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:
- AC Josephson effect: V is a fixed DC voltage
Applications:
- because it has an even number of nucleons it is transparent to NMR, and therefore is useful in solvents for NMR spectroscopy
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Ciro Santilli 37 Updated 2025-06-12 +Created 1970-01-01
Ciro Santilli 37 Updated 2025-06-12 +Created 1970-01-01Using Punch Cards by Bubbles Whiting (2016)
Source. Interview at the The Centre for Computing History.The key difference from Lagrangian mechanics is that the Hamiltonian approach groups variables into pairs of coordinates called the phase space coordinates:This leads to having two times more unknown functions than in the Lagrangian. However, it also leads to a system of partial differential equations with only first order derivatives, which is nicer. Notably, it can be more clearly seen in phase space.
- generalized coordinates, generally positions or angles
- their corresponding conjugate momenta, generally velocities, or angular velocities
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