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SUMMARY:The usual understanding of Cooper pair condensation seriously ques
 tioned physically and mathematically - Monique Combescot\, Institut des Na
 noSciences de Paris
DTSTART:20121018T131500Z
DTEND:20121018T141500Z
UID:TALK36824@talks.cam.ac.uk
CONTACT:Dr G Moller
DESCRIPTION:Conventional BCS superconductivity follows from a model\nHamil
 tonian which is approached through a variational procedure based on a\nwav
 e function ansatz: since Cooper pairs are bosonic particles\, they are lik
 ely to\ncondense all into the same state as elementary bosons do in BEC. T
 he trouble is\nthat this model Hamiltonian is exactly solvable and that th
 e exact wave function\ndiffers from the ansatz...\n\nWe have moreover show
 n\, by analytically solving Richardson-Gaudin\nequations from which the ex
 act eigenstates can be obtained\, that the average\npair energy linearly d
 ecreases with pair number\, so that the superconductor gap\ncannot be asso
 ciated to the pair energy\, as commonly said.\n\nCooper pairs are composit
 e bosons\; like semiconductor excitons\, their\nmany-body physics is fully
  controlled by the Pauli exclusion principle. This\nmakes the average pair
  energy decrease with pair number and the gap different\nfrom the broken p
 air energy\, as we mathematically find.\n\nIn this seminar\, I will presen
 t some physical understandings of\ncomposite boson many-body effects\, ass
 ociated with exciton physics and\nsemiconductor optical nonlinearities\, B
 EC-BCS cross-over in cold gases and\nintrication in Quantum Information. I
  will also give some hints on our\nresolution of Richardson-Gaudin since t
 his stayed an open math problem for 45\nyears.\n\nEnergy of N Cooper pairs
  by analytically solving the Richardson-Gaudin equations for conventional 
 superconductors: Michel Crouzeix and Monique Combescot: PRL 107\, 267001 (
 2011)
LOCATION:TCM Seminar Room\, Cavendish Laboratory
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