Superconducting correlations in metallic nanoparticles: exact solution of the BCS model by the algebraic Bethe ansatz

Abstract

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced BCS model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors that describe superconducting pairing.

revised version, 5 pages, revtex, no figures

References in corpus (4)

• Spectroscopy of discrete energy levels in ultrasmall metallic grains
• Integrable model for interacting electrons in metallic grains
• Integrable models for confined fermions: applications to metallic grains
• New mechanism for the enhancement of $sd$ dominance in interacting boson models

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