Josephson Current through a correlated quantum level: Andreev states and   Pi-junction behavior
  The Josephson transport and the electronic properties of a quantum dot characterized by a single level coupled to superconducting leads is analyzed. Different approximations are used and compared: the mean field approximation, the second order perturbation theory in the Coulomb interaction and the exact diagonalization in the zero band-width limit. The system exhibits a rich behavior as a function of the relevant parameters. We discuss in detail the conditions for the observation of Pi-junction behavior and the effect of Coulomb interactions on the Andreev states. 
E.Vecino, A.Martin-Rodero and A. Levy Yeyati