A simple perturbation theory of a quantum dot coupled to superconducting leads

The transport in a superconductor-quantum-dot-superconductor system is stud ied analytically using a simple perturbation theory. The de Josephson curre nt through a quant;um dot depends on the phase difference and the binding e nergy of the localized excited states, is not always a sine curve and is al so influenced greatly by the competition between the superconductivity and the Kondo effect. pi junction is shown analytically.