Quench Dynamics of a Superfluid Fermi Gas

With an eye toward the interpretation of so-called `cosmological' experiments performed on the low temperature phases of $^{3}$He, in which regions of the superfluid are destroyed by local heating with neutron radiation, we have studied the behavior of a Fermi gas subjected to uniform variations of an attractive BCS interaction parameter $\lambda$. In $^{3}$He the quenches induced by the rapid cooling of the hot spots back through the transition may lead to the formation of vortex loops via the Kibble-Zurek mechanism. A consideration of the free energy available in the quenched region for the production of such vortices reveals that the Kibble-Zurek scaling law gives at best a lower bound on the defect spacing. Further, for quenches which fall far outside the Ginzburg-Landau regime, the dynamics on the pair subspace, as initiated by quantum fluctuations, tends irreversibly to a self-driven steady-state with a gap $\Delta_{\infty} = \epsilon_{C}(e^{2/N(0)\lambda} - 1)^{- 1/2}$. In weak coupling this is only half the BCS gap, the extra energy being taken up by residual collective motion of the pairs.