Fermion Dynamics from Gross-Pitaevskii--like Equations

The dynamics of condensed fermions (i.e. the Unitary Fermi Gas) play a key role in understanding a range of physical systems, from dynamics in rotating traps of cold atoms, to explaining pulsar glitches in neutron stars. Density functional theory (\textsc{dft}) provides a powerful tool for modeling these dynamics, but unfortunately, simulating even a few vortices requires the use of leadership class computing. This talk will address the efficacy of using modified Gross-Pitaevskii (\textsc{gp}) like equations to model the dynamics of Fermi systems. These \textsc{gp}-like equations are significantly easier to solve, yet still capture much of the relevant physics. We shall advocate an approach of using fermionic \textsc{dft} to adjust the form of the modified \textsc{gp}-like equations, and then using the latter to model more complicated phenomena beyond the capability of the fermionic \textsc{dft}. The dynamics of vortices pinned on defects will serve as an example.