Eur. Phys. J. B 80, 41-49 (2011)
https://doi.org/10.1140/epjb/e2011-10943-2

Density dependence of the energy of N Cooper pairs

¹ Institut des NanoSciences de Paris, Université Pierre et Marie Curie, CNRS, Boite courrier 840, 4 place Jussieu, 75252 Paris Cedex 05, France
² Institut de Recherches Mathématiques de Rennes, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France

Corresponding author: ^a monique.combescot@insp.jussieu.fr

Received: 1 December 2010
Published online: 9 March 2011

Abstract

We approach the analytical resolution of Richardson's equations from which the exact energy of N Cooper pairs can be obtained, through an expansion in the dimensionless parameter associated to sample volume. We first derive the explicit solutions of these Richardson's equations for the lowest N's, up to fourth order in this parameter. From them, we deduce a compact expression of the N-pair energy, that we recover using a more general procedure. Our results support the recently found fact that the expression of the N-pair energy obtained at the lowest order stays valid up to the dense limit, the next order term being here shown to be underextensive due to a set of non-trivial cancellations.