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| HAL: hal-00647291, version 1 |
| arXiv: 1111.5801 |
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| Energy of N Cooper pair by analytically solving Richardson-Gaudin equations |
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| Michel Crouzeix 1Monique Combescot 2 |
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| (2011-11-24) |
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| This Letter provides the solution to a yet unsolved basic problem of Solid State Physics: the ground state energy of an arbitrary number of Cooper pairs interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50 year old math problem by analytically solving Richardson-Gaudin equations which give the exact energy of these $N$ pairs via $N$ parameters coupled through $N$ non-linear equations. Our result fully supports the standard BCS result obtained for a pair number equal to half the number of states feeling the potential. More importantly, it shows that the interaction part of the $N$-pair energy depends on $N$ as $N(N-1)$ only from N=1 to the dense regime, a result which evidences that Cooper pairs interact via Pauli blocking only. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| 2: | Institut des Nanosciences de Paris (INSP) |
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CNRS : UMR7588 – Université Pierre et Marie Curie [UPMC] - Paris VI |
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| Analyse numérique |
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| Subject | : | Physics/Condensed Matter/Superconductivity |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1111.5801 |
| hal-00647291, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00647291 | |
| oai:hal.archives-ouvertes.fr:hal-00647291 | |
| From: Michel Crouzeix | |
| Submitted on: Thursday, 1 December 2011 17:49:22 | |
| Updated on: Wednesday, 4 January 2012 15:52:49 | |
