Density-functional theory for the pairing Hamiltonian

We consider the pairing Hamiltonian and systematically construct its density functional in the strong-coupling limit and in the limit of large particle numbers. In the former limit, the functional is an expansion into central moments of occupation numbers. In the latter limit, the functional is known from BCS theory. Both functionals are nonlocal in structure, and the nonlocalities are in the form of simple products of local functionals. We also derive the relation between the occupation numbers and the Kohn-Sham density.