Space between the inner and bacterial outer membrane in Gram-negative bacteria

As of 2023 the most important ones economicaly were:The main application is magnetic resonance imaging. Both of these are have to be Liquid helium, i.e. they are not "high-temperature superconductor" which is a pain. One big strength they have is that they are metallic, and therefore can made into wires, which is crucial to be able to make electromagnetic coils out of them.

TODO, come on, Internet!

Bibliography.

Main theory to explain Type I superconductors very successfully.

TODO can someone please just give the final predictions of BCS, and how they compare to experiments, first of all? Then derive them.

High level concepts:

In 1962 Brian Josephson published his inaugural paper predicting the effect as Section "Possible new effects in superconductive tunnelling".

In 1963 Philip W. Anderson and John M. Rowell published their paper that first observed the effect as Section "Possible new effects in superconductive tunnelling".

Some golden notes can be found at True Genius: The Life and Science of John Bardeen page 224 and around. Philip W. Anderson commented:

As part of the course Anderson had introduced the concept of broken symmetry in superconductors. Josephson "was fascinated by the idea of broken symmetry, and wondered whether there could be any way of observing it experimentally."

The inaugural that predicted the Josephson effect.

Published on Physics Letters, then a new journal, before they split into Physics Letters A and Physics Letters B. True Genius: The Life and Science of John Bardeen mentions that this choice was made rather than the more prestigious Physical Review Letters because they were not yet so confident about the results.

Paywalled by Elsevier as of 2023 at: www.sciencedirect.com/science/article/abs/pii/0031916362913690

This is what happens when you apply a DC voltage across a Josephson junction.

It is called "AC effect" because when we apply a DC voltage, it produces an alternating current on the device.

By looking at the Josephson equations, we see that $V(t)=k$ a positive constant, then $\phi$ just increases linearly without bound.

Therefore, from the first equation:we see that the current will just vary sinusoidally between $\pm I_c$.

This meas that we can use a Josephson junction as a perfect voltage to frequency converter.

Wikipedia mentions that this frequency is $484GHz/mV$, so it is very very high, so we are not able to view individual points of the sine curve separately with our instruments.

Also it is likely not going to be very useful for many practical applications in this mode.

An I-V curve can also be seen at: Figure "Electron microscope image of a Josephson junction its I-V curve".

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 function $\mathbb{R}\to \mathbb{R}$ defined by the second of the Josephson equations plus initial conditions.

It represents an internal state of the junction.

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.

Paywalled at: journals.aps.org/prl/abstract/10.1103/PhysRevLett.7.43

The first published experimental observation of the magnetic flux quantum.

The paper that follows it in the journal is also of interest, "Theoretical Considerations Concerning Quantized Magnetic Flux In Superconducting Cylinders" by N. Byers and C. N. Yang, it starts:So there was some previous confusion about the flux quantum due to the presence of Cooper pairs or not.

Dumping the fitures at: archive.org/details/experimental-evidence-for-quantized-flux-in-superconducting-cylinders One day we can also dump the paper scans when it goes into the public domain in 2056! Public domain scientific paper by year.

As mentioned in True Genius: The Life and Science of John Bardeen page 224, the idea of symmetry breaking was a major motivation in Josephson's study of the Josephson effect.

Can be used as a very precise magnetometer.

There are high temperature yttrium barium copper oxide ones that work on liquid nitrogen.

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