Intrinsic response time of a Josephson tunnel junction

The microscopic theory of the Josephson effect is reformulated in the time domain. The four terms in the usual theory are seen to be necessary consequences of intrinsic junction delays. The tunneling current flowing in response to a voltage pulse is shown to rise in a time $\frac{\hslash }{2\Delta }$ and undergo damped energy-gap oscillations, before approaching the expected supercurrent. The theory provides a technique for calculating junction behavior when connected to an arbitrary circuit.