Quantized vortices

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Quantized vortices

A type of flow pattern exhibited by superfluids, such as liquid 4He below 2.17 K (-455.76°F). The term vortex designates the familiar whirlpool pattern where the fluid moves circularly around a central line and the velocity diminishes inversely proportionally to the distance from the center. The strength of a vortex is determined by the circulation, which is the line integral of the velocity around any path enclosing the central line. See Vortex

A superfluid is believed to be characterized by a macroscopic (that is, large-scale) quantum-mechanical wave function &psgr;. This wave function locks the superfluid into a coherent state. Since the velocity around the vortex increases without limit as the center is approached, the superfluid density and thus &psgr; must vanish at the center in order to avoid an infinite energy. Thus the central core of the vortex marks the zeros, or nodal lines, in the macroscopic wave function. See Quantum mechanics

Quantized vortex lines are usually produced by rotating a vessel containing superfluid helium. At very low rotation speeds, no vortices exist: the superfluid remains at rest while the vessel rotates. At a certain speed the first vortex appears and corresponds to the first excited rotational state of the system. If the container continues to accelerate, additional quantized vortices will appear. At any given speed the vortices form a regular array which rotates with the vessel.

Quantized vortex lines were first detected in the mid-1950s by their influences on superfluid thermal waves traveling across the lines. In the late 1950s it was discovered that electrons in liquid helium form tiny charged bubbles which can become trapped on the vortex core but can move quite freely along the line. These electron bubbles (often referred to as ions) have been one of the most useful probes of quantized vortices. Researchers have been able to use ions to detect single quantized vortex lines. In one experiment the trapped ions are pulled out at the top of the vortex lines, accelerated, and focused onto a phosphor screen. The pattern of light thus produced on the phosphor is a map of the position of the vortices where they contact the liquid meniscus (see illustration). See Liquid helium, Superfluidity

Stationary configurations of vortices which appear when a cylindrical container of superfluid 4 He is rotated about its axisenlarge picture
Stationary configurations of vortices which appear when a cylindrical container of superfluid 4He is rotated about its axis
References in periodicals archive ?
In this study, the BEC images did indeed show the presence of quantized vortices.
Because it can be shown using standard definition of Hubble law that redshift quantization implies quantized distance between galaxies in the same cluster, then one could say that this equation of quantized distance (11) is a result of topological quantized vortices (9) in astrophysical scale [5]; and it agrees with Gross-Pitaevskii (quantum phion condensate) description of CMB spectrum [1].
Now it is clear from (15) that quantized vortices could be formed by different source of flux.
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2 Quantization of celestial systems and topological quantized vortices
It is worth noting here, because vortices could be defined as elementary objects in the form of stable topological excitations [4], then equation (6) could be interpreted as Bohr-Sommerfeld-type quantization from topological quantized vortices.
Their argument was based on propagation torsion model for quantized vortices [23].