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## Main Question or Discussion Point

in deriving quantization of flux in superconductor ring, the momentum of cooper pair p:

[tex]p=\hbar\nabla\theta=e^*(\Lambda J_s + A)[/tex]

then integrate around the ring,

[tex]\hbar\oint\nabla\theta dl=e^*\oint(\Lambda J_s + A)dl[/tex]

using stoke's theorem and integrate sufficiently deep in the ring where current density is very small, the RHS becomes

[tex]RHS=e^*\Phi_s[/tex]

and the left hand side,becomes hn where n is integer.

So the quantized flux is

[tex]\Phi_s=nh/e^*[/tex]

e star is the effective cooper pair charge which is -2e.

i got confused here,why the left hand side integral becomes hn?

The argument used by the book (Van Duzer, superconductivity page 116) is that because theta is unique or differ by a multiple of 2 Pi at each point, so the integral

[tex]\oint\nabla\theta dl=2\pi n[/tex]

why?? where does n come from? theta is a scalar function of r.

please help.

thanks.

[tex]p=\hbar\nabla\theta=e^*(\Lambda J_s + A)[/tex]

then integrate around the ring,

[tex]\hbar\oint\nabla\theta dl=e^*\oint(\Lambda J_s + A)dl[/tex]

using stoke's theorem and integrate sufficiently deep in the ring where current density is very small, the RHS becomes

[tex]RHS=e^*\Phi_s[/tex]

and the left hand side,becomes hn where n is integer.

So the quantized flux is

[tex]\Phi_s=nh/e^*[/tex]

e star is the effective cooper pair charge which is -2e.

i got confused here,why the left hand side integral becomes hn?

The argument used by the book (Van Duzer, superconductivity page 116) is that because theta is unique or differ by a multiple of 2 Pi at each point, so the integral

[tex]\oint\nabla\theta dl=2\pi n[/tex]

why?? where does n come from? theta is a scalar function of r.

please help.

thanks.

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