Superfluidity |

**In General **> s.a. bose-einstein
condensation; particle statistics.

* __Properties__: Superfluids exhibit
zero viscosity, and quantized vortices when rotated or subject to a temperature gradient.

* __Method__: Study using second-waves, regions with different concentrations
of ordinary/superfluid components.

@ __General references__: Feynman RMP(57);
Khalatnikov 65; SA(76)dec; Collins PT(92)jun;
news pn(96)oct;
Guénault 03; Adams & Bry PhyA(04);
Annett 04 [intro];
Brandão NJP(05)
[order parameter and entanglement]; Balibar CP(07);
Pilati et al PRL(08)
[critical *T*, 2D and 3D]; Yu AP(08)
[as a Bose exchange effect]; Sewell & Wreszinski JPA(09)
[mathematical theory]; Dupuis PRL(09)
[unified picture]; Roberts CP(09) [drag forces on moving objects]; Tsubota et al PRP(13) [rev];
Andrianopoli PLB(14) [field-theoretical description];
Schmitt LNP-a1404 [intro, field-theoretical approach and applications]; Wreszinski a1506-conf [rev].

@ __History__: Andronikashvili 90; Donnelly PT(95)jul;
Balibar phy/06,
Griffin pw(08)aug
[discovery]; Kadanoff JSP(13)-a1303 [Lev Landau and John Bardeen, and the importance of the condensate].

**Types / Examples** > s.a. knots [quantum knots in a superfluid]; Quasiparticles; sound; turbulence.

* __Helium__: Known and studied since 1938; In ^{4}He,
pairs of atoms condense into a macroscopically coherent quantum state (Bose-Einstein
condensation) at 2.18 K, which manifests itself as a frictionless
fluid; In ^{3}He, the situation is not so simple,
and is usually described by the two-fluid model invented by Laszo Tisza
and Lev Landau in the late 1930s; He II (0 to 2.172 K) is a superfluid, highly
heat-conductive by friction-free convection and described by the Euler equation for an ideal inviscid fluid;
He I (2.172 to 4.2 K) is an ordinary fluid, governed by the Navier–Stokes equation for viscous flow;
The superfluid can also be treated, as proposed by Fritz London, Lars Onsager, and Richard Feynman,
as a macroscopic quantum state characterized by a complex wavefunction.

* __Other examples__: 2005, Evidence seen in solid hydrogen
[@ news pn(05)mar].

* __In curved spacetime__: Superfluids in intense gravitational fields are assumed to be present in neutron star and quark star cores.

@ ^{3}__He__: Bunkov et al PRL(00)
[sets of 4 atoms?]; Finne et al Nat(03)aug
+ pn(03)aug
[criterion for the onset of turbulence]; Volovik JLTP(08)cm/07 [history];
Ma & Wang PhyA(08) [new models];
Golovko a1103 [leaking out of an open container]; Volovik & Krusius Phy(12) [coherent quantum states of different chirality].

@ ^{4}__He__: Pollet et al PRL(08),
comment Balibar Phy(08)
[solid]; Guo et al PRL(10)
+ Barenghi Phy(10) [visualization of turbulent behavior of normal-fluid component]; news sn(17)mar [simulations and area law for entropy]; > s.a. condensed
matter [supersolid].

@ __In general relativity and cosmology__: Zurek Nat(85)oct [topological defects in cosmology and superfluidity];
Carter gq/99-ln
[vortex dynamics], G&C(00)ap [neutron
stars]; Casini & Montemayor gq/99 [covariant];
Volovik PRP(01)gq/00 [analogs];
Garcia de Andrade gq/05 [with
torsion]; Villegas a1511 [effect of spacetime curvature]; Huang 16 [the universe as a quantum superfluid].

@ __Examples__: Donnelly pw(97)feb
[rotons]; Kapusta PRL(04)ht [for
Dirac neutrinos]; Bulgac et al PRL(06)
[spin-1/2 fermions]; Kastrinakis AP(14)-a0901 [new
states]; news PhysOrg(10)oct [light];
Enss Phy(14) [transition between bosonic and fermionic superfluidity in 2D quantum fluids of ultracold atoms]; López et al PRL(15) [using self-propelling bacteria].

@ __Applications__: Sato & Packard PT(12)oct [superfluid He quantum interference device, SHeQUID].

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