London theory, Landau theory and Lorentz Einstein law

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London theory, Landau theory.... and Lorentz Einstein law

I am trying to learn all I can about superconductivity and discovered an interesting document in Internet. Does the Lorentz Einstein law hold true for the supercurrent :
1) of the London approach?
js = ... ∂θ/∂r - A where θ is the phase and A is the EM potential vector
2) of the Landau theory?
3)of the BCS theory?

One more question : does the London theory include the case of a rotating charge (gyromagnetic effect with A = ω x r)?
 

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Perhaps should I formulate my question in the opposite way.

The Landau theory studies in which way an exterior magnetic field interact with a supercurrent.

What does this theory actually say or propose concerning the interaction of the exterior gravitational field on the same supercurrent? Is that current gravitation-sensitive?
 

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