Vortex in A Superfluid
In a superfluid, a quantum vortex is a hole with the superfluid circulating around the vortex; the inside of the vortex may contain excited particles, air, vacuum, etc. The thickness of the vortex depends on a variety of factors; in liquid helium, the thickness is on the order of a few Angstroms.
A superfluid has the special property of having phase, given by the wavefunction, and the velocity of the superfluid is proportional to the gradient of the phase. The circulation around any closed loop in the superfluid is zero, if the region enclosed is simply connected. The superfluid is deemed irrotational. However, if the enclosed region actually contains a smaller region that is an absence of superfluid, for example a rod through the superfluid or a vortex, then the circulation is,
where is Planck's constant divided by, m is the mass of the superfluid particle, and is the phase difference around the vortex. Because the wavefunction must return to its same value after an integral number of turns around the vortex (similar to what is described in the Bohr model), then, where n is an integer. Thus, we find that the circulation is quantized:
Read more about this topic: Quantum Vortex
Famous quotes containing the word vortex:
“The Image is more than an idea. It is a vortex or cluster of fused ideas and is endowed with energy.”
—Ezra Pound (1885–1972)