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 He-3, 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 He-3, 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 that 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(infinity)=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 the residual collective motion of the pairs.