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I'm trying to understand quantized vortices in rotating Bose gases. From what I understand, any system that is described by a quantum mechanical wavefunction [tex] \psi [\tex] will be irrotational (in other words, will only be able to get angular momentum through the nucleation of quantized vorticies).

-----feel free to skip this part-------------------------

This can be shown by using the continuity equation

[tex]

\frac{\partial n}{\partial t} + \nabla \cdot (n \mathbf{v}) = 0

[\tex]

where [tex] n = |\psi|^2 [\tex] and

[tex]

\mathbf{v} = \frac{-i\hbar}{2m}\frac{\psi^*\nabla\psi-\psi\nabla\psi^*}{|\psi|^2}

[\tex]

for the probability density [tex] n [\tex]. If generic wavefunction written in polar form [tex]\psi=\psi_0 e^{i\phi}[\tex] is inserted into the velocity equation, then it is found that the velocity is the gradient of a scalar function,

[tex]

\mathbf{v} = \frac{\hbar}{m}\nabla\phi

[\tex]

which means that the wavefunction is irrotational since the curl of the gradient of a scalar is zero ([tex] \nabla \times \mathbf{v} = 0 [\tex]. However, the wavefunction can have angular momentum if it possesses a singularity in the form of a vortex.

------ end of boring derivation --------------------

Now the problem that I am having is that I've only seen vortices discussed in the context of^{4}He or in Bose-Eintein condensates. What I was wondering is

- Is it possible to see these quantized vortices in Bose gases above the condensate transition temperature?

- What about fermi gases? There are experiments in the literature in which a fermi gas is Bose-condensed and then rotated, but I was wondering if the condensation part is necessary.

I would seem to me that as long as the system is quantum in nature that it should be irrotational and be able to produce quantized vortices when rotated. Am I missing something?

Any help or comments would be greatly appreciated. Thanks!

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# Rotating Bose gases, quantum vortices

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