Uniformly Moving Josephson Junctions

Abstract

The basic equations governing the variation of fields and currents in Josephson junctions moving with a velocity u have been derived.
Minkowski’s field equations in uniformly moving junctions and the Josephson’s acceleration equation; dφ⁄dt=∂φ⁄∂t+(u·grad)φ, indicating the change of phase difference φ(r, t) per unit time when we follow the junction in its motion, can be applied to obtain the partial differencial (Sine-Gordon) equation describing the behaviour of φ(r, t).
Although the equation obtained thus can be transformed into the old equation in stationary junctions, both equations make a number of essential difference, e.g., the former considers quantized flux lines flowing through the junction without an applied voltage, while the latter considers the flux-flow state due to the applied voltage across the junction. It should be noted that the electromotive force due to motional induction plays the same part as applied voltages.