quantity

superfluid density

The density of the superfluid component of a quantum fluid.
28 related articles · 2 formulas

Description

Superfluid density is a concept from quantum mechanics that describes how much of a fluid's mass behaves as a superfluid — a phase with zero viscosity and frictionless flow. In a superfluid like helium-4 below its lambda point, not all atoms participate in the superfluid flow; a fraction remains in a 'normal' component that carries entropy and experiences dissipation. The superfluid density is that fraction's mass density, and it varies with temperature, dropping to zero at the transition temperature where superfluidity disappears.

History

The concept was introduced by Lev Landau in the 1940s as part of his two-fluid theory of superfluidity, developed to explain the unusual thermal and mechanical properties of liquid helium-4.

How it works

The two-fluid model treats a superfluid as a mixture of two interpenetrating components: a superfluid component with zero entropy and zero viscosity, and a normal component with finite entropy and viscosity. The superfluid density is the mass density of the superfluid component. It is determined experimentally by measuring the response of the fluid to rotation or oscillation — a superfluid cannot rotate like a normal fluid because it has no viscosity, so the moment of inertia is reduced. The superfluid density is the fraction of the fluid that does not participate in the normal rotational motion.

In practice

Superfluid density is a key observable in experiments on ultracold atomic gases and in studies of neutron star interiors, where superfluidity affects cooling and rotation.

Fun fact

In a superfluid, the superfluid density can be zero even at absolute zero if the fluid is confined to a narrow channel, due to quantum fluctuations.

Concept graph →

Formulas

$$T_{\mathrm{BKT}} = \frac{\pi}{2} \rho_s(0)$$
Temperature of vortex unbinding in 2D superfluids.
What is in the formula
T_BKTvariableBKT transition temperature — temperature kelvin
ρ_svariableSuperfluid density at zero temperature — superfluid density kilogram per metre
$$J_0 = \frac{\rho_s}{m}$$
Superfluid stiffness relates to density and effective mass.
What is in the formula
J_0variableBare superfluid stiffness (phase stiffness) — superfluid stiffness joule
ρ_svariableSuperfluid mass density — superfluid density kilogram per cubic metre
mvariableEffective mass of the superfluid particles (e.g., helium atom mass) — mass kilogram

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