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| HAL: hal-00687107, version 1 |
| DOI: 10.1103/PhysRevLett.107.267001 |
| Detailed view |  Export this paper |
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| Physical Review Letters 107, 26 (2011) 4 pages |
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| Energy of N Cooper Pairs by Analytically Solving the Richardson-Gaudin Equations for Conventional Superconductors |
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| Michel Crouzeix 1Monique Combescot 2 |
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| (2011) |
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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 yr old math problem by analytically solving Richardson-Gaudin equations which give the exact energy of these N pairs via N parameters coupled through N nonlinear 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 |
| hal-00687107, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00687107 | |
| oai:hal.archives-ouvertes.fr:hal-00687107 | |
| From: Marie-Annick Guillemer | |
| Submitted on: Thursday, 12 April 2012 11:59:47 | |
| Updated on: Thursday, 12 April 2012 11:59:47 | |
