# Falling to closest quantized circulation level in a rotating superfluid

To make a superfluid rotate in an annulus shaped container, we start with a normal fluid, rotate the container, then cool it to below critical temperature to get a rotating superfluid.

The allowed values of circulation in a superfluid rotating with non-zero velocity are n*h/m where n could be 1,2,3.. or -1,-2,-3.... If we impart an angular velocity less than 0.5*h/m to the normal fluid, it goes to rest when converted to the superfluid state. If we impart 0.8*h/m, it goes to quantized circulation of h/m when converted to superfluid state. The explanation I got for this from my Professor's notes is that due to the high free energy barrier between the 2 nearest quantized circulations for the superfluid, it goes to the closest one. Is this correct ? Should the circulation not always fall to the nearest lower value of quantized circulation when converted to superfluid state ? How does free energy come into role for this ?

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Where did you find this claim? – Thomas Jan 26 '14 at 0:24
@Thomas : this statement is in the notes given by my professor :- circulation level falls to closest allowed value due to free energy considerations. The reference for our course is D.R. Tilley and J. Tilley though I could not get hold of it. I changed the problem statement to be clear; sorry for the confusion. Please give your arguments or answer. – cleanplay Jan 27 '14 at 12:22