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I'm confused about Cooper pairs. What exactly is the difference of Cooper pairs to Bosons? I read that Cooper pairs are not seen as real Bosons (why?) and in Thinkham's sc book it's said that the condensate in sc is analogous, but not identical to BEC.

Thanks for help in advance!

Motionx
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  • A related answer of mine: https://physics.stackexchange.com/questions/546836/how-to-understand-the-condensation-of-cooper-pair-in-bcs-theory/547280#547280 – Rococo Dec 09 '21 at 14:36

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Cooper pairs are pairs of interacting electrons. They do obey bosonic statistics, but they are composite particles extending over many lattice periods, and their internal structure is often important. The same can be said about excitons, phonons, magnons, and other quasiparticle excitations.

Update Let me outline more precisely in which ways these differences may appear:

  • Since cooper pairs extend over many lattice periods, their internal structure is easily probed by external fields, impurities and other available perturbations. This is unlike the case of what is usually meant by bosons, such as laser cooled atoms or elementary particles, where probing the internal structure requires energies of higher orders.
  • Another issue is that cooper pairs are actually not bound states of two isolated electrons, but excitations of a many-electron system, like excitons, excitations in Fermi luquid, etc. Thus, they have finite lifetime, and their charge and spin are defined approximately - that is to say that their statistics is close to bosonic, but not quite.
  • In presence of many of interacting cooper pairs we cannot really distinguish, which two electrons belong to one pair.

It might be also instructive to compare the BCS wave function with the ground state of the bose-einstein condensate.

Roger V.
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  • Thanks for your answer. So, the Cooper pairs follow the bosonic statistics even if they are not exactly bosons, but due to Tinkham's book, it is not exactly the Bose Einstein condensate which they form. What is then the difference to the condensate in a sc to the BEC? – Motionx May 25 '21 at 15:39
  • @Motionx I added a more detailed discussion to my answer. – Roger V. May 25 '21 at 16:18
  • thank you very much :) – Motionx May 25 '21 at 16:32
  • I don't think your last point is correct. As I understand it, both BCS condensation and Bose condensation can be formulated in a grand canonical context, in which U(1) symmetry is broken and particle number is not sharply defined. Or, either can be extended to a number-conserving context via alternative definitions. Leggett discusses this in depth in his book Quantum Liquids. – Rococo Dec 09 '21 at 14:34
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    @Rococo you mean the countability? - you are probably right... not sure what I was thinking when I wrote this. Anyhow, I removed this line. – Roger V. Dec 09 '21 at 14:40