Coherent transient effects in Josephson junctions. Formulation

Abstract

Coherent transient phenomena in superconducting tunnel junctions are investigated by means of a Gorkov-Nambu, Green's-function formulation, but without making the usual factorization. In this way we are led to and justify a pseudospin-angular-momentum formulation of junction dynamics. We find that for problems involving pair-current flow between weakly coupled superconductors the system can be conveniently represented by its position on a Bloch sphere in our pseudospin space. The magnitude of the Bloch vector is set by the total number of interacting Cooper pairs whereas its orientation is specified by two angles, $\theta$ and $\phi$. The angle $\phi$ is the usual Josephson-pair phase, but the new angle $\theta$ enters our calculations for transient situations. A comparison is made between the present angular-momentum formulation and the phenomenological number-phase-angle theory.