The name is absent

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As equations under ASLDA have a similar form as the BdG equations that we are
solving, it would be convenient for us to plant it into our current code. And we are expecting
that this scheme may help us solve some technical difficulties such as including the Hartree
term in the calculation and therefore advance our understanding of the underlying physics
in polarized Fermi gas system.

3.4.5 Vortex lattice of a rotating system

With all these numerical techniques learned in this thesis and the code we have constructed,
we can move to investigate many new scenarios and underlying physics. One interesting
topic is about the vortex lattices in rotating Fermi gases. As we know, the presence of
vortex lattice is the most unambiguous evidence for superfluidity. Unlike in Bose gases,
due to the significant density depletion in the vortex core, such density variations can only
be detect experimentally in the strong coupling regime in Fermi gases [40]. There has been
some theoretical work studying the vortices in Fermi gases. Most theoretical work has been
focused on single vortex core at zero temperature [41] with very few work focused on the
vortex lattice in rotating Fermi gases [42]. On the other hand, with the recent experimental
progresses, there’s a lot of experimental [19] and theoretical [43] interests in the vortex
physics in the spin polarized or mass-imbalanced Fermi systems. BdG formalism has been
proved to be a important tool for investigating vortex physics in Bose cases, also it has been
employed in Fermi cases. Our BdG calculation based on FEM could be a powerful tool to
study the vortex physics in Fermi gases as in Bose case [44], because the FEM offers the

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