CROSSOVER FROM THE JOSEPHSON EFFECT TO BULK SUPERCONDUCTING FLOW

The crossover between ideal Josephson behavior and uniform superconduc ting flow is studied by solving exactly the Ginzburg-Landau equation f or a one-dimensional superconductor in the presence of an effective de lta-function potential of arbitrary strength. As the effective scatter ing is turned off, the pairs of Josephson solutions with equal current evolve into a uniform and a solitonic solution with nonzero phase off set. It is also argued that a microscopic description of the crossover must satisfy the self-consistency condition, which is shown to guaran tee current conservation. The adiabatic response to an external bias i s briefly described. The ac Josephson effect is shown to break down wh en the external voltage is applied at points which are sufficiently fa r from the junction.