Abstract
Quasi-particle wave interference controls both the current-voltage characteristics and the current-phase relation of a superconducting device. To illustrate this point, we show that both the Josephson current-phase relation I( φ) = I c sin( φ) and the nonlinear current-voltage characteristic known as Giaever tunneling can be understood only through mesoscopic processes occuring at the interface to the superconductor. The critical current through a one-dimensional superconducting wire or point contact, which has order of magnitude eΔ/ h, is a measure of Landau's superfluid depairing velocity Δ/ p F.
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