ABSTRACT
This chapter describes the properties of any system where superconducting regions are coupled together by links which transmit phase coherence as the superconducting wire. Microscopic theories for the current flowing through a weak link coupling together two superconductors are divided into two types, based on either perturbation theory or the Green's function method. The Green's function method is applied only to equilibrium situations, and it has the advantage over the perturbation theory method in that the latter is valid only when the weak link is a tunneling barrier. An alternative formula for the current through a weak link, in which the propagation of electrons through the link is described in terms of the electron Green's function instead of the tunneling Hamiltonian, has been derived by Josephson. The excess current is seen to be strongly dependent on the electromagnetic properties of the barrier.
