Ciro Santilli @cirosantilli  40

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

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:

A device that exhibits the Josephson effect.

TODO is there any relationship between this and the Josephson effect?

Experimental observation published as Experimental Evidence for Quantized Flux in Superconducting Cylinders.

This appears to happen to any superconducting loop, because the superconducting wave function has to be continuous.

Video "Superconducting Qubit by NTT SCL (2015)" suggests that anything in between gets cancelled out by a superposition of current in both directions.

Scientology music! So good.

Applications:

Used in:

We can almost reach the Lie algebra of any isometry group in a single go. For every $X$ in the Lie algebra we must have:because $e^{tX}$ has to be in the isometry group by definition as shown at Section "Lie algebra of a matrix Lie group".

Then:so we reach:With this relation, we can easily determine the Lie algebra of common isometries:

Bibliography:

Islam has some really nice things in it.

The way it was perverted to be used as a tool for terrorism by some is a great tragedy.

Ciro Santilli especially appreciates the ideas of

Ciro Santilli appreciates this concept of "remembering the suffering of others" a lot due to Ciro Santilli's self perceived compassionate personality and Ciro Santilli's cheapness.

Bibliography: