Title: Energy of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>Cooper Pairs by Analytically Solving the Richardson-Gaudin Equations for Conventional Superconductors
Abstract: 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.
Publication Year: 2011
Publication Date: 2011-12-22
Language: en
Type: article
Indexed In: ['crossref', 'pubmed']
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Cited By Count: 14
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