Within the framework of quasi equilibrium approximation, Josephson’s expression for current in a weakly coupled superconducting system is derived without the use of any specific microscopic model. It is based only on the existence of the off-diagonal long-range order in the two-particle reduced density matrix. Allowing for deviations from the quasi equilibrium approximation, generalised Josephson equations are obtained which include ohmic terms. The effect of relaxation and thermal fluctuations is examined in detail to emphasise the physical origin of various terms in the expression for current.

The problem of superconductivity in a metal-semiconductor system has been studied, using the dielectric formulation of superconductivity. The charge redistribution due to the quantum penetration of the metallic electrons to the semi-conductor side is approximated by a simple exponential function. The interface exciton modes are obtained within the framework of classical electrostatics, and their effect in modifying the effective electron-electron interaction near the interface is investigated. It is found that the strength of the excitonic term is small, and by itself, insufficient to lead to superconductivity. Nevertheless, it can alter the superconducting transition temperature of a metal, if it is already superconducting due to some other mechanism. This has been studied as a function of the various parameters entering in the problem.