Josephson equations

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

I (t) = I_{c} sin (φ (t)) \frac{d φ ( t )}{d t} = \frac{2 e V ( t )}{ℏ}

(2)

where:

$I_{c}$ : Josephson current
$φ$ : the Josephson phase, a function $R \to R$ defined by the second equation plus initial conditions
$V (t)$ : input voltage of the system
$I (t)$ : 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:

AC Josephson effect: V is a fixed DC voltage

Table of contents 176 2
- Josephson current ( $I_{c}$ ) Josephson equations 28
- Josephson phase ( $φ$ ) Josephson equations 22

Josephson equations

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