic [[Force|potential]] penalises the L = 0 channel — the [[Atomic_orbital|s-wave orbital]] the atoms cannot profitably use — while spin-fluctuation exchange in this strongly correlated [[Complex_system|many-body system]] favours parallel spins: the paramagnon [[Coupling|coupling]] Anderson and Brinkman invoked in 1973 to explain which phase wins where. The structural consequence is the whole story. With L = 1 and S = 1 the order parameter is not a number but a **3×3 complex matrix** A_{μi}, a [[Tensor|tensor]] joining a spin index μ to an orbital index i. That object has room for internal [[Structure|structure]] a scalar does not, and three things follow at once. The gap becomes a *function on the Fermi surface*, Δ(k̂), so quasiparticles moving in different directions see different [[Binding_energy|binding energies]]. The condensate acquires orbital and spin axes — the vectors **l** and **d** — which bend through space, are pinned by walls and by [[Superconducting_magnet|magnetic fields]], and carry [[Crystal_structure|defects]] as an ordered medium does. And more than one distinct superfluid phase becomes possible in the same substance, a genuine [[Multistability|multistability]] of the [[Thermodynamic_equilibrium|equilibrium]] state rather than a [[Nonlinear_system|nonlinear]] curiosity. The **ABM (Anderson–Brinkman–Morel) axial state** is the A phase. Its orbital part is m + i n with l = m × n, giving |Δ(k̂)| = Δ_A sin θ measured from **l**, so the gap vanishes *exactly* at two antipodal **point nodes**, k̂ = ±l. Those nodes leave gapless [[Fermion|fermionic]] quasiparticles travelling along **l** even deep in the superfluid state, and they belong to the pairing [[Geometry|symmetry]], not to the [[Thermodynamics|temperature]]: they do not close up as the liquid is cooled. A is an equal-spin-pairing state whose **d** is a single fixed unit vector, locked parallel to **l** in bulk [[Thermodynamic_equilibrium|equilibrium]] by the nuclear dipole–dipole [[Coupling|coupling]] — the lock producing the longitudinal [[Nuclear_magnetic_resonance|NMR]] [[Frequency_domain|frequency]] shift, the [[Signal|signal]] that identified the phase. A naming caution: "ABM" conflates two papers a decade apart. Anderson and Morel proposed the state in 1961, with an [[Estimation_theory|estimated]] transition "below 0.02 K", an order of magnitude too warm; Anderson and Brinkman explained its stabilisation in 1973. Cite both. The **BW (Balian–Werthamer) state** is the B phase: A_{μi} = Δ_B R_{μi}(n, θ_L). Here the gap *magnitude* is isotropic — as isotropic as s-wave — so nothing in the shape of Δ(k̂) separates B from an ordinary BCS [[Superconductivity|superconducting]] condensate, and no [[Sensor|probe]] of gap size alone can [[Detection_theory|discriminate]] them. The whole difference lives in the spin channel: d(k̂) = R·k̂ is a hedgehog rigidly rotated by the Leggett angle θ_L = arccos(−1/4) = 104.5°, a fixed element of [[Lie_group|the rotation group]], not an adjustable [[Mathematical_model|model]] parameter. Balian and Werthamer's 1963 paper predicts the spin susceptibility falling to two-thirds of normal, and that is the measurable which separates the two. Hence the d-vector toggle in the microsim above: with the arrows off, the [[Geometry|geometry]] of the sphere is silent and B and s-wave are the same picture. ## The temperatures, stated with their pressures A ³He transition temperature quoted without a pressure is not a measurement, it is a fragment. Two [[Accuracy_and_precision|scales]] are also in simultaneous use — Greywall 1986, still ubiquitous in the literature, and PLTS-2000, adopted by the CIPM — and the [[Repeatability|conversion]] between them is not negligible at [[Cryogenics|millikelvin]] resolution. | Transition | Greywall 1986 | PLTS-2000 (official) | Pressure | |---|---|---|---| | Tc (A), **melting pressure** | 2.491 mK | 2.444 mK | 34.338 bar / 3.43407 MPa | | T_AB, melting pressure | 1.932 mK | 1.896 mK | 34.358 bar / 3.43609 MPa | | Solid Néel transition | 0.931 mK | 0.902 mK | 34.391 bar / 3.43934 MPa | | Tc, **zero pressure (SVP)** | 0.929 mK | 0.908 mK | 0 bar | | Polycritical point (PCP) | — | 2.273 mK | 21.22 bar | Four corrections follow directly, and this is where the article earns its keep. **"Superfluid ³He transitions at 2.491 mK" is wrong as stated** — which is how English Wikipedia gives it, with no pressure attached. 2.491 mK is the A-transition *at melting pressure*, 34.338 bar, on Greywall's scale; on PLTS-2000 the same [[Phase_transition|transition]] is 2.444 mK. Quote the number with its pressure and its scale, or do not quote it: a [[Signal|datum]] stripped of its conditions is not a [[Mathematical_model|model]] input. **There is no A phase at zero pressure.** In zero [[Superconducting_magnet|magnetic field]] the A phase exists only above the polycritical point, at 21.22 bar and 2.273 mK. At saturated vapour pressure the liquid goes normal → **B** directly; there is no A→B transition to see. Any account that has ³He passing through A on its way to B at low pressure describes a phase diagram that does not exist — and the [[Phase_space|phase-space]] [[Geometry|topology]] is the point, since the polycritical point is where three [[Thermodynamic_equilibrium|equilibrium]] surfaces meet. **Do not quote 2.7 mK as current.** The ~2.7 mK and ~2.1 mK figures in the discovery papers and in older reviews sit on a pre-1986 [[Cryogenics|temperature scale]]. Greywall notes explicitly that his 2.49 mK "differs quite substantially from the currently accepted value of about 2.7 mK." Those values are obsolete, not alternative — a [[Repeatability|scale]] artefact, not a disagreement about the [[Physics|physics]]. **Watch the 0.93 mK trap.** On the Greywall scale the solid ³He Néel transition (0.931 mK, at 34.391 bar on the melting curve) and the zero-pressure superfluid Tc (0.929 mK, at 0 bar) are numerically almost identical and physically unrelated: one is nuclear magnetic ordering in the *solid* [[Crystal_structure|lattice]], the other is Cooper pairing in the *[[Liquid_helium|liquid]]* thirty-four bar lower. Secondary sources swap them constantly. PLTS-2000 separates them a little (0.902 against 0.908 mK) but does not remove the hazard; only carrying the [[Thermodynamics|pressure]] and the [[Phase_transition|phase]] alongside the [[Signal|number]] does. ## The discovery, told accurately Douglas Osheroff, Robert Richardson and David Lee, at Cornell in 1972, saw two small anomalies — which they labelled A and B — in the pressurisation curves of ³He along the melting curve during Pomeranchuk [[Cryogenics|cooling]]. Their first paper, *Physical Review Letters* **28**, 885 (3 April 1972), is titled **"Evidence for a New Phase of Solid He³"**, and that title is not incidental: they attributed the features to the [[Crystal_structure|solid]]. The identification of the new phases as belonging to the [[Liquid_helium|liquid]] came in the second paper, *Physical Review Letters* **29**, 920, on [[Nuclear_magnetic_resonance|NMR]] evidence. Attributing the discovery of superfluid *liquid* ³He to PRL 28, 885 is a small [[Repeatability|bibliographic]] slip repeated everywhere, including in otherwise careful reviews — a reminder that a [[Science|scientific]] result and its first [[Signal|signature]] are not the same [[Physical_system|object]]. Anthony Leggett supplied the theory. Writing in the same PRL volume as the second Cornell paper — PRL **29**, 1227, three hundred and seven pages later — he identified the new phases as anisotropic p-wave, spin-triplet superfluids, then over three years built the spin-dynamics framework (the Leggett equations) that turned NMR line shifts into a phase-identification tool: a [[Differential_equation|differential-equation]] [[Mathematical_model|model]] whose [[Oscillation|oscillation]] [[Frequency_domain|frequencies]] are directly measurable. His 1975 *Reviews of Modern Physics* article fixed the ABM/BW assignment. The [[Science|science]] was recognised twice: the 1996 Nobel Prize in [[Physics|Physics]] to Lee, Osheroff and Richardson "for their discovery of superfluidity in helium-3," and the 2003 prize to Leggett, jointly with Alexei Abrikosov and Vitaly Ginzburg, "for pioneering contributions to the theory of [[Superconductivity|superconductors]] and superfluids." Leggett died on 8 March 2026. ## Why it is a reference system Superfluid ³He is the best-characterised unconventional paired condensate in existence, and its value now is largely as a template. It is a bulk, chemically pure, isotopically clean [[Experimental_system|experimental system]] with no lattice, no disorder and no doping, so the pairing symmetry can be studied without the confounds that dog every solid-state candidate: the [[Materials_science|materials science]] is subtracted and only the [[Physics|physics]] is left. That makes it the working [[Mathematical_model|model]] for three things it is not — a rare case in which the [[Complex_system|many-body system]] under study is simpler than the systems it explains. It is the model for **p-wave and other unconventional [[Superconductivity|superconductors]]**: the vocabulary of anisotropic gaps, nodal quasiparticles, multi-component order parameters and spin-triplet pairing in real [[Materials_science|materials]] was built on ³He first and exported afterwards. It is the model for **topological superfluids**: the A phase's two point nodes are Weyl points in the [[Configuration_space_(physics)|momentum-space]] structure, the B phase is fully gapped with a bulk invariant protected by time-reversal [[Geometry|symmetry]] — an [[Euler_characteristic|integer invariant]] of a map from the Fermi surface into the order-parameter space — and both host surface and vortex-core bound states, so ³He is where predictions about protected boundary modes can be tested in a [[Physical_system|system]] whose Hamiltonian is genuinely known. And it is the model for **fermionic pairing in neutron-star interiors**, where the [[Neutron|neutron]] fluid is expected to pair in a spin-triplet channel and the observable consequences — vortex pinning, glitches, [[Heat_transfer|cooling]] rates — follow from exactly the physics ³He shows in a millikelvin cell. Volovik's monograph presses further: the low-energy [[Structure|structure]] of the ³He-A order parameter reproduces the kinematics of relativistic quantum field theory, so the liquid doubles as a bench analogue for [[Physics|physics]] at a wholly different scale. ## Quantized vortices and the circulation quantum The cleanest place to see the pairing made measurable is the circulation quantum. Single-valuedness of the condensate phase forces the circulation around a [[Fluid_dynamics|vortex]] line to be an integer multiple of h/M, where M is the mass of whatever condensed. In ⁴He the condensing object is the [[Atomic_mass|atom]] itself — already a [[Boson|boson]] — so h/m₄ = 9.969 × 10⁻⁸ m²/s. In superfluid ³He the condensing object is a **pair**, of mass 2m₃, so h/2m₃ = 6.615 × 10⁻⁸ m²/s. The factor of two in the ³He denominator *is* the pairing, made into a laboratory observable: the two [[Velocity|circulation]] quanta stand in the ratio 2m₃/m₄, and nothing else about the two liquids enters. (Both are computed here from h = 6.626 070 15 × 10⁻³⁴ J s, [[Accuracy_and_precision|exact]] by the 2019 SI, and the ⁴He and ³He [[Atomic_mass|atomic masses]].) The same logic runs through [[Superconductivity|superconductivity]], where the charged analogue is the flux quantum h/2e and the identical factor of two carries the identical meaning; and it is why the vortex panel in the microsim accumulates a phase-winding [[Numerical_integration|line integral]] closing at exactly one quantum per lap. A superfluid is not merely a paired liquid: pairing gives you a gap, but it is the [[Self-organization|self-organised]] [[Geometry|topology]] of the phase that gives you superflow. ## Sources - **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). — One of the two simultaneous 1938 reports of superfluidity in ⁴He. *(Not in RESEARCH.md; metadata verified independently via Crossref.)* - **Allen, J. F.; Misener, A. D. (1938).** "Flow of Liquid Helium II." *Nature* **141**(3558), 75. DOI [10.1038/141075a0](https://doi.org/10.1038/141075a0). — The companion report, same issue, one page later. *(Not in RESEARCH.md; metadata verified independently via Crossref.)* - **BIPM (2018).** *Guide to the Realization of the ITS-90 — Vapour-Pressure Scales.* [PDF](https://www.bipm.org/documents/20126/41773843/Guide_ITS-90_3_VPS_p_2018.pdf/dcd65f47-8699-d2f2-cace-44885f4f49fb). — Source of the lambda point as **2.1768 K, 5041.8 Pa**, the value at which the two ⁴He vapour-pressure equations coincide. - **Osheroff, D. D.; Richardson, R. C.; Lee, D. M. (1972).** "Evidence for a New Phase of Solid He³." *Phys. Rev. Lett.* **28**(14), 885–888. DOI [10.1103/PhysRevLett.28.885](https://doi.org/10.1103/PhysRevLett.28.885). — The discovery paper; its title records the initial, incorrect attribution to the solid. - **Osheroff, D. D.; Gully, W. J.; Richardson, R. C.; Lee, D. M. (1972).** "New Magnetic Phenomena in Liquid He³ below 3 mK." *Phys. Rev. Lett.* **29**(14), 920–923. DOI [10.1103/PhysRevLett.29.920](https://doi.org/10.1103/PhysRevLett.29.920). — The NMR paper that places the transitions in the liquid; this is the one to cite for the discovery of superfluid ³He. - **Anderson, P. W.; Morel, P. (1961).** "Generalized Bardeen-Cooper-Schrieffer States and the Proposed Low-Temperature Phase of Liquid He³." *Phys. Rev.* **123**(6), 1911. DOI [10.1103/PhysRev.123.1911](https://doi.org/10.1103/PhysRev.123.1911). — The axial, equal-spin-pairing state later identified with the A phase. - **Balian, R.; Werthamer, N. R. (1963).** "Superconductivity with Pairs in a Relative p Wave." *Phys. Rev.* **131**(4), 1553. DOI [10.1103/PhysRev.131.1553](https://doi.org/10.1103/PhysRev.131.1553). — The isotropic-gap triplet state later identified with the B phase; predicts susceptibility falling to 2/3 of normal. - **Anderson, P. W.; Brinkman, W. F. (1973).** "Anisotropic Superfluidity in ³He: A Possible Interpretation of Its Stability as a Spin-Fluctuation Effect." *Phys. Rev. Lett.* **30**(22), 1108. DOI [10.1103/PhysRevLett.30.1108](https://doi.org/10.1103/PhysRevLett.30.1108). — Why the A state is stabilised at higher T and P; the "B" of "ABM." - **Leggett, A. J. (1972).** "Interpretation of Recent Results on He³ below 3 mK: A New Liquid Phase?" *Phys. Rev. Lett.* **29**(14), 1227–1230. DOI [10.1103/PhysRevLett.29.1227](https://doi.org/10.1103/PhysRevLett.29.1227). — Identifies the phases as p-wave, spin-triplet anisotropic superfluids. *(RESEARCH.md notes this DOI is constructed from the standard APS pattern; volume and pages are independently verified.)* - **Leggett, A. J. (1975).** "A theoretical description of the new phases of liquid ³He." *Rev. Mod. Phys.* **47**(2), 331–414. DOI [10.1103/RevModPhys.47.331](https://doi.org/10.1103/RevModPhys.47.331). — The review that fixed the ABM/BW identification of A and B and set out the spin-dynamics framework. - **Leggett, A. J. (2004).** "Nobel Lecture: Superfluid ³He: the early days as seen by a theorist." *Rev. Mod. Phys.* **76**(3), 999–1014. DOI [10.1103/RevModPhys.76.999](https://doi.org/10.1103/RevModPhys.76.999). — First-hand account of the 1972–75 theory. - **Greywall, D. S. (1986).** "³He specific heat and thermometry at millikelvin temperatures." *Phys. Rev. B* **33**(11), 7520. DOI [10.1103/PhysRevB.33.7520](https://doi.org/10.1103/PhysRevB.33.7520). — The Greywall scale: Tc(melting) = 2.491 mK, Tc(0 bar) = 0.929 mK; and the explicit remark that 2.49 mK "differs quite substantially" from the older ~2.7 mK. - **Tian, Y.; Smith, E.; Parpia, J. (2022).** "Conversion Between ³He Melting Curve Scales Below 100 mK." *J. Low Temp. Phys.* **208**(3), 298–311. DOI [10.1007/s10909-022-02721-z](https://doi.org/10.1007/s10909-022-02721-z). — The paper to cite for any Greywall ↔ PLTS-2000 conversion; source of both the 0-bar values and the melting-curve fixed points on both scales. - **PLTS-2000**, Provisional Low Temperature Scale 0.9 mK – 1 K, adopted by the CIPM (2000). [PTB fixed-point table](https://www.ptb.de/cms/en/ptb/fachabteilungen/abt7/fb-74/ag-744/the-provisional-low-temperature-scale-of-2000-plts-2000.html). — The official scale and its fixed points, including the melting pressures quoted above. - **Nature Communications 13, 7871 (2022).** DOI [10.1038/s41467-022-35532-7](https://doi.org/10.1038/s41467-022-35532-7). — Source for the polycritical point at 2.273 mK, 21.22 bar, below which there is no A phase in zero field. - **Mühlschlegel, B. (1959).** "Die thermodynamischen Funktionen des Supraleiters." *Z. Physik* **155**, 313–327. DOI [10.1007/BF01332932](https://doi.org/10.1007/BF01332932). — The tabulated numerical solution of the weak-coupling BCS gap equation against which the microsim's solver is checked. *(Not in RESEARCH.md; metadata verified independently via Crossref.)* - **Vollhardt, D.; Wölfle, P. (1990).** *The Superfluid Phases of Helium 3.* Taylor & Francis, London. ISBN 978-0-85066-412-6; CRC reissue 2003, DOI [10.1201/b12808](https://doi.org/10.1201/b12808). — The standard monograph for the phenomenology and theory of the ³He phases. - **Volovik, G. E. (2003).** *The Universe in a Helium Droplet.* Oxford University Press, International Series of Monographs on Physics 117. ISBN 978-0-19-850782-6. — The reference for the topological reading of the A and B phases and for the field-theory analogies. *(Not in RESEARCH.md; bibliographic details verified independently.)* - **The Nobel Prize in Physics 1996** — Lee, Osheroff, Richardson, "for their discovery of superfluidity in helium-3." [nobelprize.org](https://www.nobelprize.org/prizes/physics/1996/summary/). **The Nobel Prize in Physics 2003** — Abrikosov, Ginzburg, Leggett, "for pioneering contributions to the theory of superconductors and superfluids," announced 7 October 2003. [nobelprize.org](https://www.nobelprize.org/prizes/physics/2003/press-release/). *Built to the [[WT!Three_js_Microsim_Master_Class|three.js Master Class]].* <!-- COMPENDIUMLINK:BEGIN g19 — generated from _registry/plans/THURY_COMPENDIUM_SECTIONS.md; do not hand-edit inside --> **Part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]]** — main article for section 13, *Superfluidity*. Related sections: [[Vorticity]] · [[Liquid–liquid_critical_point]] · [[Nuclear_fusion]] · [[Cryogenics]]. <!-- COMPENDIUMLINK:END --> <!-- THURYSIM:BEGIN g21 — Thury Compendium microsim (framework build, specs/sims/Superfluidity.json); do not hand-edit inside --> **Microsim — three.js (Wikitube framework):** *Superfluidity* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/thury/Superfluidity.html" data-title="Superfluidity"></div> *Built from `MICROSIM_GUIDE/specs/sims/Superfluidity.json`; part of the [[WT!Thury_Hydrodynamics_Compendium|Thury Hydrodynamics Compendium]] set.* <!-- THURYSIM:END --> ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Superfluidity) : [Wikitube](https://en.wikitube.io/wiki/Superfluidity) ## Previous hub tags Hubs: `Life_Physics`. Portals: [[PORTAL_Helium-3]], [[PORTAL_Helium]].