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 from 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];
Singh & Mathey a2010 [2D ultracold Bose gas].

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

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