Series Josephson Effect

Hi there,

I've recently learned about Josephson junctions, the DC/AC Josephson effects, and SQUIDS. I've been given a set of problems to complete, and one of them is:

'Calculate the supercurrent through two Josephson Junctions in series. Consider constructing the schrodinger equations corresponding to the individual junctions.'

So by Kirchoff's current law the current through the two junctions is the same. I've studied Josehpson's approach using the coupling constant and the schrodinger equations for each half of the junction. I'm struggling however to figure out what to do in terms of actually calculating a supercurrent through them.

In a series array of Josephson junctions, would the coupling constant between each junction be different? I need to couple the Schrodinger equations somehow for both junctions. Any pointers would be much appreciated!

As an aside, out of interest, I know SQUID's have HUGE applications in industry, but do Series arrays of Josephson junctions have any applications to industry?

Many thanks!

EDIT: Basically, my question boils down to: Do I treat the junctions as 4 weakly coupled systems (superconductors), or treat them as two separated coupled systems? Thanks!

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Why didn't the Landau school discover the Josephson effect?

Not sure this is the correct subreddit for this type of question.

Josephson discovered 'his' effect from a microscopic picture of Cooper pairs tunnelling, but at least the basic DC Josephson effect follows very quickly from the Ginzburg-Landau equations with appropriate boundary conditions, and could have been discovered by anyone following the publication of the Ginzburg-Landau paper in 1950. Furthermore, thinking about a "macroscopic wavefunction" that can have overlap with another one across an thin barrier seems like a typical Landau-style way of thinking.

Does anyone have any insight as to why neither Landau himself nor anyone in his circle came up with this idea? Was it perhaps a too "practical", device-oriented problem (although it has very deep significance for the nature of ordered states, and broken symmetry)?

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Dynamical Casimir effect in a Josephson metamaterial pnas.org/content/110/11/4…
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Possible resonance effect of axionic dark matter in Josephson junctions arxiv.org/abs/arXiv:1309.…
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Dynamical Casimir effect in a Josephson metamaterial : materials reddit.com/r/materials/co…
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Josephson junctions (DC effect)

So I have been reading about the josephson effect in feynmann's lectures, and I like his derivation as it is nice and intuitive, certainly applied to the AC effect, which I feel I understand. However I am not sure I understand the DC effect. The josephson relations state that I_j = I_c sin phi, meaning that a phase difference between superconductors drives a current, with zero voltage drop, so that does that mean for two superconductors brought together into a SIS junction would result in a spontaneous current flow from one to the other?

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[1309.3790, PRL] Possible resonance effect of axionic dark matter in Josephson junctions arxiv.org/abs/1309.3790
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'Magnetic Josephson effect' seen for the first time - physicsworld.com physicsworld.com/cws/arti…
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Born today : January 4th - Brian Josephson, Theoretical Physicist, Professor, Nobel Laureate, "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects." en.wikipedia.org/wiki/Bri…
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[The Ambassador] Part 3 - Rust

Part2

Transit

Nala quickly fell into a regular routine which involved spending a lot of time with Mark in the recreation rooms trying different games and activities. Mark, with no patients to doctor, also had little to do, which was a relief to Nala because apparently only Mark, Ms. Mwangi, and the Captain spoke rladii. Nala couldn’t read any of the text or understand any of the spoken language in video media, so she was limited in which entertainment she could enjoy and who she could enjoy it with.

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Pun intended.
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These aren't dad jokes...

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