Validating simple dynamical simulations of the unitary Fermi gas

We present a comparison between simulated dynamics of the unitary fermion gas using the superfluid local density approximation (SLDA) and a simplified bosonic model, the extended Thomas Fermi (ETF) with a unitary equation of state. Small amplitude fluctuations have similar dynamics in both theories for frequencies far below the pair breaking threshold and wave vectors much smaller than the Fermi momentum, and the low frequency linear responses match well for surprisingly large wave vectors, even up to the Fermi momentum. For non-linear dynamics such as vortex generation, the ETF provides a semi-quantitative description of SLDA dynamics as long as the fluctuations do not have significant power near the pair breaking threshold, otherwise the dynamics of the ETF cannot be trusted. Nonlinearities in the ETF tends to generate high-frequency fluctuations, and with no normal component to remove this energy from the superfluid, features like vortex lattices cannot relax and crystallize as they do in the SLDA. We present a heuristic diagnostic for validating the reliability of ETF dynamics by considering the approximate conservation of square of the gap: $\int|\Delta|^2$.