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 manyparticle wavefunction. A ²ux quantum is the equivalent of about 10 4 electrons. So if the ²ux has to change with one ²ux quantum there has to occur a transition of many electrons, which is very improbable, or the system must go through intermediary states where the ²ux is not quantized so they have a higher energy. This is also very improbable. Some useful mathematical relations are: ∞ ´ xdx e ax + 1 = π 2 12 a 2 , ∞ ´∞ x 2 dx (e x + 1) 2 = π 2 3 , ∞ ´ x 3 dx e x + 1 = π 4 15 And, when ∞ µ n =0 (1) n = 1 2 follows: ∞ ´ sin( px ) dx = ∞ ´ cos( px ) dx = 1 p ....
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 Spring '10
 Ye
 Current, Superconductivity, Fundamental physics concepts, J.C.A. Wevers, Macroscopic quantum interference, coherent manyparticle wavefunction

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