Dynamical mean-field equations for strongly interacting fermionic atoms in a potential trap

We derive a set of dynamical mean-field equations for strongly interacting fermionic atoms in a potential trap across a Feshbach resonance. Our derivation is based on a variational ansatz, which generalizes the crossover wavefunction to the inhomogeneous case, and the assumption that the order parameter is slowly varying over the size of the Cooper pairs. The equations reduce to a generalized time-dependent Gross-Pitaevskii equation on the BEC side of the resonance. We discuss an iterative method to solve these mean-field equations, and present the solution for a harmonic trap as an illustrating example to self-consistently verify the approximations made in our derivation.