Nonequilibrium dynamics and thermodynamics of a degenerate Fermi gas across a Feshbach resonance

We consider a two-species degenerate Fermi gas coupled by a diatomic Feshbach resonance. We show that the resulting superfluid can exhibit a form of coherent BEC-to-BCS oscillations in response to a nonadiabatic change in the system's parameters, such as for example a sudden shift in the position of the Feshbach resonance. In the narrow resonance limit, the resulting soliton-like collisionless dynamics can be calculated analytically. In equilibrium the thermodynamics can be accurately computed across the full range of BCS-BEC crossover, with corrections controlled by the ratio of the resonance width to the Fermi energy.