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Quantized Vortices


In an ordinary classical fluid the liquid can rotate at any speed. In superfluid helium-4 the velocity v_x of the superfluid component is quantized by the condition that

path integral of v_x dl = n(h/m)

where h is Planck's constant, m is the mass of one helium atom, and n is an integer. Consistent with this equation, the flow satisfies the condition curl v_x= 0 everywhere except along vortex lines where the velocity is singular. In the vicinity of a vortex line the liquid velocity is very large. An electron bubble is attracted to a vortex line because the bubble, which is empty apart from the electron, displaces liquid with a high kinetic energy.