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Two equations derived from first principles by Brian Josephson that characterize the device, somewhat like an I-V curve:
  • : Josephson current
  • : the Josephson phase, a function defined by the second equation plus initial conditions
  • : input voltage of the system
  • : current across the junction, determined by the input voltage
Note how these equations are not a typical I-V curve, as they are not an instantaneous dependency between voltage and current: the history of the voltage matters! Or in other words, the system has an internal state, represented by the Josephson phase at a given point in time.
To understand them better, it is important to look at some important cases separately: