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The usual understanding of Cooper pair condensation seriously questioned physically and mathematically

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Conventional BCS superconductivity follows from a model Hamiltonian which is approached through a variational procedure based on a wave function ansatz: since Cooper pairs are bosonic particles, they are likely to condense all into the same state as elementary bosons do in BEC . The trouble is that this model Hamiltonian is exactly solvable and that the exact wave function differs from the ansatz…

We have moreover shown, by analytically solving Richardson-Gaudin equations from which the exact eigenstates can be obtained, that the average pair energy linearly decreases with pair number, so that the superconductor gap cannot be associated to the pair energy, as commonly said.

Cooper pairs are composite bosons; like semiconductor excitons, their many-body physics is fully controlled by the Pauli exclusion principle. This makes the average pair energy decrease with pair number and the gap different from the broken pair energy, as we mathematically find.

In this seminar, I will present some physical understandings of composite boson many-body effects, associated with exciton physics and semiconductor optical nonlinearities, BEC -BCS cross-over in cold gases and intrication in Quantum Information. I will also give some hints on our resolution of Richardson-Gaudin since this stayed an open math problem for 45 years.

Energy of N Cooper pairs by analytically solving the Richardson-Gaudin equations for conventional superconductors: Michel Crouzeix and Monique Combescot: PRL 107 , 267001 (2011)

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