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A superconducting coil acts mostly as a perfect inductor, so it resists current variations. If it is plugged to an AC voltage source, it will pass an AC current corresponding to its inductance. When shorted, it will continue running the current that was running through it just before shorting (as $V=0=L di/dt$). So you're going to end up with a constant ...

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The BCS wave function is a superposition of components with definite particle number $N=0,2,4,\ldots$. In the infinite volume limit, the particle number is sharply peaked around $N=nV$, where $V$ is the volume and $n$ is the partcle density. It is intuitively clear that projecting the BCS state on a definite particle number should not make a difference. This ...

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A generic procedure to obtain the particle-hole conjugate of a quantum Hall wavefunction is described in http://journals.aps.org/prb/abstract/10.1103/PhysRevB.29.6012. It is not clear whether this is the most "general" form. But even for the Pfaffian state, we do not know the most general form either.

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It's a good idea. The basic reason no one's done it is that diamagnets are 4-5 orders of magnitude smaller permeability. Added to which, if you have a superconducting set up you can get a superconducting magnet which is multiples stronger than a permanent magnet. The set up you show would probably need to be ~1000 times higher to work. Maybe in space ...

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Diamagnetic forces are too weak at room temperature to provide adequate levitation/stabilization of flywheels that weigh more than a few grams. Nice for demos of floating pyrolytic graphite flakes between bismuth blocks, but not interesting from the viewpoint of practical energy storage. The only exception to this is superconductors, which are basically ...

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Let $|\psi\rangle$ be an eigenstate of $H$ with eigenvalue $E$. $\lambda$ is an external parameter that $H$ depends on. In your case it is $\Delta\phi$. Then  \dfrac{\partial}{\partial\lambda} \langle \psi |H|\psi\rangle=\langle\psi|\dfrac{\partial H}{\partial \lambda}|\psi\rangle+(\dfrac{\partial}{\partial\lambda} \langle\psi|)H|\psi\rangle+\langle ...

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First, thanks to all who provided answers and ideas above. They really helped clarify things greatly. I think I have come to a plausible answer below. If one wants to consider a "quasi-photon", then the medium (consisting of ions, localized electrons etc) has to be treated as a part of the vacuum upon which you build your field theory. However, this medium ...

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Okay, I had all sorts of complicated thoughts about this but I think it is actually very simple: the photon in a medium doesn't have an effective mass, and Rod Vance's equation is actually therefore incorrect. Call it a proof by contradiction: a nonzero mass for a photon in a medium would mean that there is some nonzero energy that a photon must have to ...

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The problem is that the system of one ring balanced on another is an unstable equilibrium. The rings will slide sideways and fall off. You've spotted this and you state in your question: Using some simple mechanical restraining to keep the rings from sliding away horizontally from co-axiality But your mechanical restraining would be far from simple. ...

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Suppose light, i.e. a quantum superposition of free photons and excited matter states, is travelling in a medium with refractive index $n$. Then we can in principle boost to an inertial frame which is at rest relative to the superposition travelling in the medium: we see a stationary region of excitation as we ride alongside the glass, and the latter zips by ...

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