Energy of N Cooper Pairs by Analytically Solving the Richardson-Gaudin Equations for Conventional Superconductors
Michel Crouzeix, Monique Combescot
DOI 10.1103/PhysRevLett.107.267001 · Physical Review Letters
Active bibliographic source — not scientific approval
Bibliographic access preserves source history; it does not approve extracted materials or validate reported claims. Review warnings on each occurrence separately.
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.
Similar papers
Energy of N Cooper pair by analytically solving Richardson-Gaudin equations
similarity 0.94Michel Crouzeix & Monique Combescot · 2011 · arXiv:1111.5801
Source status unknown — claims are unverified
From one to Cooper pairs, step by step
similarity 0.92W. V. Pogosov & M. Combescot · 2011 · arXiv:1103.1147
Source status unknown — claims are unverified