Dynamical mean-field equations for strongly interacting fermionic atoms in arbitrary potential traps

We derive a set of general dynamical mean-field equations for strongly interacting fermionic atoms in arbitrary slowly varying potential traps. Our derivation generalizes the ansatz of the crossover wave function to the inhomogeneous case. The equations reduce to a time-dependent Gross-Pitaevskii equation on the BEC side of the resonance. We discuss an iteration method to solve these mean-field equations, and present the solution for a harmonic trap as an illustrating example, which self-consistently verifies the approximations made in our derivation.