# Josephson equations

Two equations derived from first principles by Brian Josephson that characterize the device, somewhat like an I-V curve:
where:
• : 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:

## Josephson current ()

Maximum current that can flow across a Josephson junction, as can be directly seen from the Josephson equations.
Is a fixed characteristic value of the physical construction of the junction.

## Josephson phase ()

A function defined by the second of the Josephson equations plus initial conditions.
It represents an internal state of the junction.