Can Cooper Pairs in Superconductors Interact Over Long Distances?

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SUMMARY

Cooper pairs in superconductors can interact over distances of 100 to 1000 lattice spacings due to phonon interactions, forming boson states. The discussion highlights that these pairs frequently change partners, influenced by intervening mobile electrons, which allows their wavefunctions to overlap. However, the possibility of Cooper pairs interacting over distances significantly greater than 1000 lattice sites, such as 100,000 lattice sites, remains uncertain and is a topic of inquiry.

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Do the de Broglie wavelengths of Cooper pairs, in a superconductor, overlap one another, over distances of say hundreds, or thousands of lattice spacings?
 
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Unfortunately I typed the above question just before leaving a coffee shop, and didn't mean to say it that way. I've long known that Cooper pairs of opposite spin form boson states due to phonon interaction over 100 to 1000 lattice spacings, and that because there are many intervening mobile electrons that Cooper pairs change partners constantly over a distance of up to 1000 lattice site spacings, as their wavefunctions overlap.

The question I had in mind was.is it possible for the wavefunctions of Cooper pairs much more distant apart than 1000 lattice sites, say 100,000 lattice sites (or more) to interact with one another?
 

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