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phys documents (dragged) 76 - equilibrium: a state with...

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70 Physics Formulary by ir. J.C.A. Wevers 12.8.4 Macroscopic quantum interference From θ 2 - θ 1 =2 e Ψ / ¯ h follows for two parallel junctions: δ b - δ a = 2 e Ψ ¯ h , so J = J a + J b =2 J 0 sin ± δ 0 cos ± e Ψ ¯ h ² This gives maxima if e Ψ / ¯ h = s π . 12.8.5 The London equation A current density in a superconductor proportional to the vector potential ± A is postulated: ± J = - ± A μ 0 λ 2 L or rot ± J = - ± B μ 0 λ 2 L where λ L = ³ ε 0 mc 2 /nq 2 . From this follows: 2 ± B = ± B/ λ 2 L . The Meissner effect is the solution of this equation: ± B ( x )= B 0 exp( - x/ λ L ) . Magnetic ±elds within a superconductor drop exponentially. 12.8.6 The BCS model The BCS model can explain superconductivity in metals. (So far there is no explanation for high- T c supercon- ductance). A new ground state where the electrons behave like independent fermions is postulated. Because of the in- teraction with the lattice these pseudo-particles exhibit a mutual attraction. This causes two electrons with opposite spin to combine to a Cooper pair . It can be proved that this ground state is perfect diamagnetic. The in±nite conductivity is more dif±cult to explain because a ring with a persisting current is not a real
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Unformatted text preview: equilibrium: a state with zero current has a lower energy. Flux quantization prevents transitions between these states. Flux quantization is related to the existence of a coherent many-particle wavefunction. A ux quantum is the equivalent of about 10 4 electrons. So if the ux has to change with one ux quantum there has to occur a transition of many electrons, which is very improbable, or the system must go through intermediary states where the ux is not quantized so they have a higher energy. This is also very improbable. Some useful mathematical relations are: xdx e ax + 1 = 2 12 a 2 , - x 2 dx (e x + 1) 2 = 2 3 , x 3 dx e x + 1 = 4 15 And, when n =0 (-1) n = 1 2 follows: sin( px ) dx = cos( px ) dx = 1 p ....
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This note was uploaded on 01/30/2011 for the course PHYSICS 208 taught by Professor Ye during the Spring '10 term at Blinn College.

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