Superfluidity and binary-correlations within clusters of fermions

We propose a method for simulating the behaviour of small clusters of particles that explicitly accounts for all mean-field and binary-correlation effects. Our approach leads to a set of variational equations that can be used to study both the dynamics and thermodynamics of these clusters. As an illustration of this method, we explore the BCS-BEC crossover in the simple model of four fermions, interacting with finite-range potentials, in a harmonic potential. We find, in the crossover regime, that the particles prefer to occupy two distinct pair states as opposed to the one assumed by BCS theory.