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Kind of complicated thing to answer, best way is to do an experiment and not rely on math completely! and the fact that this is still unknown territory. I will try my best, watch this ted talk very helpful: https://www.youtube.com/watch?v=PXHczjOg06w Superconductivity is a phenomena of absolutely 0 electrical resistance. Given that a material is ...

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It is a standard procedure that you can find in any good quantum mechanical book. I suggest Messiah, since it's the best I know ! Everyone should check the Messiah before asking on this web-site ;-) I call $\Phi$ the 4-spinor, it is defined as $$\Phi\equiv\left(\begin{array}{c} u\\ v \end{array}\right)\;;\;\Phi^{\dagger}\equiv\left(\begin{array}{cc} ... 1 As radio amateurs we've all learned the various relationships of power, voltage, current and resistance as expressed in Ohm's Law Ohm's law is:$$ E = IR \tag{1} $$This doesn't directly say anything about power. There is the related Joule's first law, which relates to electrical power converted to heat in resistive materials:$$ P = I^2 R \tag{2} $$... 3 As Kevin Reid aptly explains, the circuit you have drawn is not realizable. But, let's take the closest physical thing you could build, assuming: your voltage source can supply enough energy that we don't hit its limits like all physical things, this apparatus has non-zero size Then, the circuit you actually built is this: simulate this circuit ... 4 … an ideal power source capable of providing infinite current with no drop in the voltage it supplies. … Let's ignore the effects of current density on superconductors for now. … In these phrases is the explanation for the contradictory possibilities you have computed: you have supposed an impossible circuit. As a mathematical model, the behavior of ... 1 If time-reversal symmetry is broken at the surface of a topological insulator, a gap could open at the Dirac point of the topological surface state. The Dirac point, where forward- and backward-moving electrons have the same energy, is located at a time-reversal invariant momentum point (also called a Kramer's point) in the reciprocal space (the crystal ... 0 I hope the cylinder is, although long, not infinitely long? I mean the field must extend beyond the cylinder’s ends. The problem is not well-formulated because the resulting state in the second case depends on how exactly the transition to superconductivity is effected. If you cool the cylinder from inside, it will expunge the magnetic field outwards and ... 1 The BdG equation reads, in full spin-space, and for a s-wave superconductors$$\left(\begin{array}{cccc} H_{0}\left(p\right) & 0 & 0 & \Delta\\ 0 & H_{0}\left(p\right) & -\Delta & 0\\ 0 & \Delta^{\ast} & -H_{0}^{\ast}\left(-p\right) & 0\\ -\Delta^{\ast} & 0 & 0 & -H_{0}^{\ast}\left(-p\right) ...

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While both the answers given in some sense are correct, the true reason has to do with energetic considerations. It is a matter of what is stronger and can be phrased as the following question: Will the wavefunction alter itself to accommodate the flux, or will the flux quantize itself because the wavefunction is trying to remain single valued? As an ...

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EDIT: I come back to this answer, since I've seen this review this morning: Scattering matrix approach to the description of quantum electron transport by Lesovik and Sadovskyy, published in Physiks Uspekhi recently (the link is to arXiv actually). It seems to me Lesovik and Sadovskyy made a really nice introduction to the Andreev and Josephson problems. ...

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This question has is indeed a little bit on the philosophical side (or perhaps this answer is!) It is much easier (and probably scientifically more accurate) to state when a system is not BCS Cooper-paired than it is to say when it is. We can say that we have evidence that a material is a BCS-type superconductor, but we cannot say it is one with 100% ...

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